Multi-Objective Optimization of Raw Mix Design and Alternative Fuel Blending for Sustainable Cement Production

Abstract

Cement production is a carbon-intensive process that contributes significantly to global greenhouse gas emissions. Approximately 50–60% of these emissions result from limestone calcination, while 30–40% result from fossil fuel combustion in kilns. This study presents a multi-objective optimization (MOO) framework that integrates raw mix design and alternative fuel blending to simultaneously reduce production costs and carbon dioxide (CO₂) emissions while maintaining clinker quality. A hybrid Genetic Algorithm–Linear Programming (GA-LP) model was developed to navigate the balance between economic and environmental objectives under stringent chemical and operational constraints. The approach models the impact of raw materials and fuel ash on critical clinker quality indices: the Lime Saturation Factor (LSF), Silica Modulus (SM), and Alumina Modulus (AM). It incorporates practical constraints such as maximum substitution rates and specific fuel compositions. A case study inspired by a medium-sized African cement plant demonstrates the utility of the model. The results reveal a Pareto front of optimal solutions, highlighting that a 20% reduction in CO₂ emissions from 928 to 740 kg/ton clinker is achievable with only a 24% cost increase. Optimal strategies include 10% fly ash and 30–50% alternative fuels, such as biomass, tire-derived fuel (TDF), and dynamic raw mix adjustments based on fuel ash contributions. Sensitivity analysis further illustrates how biomass cost and LSF targets affect clinker performance, emissions, and fuel shares. The GA-LP hybrid model is validated through process simulation and benchmarked against African case studies. Overall, the findings provide cement producers and policymakers with a robust decision-support tool to evaluate and adopt sustainable production strategies aligned with net-zero targets and emerging carbon regulations.

1. Introduction

Cement production is one of the most energy- and carbon-intensive industrial processes, releasing roughly 0.8–0.9 tons of carbon dioxide (CO₂) per ton of cement produced [1,2]. The cement industry is responsible for about 5–8% of global CO₂ emissions [3]. This is primarily due to two factors: the calcination of limestone and the combustion of fossil fuels. Both processes are energy-intensive and emit significant amounts of carbon [4]. In a typical cement plant, approximately 50–60% of process CO₂ emissions from clinker production result from limestone calcination. An additional 30–40% originate from the combustion of fossil fuels in the kiln. The remaining emissions are attributed to electricity consumption [5,6,7,8]. This dual source of emissions, combined with high energy consumption and natural resource dependency, underscores the critical influence of both raw material composition and fuel mix on the carbon footprint of cement production [9]. These emissions pose significant sustainability challenges. International climate agreements such as the Kyoto Protocol and the Paris Agreement have identified the cement industry as a critical sector, urging manufacturers to adopt green strategies, including raw material optimization and alternative fuel utilization [10]. The industry also consumes 30–40% of production costs in energy, motivating efficiency improvements [11]. As global urbanization and infrastructure development continue, cement demand is projected to grow to 3.7–4.4 billion tons by 2050 [3], worsening environmental impacts. In response, cement plants worldwide, including those in Africa, are under pressure to improve their sustainability and reduce greenhouse gas (GHG) emissions and energy costs [12,13]. Achieving these goals requires innovative approaches that address multiple objectives simultaneously, rather than optimizing for a single criterion in isolation.

One promising approach to reducing the carbon footprint of cement is multi-objective optimization (MOO). MOO methods enable decision-makers to analyze and identify Pareto-optimal solutions, where improving one objective necessarily leads to the deterioration of at least one other. In particular, two key controls for CO₂ mitigation are as follows: (1) Raw mix design optimization, which involves replacing or supplementing traditional raw materials like high-grade limestone with alternative materials, such as industrial wastes and supplementary cementitious materials (SCMs), to reduce calcination emissions. In cement production, raw mix design refers to selecting and proportioning raw materials to yield clinker of acceptable quality [14,15]. (2) Alternative fuel blending, which involves substituting traditional fossil fuels like coal, oil, or petcoke with lower-carbon or carbon-neutral fuels, such as biomass and refuse-derived fuel (RDF), in the kiln [10,16,17]. These measures can significantly reduce emissions per ton of clinker, but often at high costs or with extensive process adjustments. However, such substitutions impact the chemical composition of the kiln feed and thermal behavior during processing, potentially impacting clinker quality and plant performance.

Producing quality clinker requires careful control of the raw mix composition. The proportions of key oxides, primarily CaO, SiO₂, Al₂O₃, and Fe₂O₃, must fall within certain limits to ensure the formation of the desired clinker phases and to avoid excessive liquid phase or free lime in the kiln [18]. To quantify clinker quality, cement chemists use several modulus indices calculated from the oxide composition. The most common are the Lime Saturation Factor (LSF), representing the ratio of available CaO to the amount needed to form alite and belite (the ideal clinker LSF is typically 90–100%); the Silica Modulus (SM), which represents the ratio of SiO₂ to (Al₂O₃ + Fe₂O₃), indicating the silica content relative to the total fluxes (typical SM ~2.0–3.0); and the Alumina Modulus (AM), the ratio of Al₂O₃ to Fe₂O₃, which reflects the balance between aluminum and iron (usually 1.0–2.5 for Portland clinker) [19]. These indices must remain within specific ranges to meet national standards or plant-specific requirements. For instance, Egyptian standards may specify an LSF between 0.97 and 1.10 (97–110%), a Silica Modulus (SM) of approximately 2.3–2.7, and an Alumina Modulus (AM) of around 1.3–2.5 [18]. A raw mix with an excessively high LSF can result in free CaO in the clinker, leading to unsoundness, whereas a low LSF can reduce strength. Likewise, the SM and AM affect the burnability of the mix and the overall cement performance. Balancing these quality constraints while minimizing production costs constitutes a typical raw mix optimization challenge [10]. For example, replacing limestone with pozzolans, such as fly ash and calcined clay, can reduce calcination-related CO₂ emissions, but may alter clinker quality parameters, potentially increasing raw material costs. Similarly, replacing coal with RDF can lower fuel-related CO₂ emissions by approximately 2.25 kg CO₂/kg [20], but introduces challenges regarding fuel consistency, combustion stability, and potential toxicity [21]

In cement production, the MOO approach can simultaneously minimize production costs and CO₂ emissions while meeting clinker quality specifications. This allows a cement plant to identify an optimal combination of raw mix and fuel blend that balances sustainability (reduced carbon emissions), economic efficiency (cost reduction), and compliance with product quality standards. Optimizing the raw mix is essential for achieving both clinker quality and energy efficiency. The mix must satisfy specific chemical moduli, such as the LSF, SM, and AM, to ensure the formation of appropriate clinker [19,21]. An LSF near 1.0 indicates a balanced lime content; values below 0.90 can lead to excess belite and reduced early strength, while values above 1.0 result in unreacted free lime in the clinker [19,21]. Traditionally, raw mix design has been modeled as a cost minimization problem under quality constraints, with linear programming (LP) used to blend raw feeds under chemical constraints [18,21], while fuel optimization has used LP or mixed-integer models to minimize costs and emissions [22]. Previous studies have shown the potential of such approaches. For instance, LP has been used for optimal raw mix design under quality constraints [10,18]. However, modern sustainability considerations extend this approach to include the use of industrial by-products and mineral additives such as fly ash, slag, or low-grade limestone as partial substitutes for limestone. These substitutions reduce CO₂ emissions from calcination and may also yield cost or energy savings [7,21].

This study focuses on a hybrid Genetic Algorithm–Linear Programming (GA–LP) framework for multi-objective optimization of raw mix design and alternative fuel blending in cement production. The goal is to support sustainable cement production by finding optimal combinations of raw materials and fuel substitutes that reduce CO₂ emissions and cost simultaneously without compromising clinker quality. While previous studies have applied either GA or LP independently for cement process optimization, this study introduces a novel hybrid GA–LP framework. This dual-layer optimization model leverages the global search capacity of GA to explore diverse solution spaces, while LP is employed to enforce operational constraints and ensure rigorous compositional compliance. The framework enables simultaneous optimization of CO₂ emissions, production cost, and alternative fuel substitution objectives that are often addressed in isolation in the existing literature. Unlike prior models that either neglect critical chemical parameters or simplify thermal system limitations, our approach integrates these constraints directly into the optimization loop. Moreover, the model is validated using operational data from African cement plants, thereby demonstrating its adaptability to regional resource profiles and policy environments.

Table 1. Summary of cement optimization models using GA–LP methods.

Study	Optimization Method	Objective	Constraints	Limitations
Petrasinovic, Miletic, Rankovic, Duric and Novakovic [23]	LP	Minimize raw material cost	LSF, SM, AM; material limits	Single-objective; no fuel/emissions
Małgorzata [24]	LP	Maximize alternative fuel usage	Fuel quality (CV, Cl, S)	No raw mix; single-objective
Joseph and Obodeh [19]	GA	Minimize production cost	LSF ~93%, SM ~2.9, AM ~1.3	Environmental benefits not optimized
Hassan et al. [18]	GA	Minimize raw mix cost	CaCO3 > 82.5%; LSF, SM, AM, LOI	No fuel optimization; purely linear
Babazadeh, Ezati and Sabbaghnia [25]	LP	Minimize total cost (production, transport, inventory)	Fixed demand/supply; cost targets	No emissions; single-objective; deterministic
Ponnusamy et al. [10]	LP	Minimize raw mix cost	LSF, SM, AM; Bogue chemistry	Fixed composition; no emissions or uncertainty
Rijal, Indrapriyatna and Adi [26]	LP	Minimize raw mix cost with alternative material	Compressive strength ≥ 200 kg/cm2	Scenario-specific; no thermal/fuel consideration
Kondapally, Chepuri, Elluri and Siva Konda Reddy [27]	GA	Minimize cement content (cost) while meeting strength constraints	Target compressive strength	Focuses on concrete and compressive strength; CO2 and clinker quality not addressed

summarizes past models on cement optimization and their limitations.

No previous studies integrating hybrid GA–LP for cement raw mix and fuel optimization were identified in the literature. Existing studies use either GA or LP separately. This study differs by employing a hybrid GA–LP model for clinker-level optimization that integrates raw mix chemistry (LSF, SM, AM), thermal constraints, and alternative fuel blending to minimize CO₂ emissions, maximize fuel substitution, and reduce production costs, with quality constraints enforced for real-world applicability in a medium-sized African cement plant context.

The remainder of the paper is organized as follows: Section 2 reviews the relevant literature on cement raw mix optimization, alternative fuel usage (with emphasis on African cement plants), and multi-objective decision models. Section 3 describes the methodology, including the GA–LP hybrid approach, mathematical formulation of objectives/constraints, key quality indices, and implementation details. Section 4 presents the results of simulation studies, including optimal raw mix and fuel blends, the cost–emissions Pareto front, and insights from a case study inspired by an African cement plant. It also provides a discussion in the context of the existing literature. Section 5 concludes with a summary of findings, implications for the industry, and recommendations for future work.

2. Literature Review

2.1. Cement Alternative Fuel, Sustainability Challenges, and Mitigation Strategies

Substituting fossil fuels with waste-derived energy sources is a core emissions mitigation strategy in cement kilns. Common substitutes include biomass residues (rice husk, sugarcane bagasse, palm kernel shells), RDF, scrap tires, waste oils, solvents, sewage sludge, and other industrial by-products [28,29]. Many of these are carbon-neutral or emit less net CO₂ than conventional fuels. Additionally, some are low-cost or come with tipping fees. Nonetheless, they often have a lower calorific value, higher moisture, and inconsistent composition, posing challenges for stable kiln operation [17,29]. For instance, biomass typically has a lower energy density and higher water content, affecting flame temperature; some wastes introduce contaminants like chlorine or heavy metals [29]. Still, their environmental and economic benefits support their widespread adoption. CEMBUREAU reports that substitution rates in the EU average 52%, with some facilities achieving 90–95% [30]. Holcim notes near-100% substitution in some European plants [31].

Co-firing RDF, biomass residues, used tires, and industrial wastes has gained momentum as a fossil fuel alternative. Co-processing serves a dual function: energy recovery and waste destruction, with ash incorporated into clinker. Schuhmacher, Nadal and Domingo [32] evaluated the co-firing of petroleum coke with 20% sewage sludge in Spain, finding modest reductions in emissions like NO_x and heavy metals with minimal operational disruption. Georgiopoulou and Lyberatos [33] assessed LCA scenarios for 10% coal replacement with RDF, tire-derived fuel (TDF), or sludge in Greece. RDF was most beneficial due to its high biogenic content and calorific value, while sludge performed worst due to its high moisture and low energy content.

Nadal, Schuhmacher and Domingo [34] reported that a Catalonian cement plant replacing 20% of its thermal demand with sludge reduced its CO₂ emissions by 144,000 tonnes over three years, saving EUR 2.88 million. Health risk analysis showed a net benefit without added toxic exposure. Nidheesh and Kumar [35] estimated that switching entirely to biomass could reduce global emissions by up to 40%, though supply, fuel property, and technical constraints limit substitution. Ishak and Hashim [36] identified five mitigation routes: energy efficiency, waste heat recovery, fuel switching, clinker substitution with SCMs, and carbon capture. Most facilities manage only partial substitution (20–50%), depending on local conditions, with realistic CO₂ reductions of 10–30%. Their work emphasizes the practical potential of fuel diversification and process upgrades.

In Africa, initiatives to scale up non-conventional fuels face both progress and hurdles. International Finance Corporation (IFC) studies in Senegal, Nigeria, Ethiopia, and Kenya support adoption [37]. Ethiopia uses sugarcane bagasse and coffee husks, while Kenya and Senegal are trialing landfill-derived RDF [37,38]. Barriers include logistics, preprocessing (e.g., shredding, drying), and maintaining operational consistency. The Global Cement and Concrete Association (GCCA) forecasts a global thermal substitution rate of at least 40% to meet 2050 net-zero targets from the current 4% [3,39]. Achieving this requires policy incentives, landfill restrictions, and advanced feeding and combustion systems.

African plants historically show low fuel substitution (<20%) due to limited infrastructure and investment [37]. However, IFC studies and case studies report progress. Dangote Cement co-processed 67,200 tons of waste in H1 2022, boosting substitution by 25% [29,37,40]. Countries like Senegal, South Africa, Tunisia, and Ethiopia are pursuing biomass and RDF integration as part of broader sustainability and waste strategies [37,41]. Waste-derived fuels are crucial for low-carbon production, but economic viability and kiln compatibility must be carefully balanced, making this an ideal context for the application of MOO.

Several studies confirm that waste fuels reduce emissions and can lower costs. Beltran and Arnesh [42] showed that a mix with 20% used tires and waste oil cut CO₂ by 16.76% in South Africa. Waste oil emits 44.55% less CO₂ per energy unit than coal; tires emit about 25% less. In Togo, Beguedou et al. [29] showed a 15% CO₂ cut and stable operation using 80% RDF and 20% biomass at 50% substitution. Kiln feed was adjusted via a higher LSF to counter the added ash. This underscores the link between raw mix and fuel characteristics. Joseph and Obodeh [19] found that agricultural residues (e.g., rice husk, bagasse, groundnut shells) reduced fuel costs by 30–70% in Nigeria while maintaining clinker standards (LSF 93%, SM 2.9, AM 1.3). Their work showed that PSO, GA, and Pattern Search could optimize fuel blending to reduce both costs and emissions. Common constraints in Africa remain: fuel availability, preprocessing, and capital requirements [29].

2.2. Raw Mix Optimization and Quality Control

Proper proportioning of raw materials such as limestone, clay, and iron ore is vital for product quality and emissions control. It governs clinker properties like the LSF, SM, and AM while also influencing calcination emissions. MOO techniques have helped to balance costs, emissions, and performance. Linear programming and evolutionary methods identify optimal raw meal formulas that meet CaO, SiO₂, and Al₂O₃ targets with minimal CaCO₃ [43]. Traditional models focus on one goal at a time; newer approaches recognize interdependence across cost, environment, and quality [21]. Initial studies applied LP and operations research to minimize costs while enforcing chemical limits [10]. Many studies use LP or MILP to account for raw material chemistries, prices, and modulus constraints [10,18,19,21,25]. Li et al. [43] developed a nonlinear time-varying model with a grid interior point solver in MATLAB-GUI (MATLAB R2023a) to handle fluctuating raw chemistries. Their model maintained stability in clinker indices like the LSF, SR, and AR.

More recently, the optimization of both raw materials and fuels has gained focus. Hassan et al. [18] used LP to optimize feed composition at the Al-Askari plant (Egypt), meeting chemical specs with minimal cost. Babazadeh et al. [25] applied LP in Iran and ran a sensitivity analysis to confirm cost efficiency. Rijal et al. [26] optimized clinker ratios at PT Semen Padang (Indonesia) using MATLAB-LP. These models show cost savings and stable quality when applied. Carpio et al. [21] used PSO to optimize raw and fuel mixes. Their framework addressed clinker standards, fuel diversity, and emissions constraints. Later, Carpio, Coelho, Silva and Jorge [44] combined SQP, GA, and DE to solve complex fuel mix problems, validating PSO’s effectiveness against classical methods.

While LP is effective, it handles only cost and assumes certainty. Real-world decisions juggle emissions limits, energy usage, and material variability. Advanced tools, such as stochastic programming, fuzzy logic, GA, and PSO, allow for more nuanced modeling. Joseph and Obodeh [19] used PSO in Nigeria for cost–emissions balance, noting that it demonstrated better nonlinear handling than LP. Some studies now pair simulation and optimization. Kääntee, Zevenhoven, Backman and Hupa [45] used Aspen Plus to simulate clinker chemistry and emissions with different fuels, showing how simulation-enhanced models improve accuracy.

Other studies have targeted other aspects like energy intensity. Kaddatz, Rasul and Rahman [46] used Excel-based models to study spent carbon lining (SCL), lubricants, and tires. SCL increased emissions, but reduced feed demand; lubricants performed best overall. Rahman, Rasul, Khan and Sharma [47] provided an overview of the effects of alternative fuels on cement plant performance. They noted that fuel changes must be managed to maintain clinker specs and heat balance. Most studies overlook the interplay of fuel ash and raw mix composition. Doh Dinga and Wen [48] used many-objective optimization in China, with up to 10 objectives, modeling emissions, cost, and efficiency. Though strategic, their work did not detail clinker formulation. Kondapally et al. [27] optimized concrete mix design (not clinker) to reduce cement use by 6–10% via GA while preserving strength.

2.3. Integrated Optimization of Raw Materials and Fuels

Because ash from combustion alters clinker chemistry, raw material optimization and fuel optimization must be performed together. Coal ash (~5–15% of feed) adds SiO₂, Al₂O₃, Fe₂O₃; biomass ash may add CaO, offsetting limestone needs [29]. Separate treatment of these variables leads to suboptimal outcomes. Kookos et al. [22] developed an MILP model for joint raw material–fuel selection, applying blending and energy constraints. Their case study showed how to guide quarry selection or waste fuel investment. Ishak and Hashim [49] proposed a multi-objective MILP model to minimize both emissions and operating costs. Their model included co-processing, system upgrades, and capture tech. The results showed that sharp emissions cuts were achieved while clinker targets were met.

Clinker phases—C₃S, C₂S, C₃A, and C₄AF—depend on the LSF, SM, and AM ratios [50,51]. Traditionally, plant chemists adjusted inputs manually, but LP has enabled precision [10,50]. Hassan et al. [18] optimized raw mix (Egypt), suggesting proportions of 82.50% limestone, 14.08% shale, 2.5% bauxite, and 0.92% iron ore. Minor changes in CaO purity were achieved by incorporating lower-grade limestone, extending quarry life. Ponnusamy et al. [10] included industrial waste (e.g., fly ash), adjusting the LSF via Bogue calculations. Their model reduced the limestone share to 85.03%, cut calcination emissions, and achieved a cost of 6.845 RM/ton. These findings show that a raw mix can be engineered for efficiency, provided that chemical balances are respected. Hao, An, Yang, Zhang and Liu [52] used adaptive evolutionary MOO to optimize coal and electricity use while keeping quality intact. The model yielded sets, e.g., cost vs. CO₂, helping operators to choose optimal fuel strategies.

In conclusion, despite the breadth of studies on raw mix design optimization, most of the models reviewed either optimize a single objective or fail to integrate clinker chemistry, alternative fuel substitution, and thermal optimization. Some focus solely on energy or emissions reduction, without simultaneously considering cost or quality implications. Others employ single-objective LP or basic GA approaches that do not fully capture constraints like chemical moduli or fuel blending feasibility. LP models offer computational precision, but lack flexibility in handling nonlinearity and multiple competing goals, while GA provides broader search capability at the cost of solution specificity. As shown in Table 1, most previous models have overlooked the interplay between alternative fuels and raw mix.

This study seeks to fill these gaps by developing a hybrid GA–LP optimization model that jointly optimizes raw mix and fuel composition, maintains strict quality control, and targets sustainable, cost-effective cement production, while maximizing alternative fuel substitution grounded in African cement plants. The model leverages the global search capability of GA and LP to meet multiple goals. It seeks cost-effective, emissions-conscious solutions while enforcing strict quality constraints, including chemical moduli and energy needs. This integrated approach represents a methodological advancement over earlier models and positions the study as a practical decision-support tool for sustainable cement production. The next section outlines the methodology, detailing objective formulations, imposed constraints, and implementation procedures for the integrated GA-LP solver.

3. Methodology

3.1. Overview of GA-LP Hybrid Optimization Approach

To solve the multi-objective problem of cement raw mix and fuel blending optimization, we developed a Genetic Algorithm–Linear Programming (GA-LP) hybrid model. The rationale for a hybrid approach is the exploitation of GA’s ability to perform a global search across a complex, multi-modal solution space and LP’s efficiency in handling linear constraints and fine-tuning solutions. This combination is well suited to cement production optimization, which involves both discrete choices (e.g., whether to include a particular alternative fuel or raw material) and continuous proportioning of materials. Similar hybrid strategies have been used in mining and process industries, showing improved convergence and solution quality. Figure 1 illustrates the overall GA–LP optimization framework, including key stages such as data input, raw mix generation, constraint checking, LP-based refinement, and stopping criteria evaluation. The framework integrates raw material and fuel blending based on genetic algorithm exploration and linear programming refinement, incorporating clinker quality constraints and simulation-based validation.

3.1.1. Problem Formulation

We consider a cement plant that can utilize $N$ different raw materials and $M$ different fuels. Raw materials might include limestone, the primary source of CaO; clay or shale (for SiO₂, Al₂O₃); sand (SiO₂); iron ore or laterite (Fe₂O₃); and possibly alternative additives like slag or ash. Fuels include traditional fuels (coal, petroleum coke) and alternative fuels (biomass, industrial waste, tires, etc.), each with a known calorific value and composition of ash.

3.1.2. Decision Variables and Constraints

The decision variables in the optimization are as follows:

• $x_i$ = the fraction of each raw material $i$ in the raw mix ($i=1\dots \dots N)$, expressed as a proportion of the total kiln feed (on a dry basis).
• $y_j$ = the fraction of each fuel $j$ in the total fuel heat input ($j=1\dots \dots M)$, expressed on an energy basis so that ${\displaystyle \sum }_j{y}_j$ = 1 corresponds to 100% of heat from fuels.

These variables are subject to physical bounds $(x_i\ge 0, {\displaystyle \sum }_i{x}_i=1; y_i\ge 0, {\displaystyle \sum }_j{y}_j=1$) and additional constraints described below. The objectives to be minimized are as follows.

3.1.3. Optimization Objectives

• Objective 1: Total Cost (C). This includes raw material costs and fuel costs. We calculate it as follows:

  $$\mathrm{C}={\displaystyle \sum }_{i=1}^N{x}_i\times c_i^{raw}+{\displaystyle \sum }_{j=1}^{M}H\times y_j\times c_j^{fuel}$$

  (1)

  where $x_i$ = the fraction of each raw material $i$ in the total raw mix, $y_j$ = the fraction of each fuel $j$ in the total fuel heat input, $c_i^{raw}$ is the unit cost of raw material $i$ (e.g., $/ton), and $c_j^{fuel}$ is the unit cost of fuel $j$ (e.g., $/GJ). $H$ is the specific heat consumption of the kiln system (GJ per ton of clinker). For optimization, H is treated as constant for simplicity in this study. However, we recognize that fuel properties, particularly moisture content and calorific variability in biomass and waste-derived fuels, can influence combustion efficiency and promote adequate heat consumption. Future extensions of the model could incorporate moisture-adjusted or fuel-specific H values to reflect real-world combustion dynamics better. The cost objective thus represents USD/ton of clinker produced. This formulation assumes that all raw mix goes to clinker, ignoring bypass dust losses for ease.
• Objective 2: CO₂ Emissions ($E$). We consider direct CO₂ emissions from calcination and fuel combustion per ton of clinker:

  $$E={\displaystyle \sum }_{\mathrm{i}=1}^N{x}_i\times {{\mathrm{CO}}_2}_i^{raw}+{\displaystyle \sum }_{j=1}^{M}H\times y_j\times {{\mathrm{CO}}_2}_j^{fuel}$$

  (2)

  where ${{\mathrm{CO}}_2}_i^{raw}$ is the CO₂ emitted from processing raw material $i$ per ton of clinker. For limestone, ${{\mathrm{CO}}_2}^{raw}$ is approximately 0.44 USD kg CO₂ per 1 kg CaCO₃, since 44% of the CaCO₃ is released as CO₂ in calcination. Other raw materials may release small amounts of CO₂ if they contain carbonates or if their processing incurs emissions. ${{\mathrm{CO}}_2}_j^{fuel}$ is the CO₂ per GJ of fuel $j$ burned, accounting for carbon content and combustion efficiency. For fossil fuels, this is calculated from their carbon content (e.g., coal 95 kg CO₂/GJ; natural gas 56 kg/GJ). For biomass and certain wastes, the net ${{\mathrm{CO}}_2}_j^{fuel}$ can be considered to be zero or reduced, assuming biogenic carbon neutrality. Our model allows the user to specify these values; for example, in the case study, we assign biomass a net emissions factor of zero kg/GJ if fully renewable, and assign tire-derived fuel about 85% of the factor of coal, since a portion is biogenic rubber. The total $E$ is in kg CO₂/ton clinker.
• Optimization framework: The optimization thus seeks solutions that minimize $(C,E$) in a Pareto sense. This is a classic multi-objective optimization scenario; typically, there is a balance because the cheapest raw materials or fuels, e.g., high-sulfur petcoke might not be the lowest-carbon option, and vice versa. Rather than combine the objectives with arbitrary weights, we use a Pareto approach to identify a set of non-dominated solutions (each representing a different compromise between cost and emissions).

3.2. Constraints

The model includes several crucial constraints to ensure feasibility and product quality.

3.2.1. Quality (Chemical) Constraints

These ensure that the raw mix composition yields acceptable clinker moduli. We calculate the LSF, SM, and AM from the raw mix oxide composition (including contributions from fuel ash). For each index, we require the following:

$$LS{F}_{min}\le LSF\left(x,y\right)\le LS{F}_{max,}$$

(3)

$$S{M}_{min}\le SM\left(x,y\right)\le S{M}_{max,}$$

(4)

$$A{m}_{min}\le AM\left(x,y\right)\le A{M}_{max,}$$

(5)

The oxide composition is obtained by summing the contributions from each raw material. $x_i$ has known percentages of CaO, SiO₂, Al₂O₃, Fe₂O₃, etc., plus the ash from each fuel; each $y_j$ contributes oxides via its ash fraction.

The digital parameters in Equation (6) represent oxide mass fractions obtained from standard compositional analysis of raw materials. The LSF, SM, and AM moduli are widely used in cement chemistry to assess and control clinker quality, as established in Bogue’s formulations and elaborated in standards like ASTM C150 [53]. For example, if limestone provides mainly CaO and clay provides ${\displaystyle \frac{{SiO}_2}{{Al}_2{O}_3}}$, the LSF in the mix is roughly as follows:

$${\displaystyle \frac{CaO}{2.8Si{O}_2+1.2A{l}_2{O}_3+0.65F{e}_2{O}_3}}$$

(6)

The model computes these ratios and constrains them. This ensures the chosen mix will produce clinker of normal phase composition. In our implementation, these constraints are linearized via known formulae (since each oxide percentage is a linear function of $x_i$ and $y_j$). If needed, additional chemical constraints can be added, e.g., the maximum MgO or alkali content in clinker, which is important for durability.

3.2.2. Process Constraints

These include the raw mix sum constraint ${\displaystyle \sum }_i{x}_i=1$ (all fractions sum to 100%), and the fuel mix sum ${\displaystyle \sum }_j{y}_j=1$ (100% energy from defined fuels). We also include constraints on individual material/fuel usage if applicable, such as availability limits or substitution limits. A plant may cap certain alternative fuels due to supply or technical limits, e.g., $y_{biomass}\le$ 0.50 if the biomass supply is limited to 50% of the heat. Similarly, if an alternative raw material is available only in small quantities, an upper bound can be set on its $x_i$. These constraints reflect practical limitations. In our case study, we imposed a max of 30% tire fuel due to feeding system constraints and required a minimum of 50% limestone in the raw mix due to quarry feed needs.

3.2.3. Energy and Throughput Constraint

To ensure the solution meets the kiln’s energy demand for a given clinker output, we include, in normalized form,

$${\displaystyle \sum }_j{y}_j\times LH{V}_j=1$$

(7)

where $LH{V}_j$ is the normalized lower heating value of fuel $j$ relative to a reference. This is essentially the same as $\sum y_j$ = 1 when defined on an energy basis. If the model were to decide absolute amounts, we would fix the clinker output and require that the fuel mix provide at least the total energy $H$ (GJ/ton * output tons). We also ensure the kiln feed rate meets the clinker production requirement, taking into account that some raw mix mass is lost as CO₂, roughly a 35% mass loss from limestone.

$$\mathrm{Raw}\mathrm{feed}\mathrm{per}\mathrm{ton}\mathrm{clinker}={\displaystyle \frac{1}{1-fraction of carbonates}}$$

(8)

This detail is handled implicitly when computing emissions.

3.2.4. Operational Constraints

These include any ratio or performance constraints to maintain smooth operation. For example, the alkali/sulfur balance in the kiln system should stay within certain limits to avoid buildups (sometimes expressed as an alkali-to-sulfur ratio constraint). Another is constraint is the minimum flame temperature or burner flame momentum, which could be indirectly enforced by limiting the fraction of very low calorific fuel. In our framework, such constraints can be added as needed for specific cases. In the present model demonstration, we focus on the core chemistry and supply constraints, assuming the plant can adapt the operating parameters to the solutions found within reason.

3.3. Hybrid Solver Structure

The optimization problem is formulated as a mixed-integer nonlinear programming (MINLP) problem; if tackled directly, it is nonlinear due to the moduli ratios, and potentially integer depending on whether binary decisions for using a material are included or not. However, by fixing the set of materials and fuels, i.e., ensuring there are no binary on/off decisions in the formulation and linearizing moduli constraints, which is possible via the rearrangement of linear terms and bounds on ratios, we can approximate it as a continuous nonlinear, but mostly quasi-linear, problem. We employ a Genetic Algorithm for the multi-objective search, specifically a variant of the NSGA-II algorithm for Pareto optimization. Within the GA, we incorporate an LP-based repair and local improvement step.

• GA encoding strategy: This explains how the solution vectors $\left[x_{1, \dots \dots }, x_{N-1}, y_{1, \dots .}, y_M-1\right]$ are encoded in the genetic algorithm using the $N-1$ and $M-1$ parameters to satisfy unit-sum constraints. The GA initializes a population of random feasible solutions respecting basic bounds.
• Fitness evaluation: For each candidate solution, a linear programming (LP) step is used to enforce all linear constraints, including quality-related ones (e.g., chemical moduli), which are approximated as needed. The GA-suggested variables $x_i$ and $y_j$ are adjusted minimally through this LP to yield a feasible or near-feasible solution. The adjusted values are then used to compute the objective functions total cost ($C$) and CO₂ emissions ($E$) based on the defined equations.
• Genetic operators: Selection, crossover, and mutation are applied with mechanisms designed to maintain feasibility. Uniform crossover combines fractions from two parent solutions, while mutation slightly perturbs individual values. After each operation, $x$ and $y$ vectors are re-normalized to ensure they sum to one. A quick feasibility check is performed and LP correction is applied if needed. The GA is executed over many generations, using an elitist strategy to retain non-dominated solutions and crowding distance to preserve diversity along the Pareto front, following NSGA-II guidelines.
• Pareto front extraction: Upon reaching the termination criteria, such as a fixed number of generations or convergence of the solution set, the algorithm outputs a Pareto front comprising non-dominated solutions. Each point represents a trade-off between cost and emissions, offering the decision-maker a range of options based on their specific priorities.

Once the termination criteria are met, for example, the number of generations or convergence of the front, the output is a set of non-dominated solutions, each with an associated cost and emissions value. These solutions are candidates for the decision-maker to choose from, depending on priority and cost vs. emissions. This GA-LP approach combines exploration—using the GA—with exact satisfaction of hard constraints—using LP. This prevents the GA from becoming stuck in infeasible or suboptimal regions, and yields high-quality solutions that LP alone with single-objective assumptions might miss. The use of a multi-objective GA means we obtain not just one solution, but a spectrum of solutions, from cost-optimal to emissions-optimal.

3.4. Mathematical Formulation

For clarity, the key equations are summarized below. Let the clinker production rate be normalized to 1 ton for calculation purposes:

• Raw mix composition:

  $${\displaystyle \sum }_{i=1}^N{x}_i=1, with 0\le x_i\le 1$$

  (9)

  Each raw material $i$ has an oxide content $(a_{i,CaO}, a_{i,Si{O}_2}, a_{i,A{l}_2{O}_3}, a_{i,Si{O}_2}, a_{i,F{e}_2{O}_3},\dots )$ on a mass percent basis. Fuel $\mathrm{j}$ has an ash content fraction $f_j^{ash}$ and ash oxides $(b_{j,CaO}, b_{j,Si{O}_2}, \dots )$ per unit of fuel mass.
• Fuel mix:

  $${\displaystyle \sum }_{j=1}^M{y}_j=1, with 0\le y_j\le 1$$

  (10)

  Each fuel has a calorific value $LH{V}_i$ (MJ/kg or GJ/ton). For convenience, we define $e_j^{fuel}$ = CO₂ emissions (kg) per MJ of fuel $j$ (taking into account carbon content and oxidation). Similarly, $c_j^{fuel}$ = cost per MJ.

3.4.1. Quality (Modulus) Calculations

First, the total oxide fractions in the clinker raw feed are computed, including in its ash, and this is carried out similarly for Al₂O₃ and Fe₂O₃.

$${\mathrm{CaO}}_{mix}={\displaystyle \sum }_i{x}_i\times a_{i,\mathrm{CaO}}+{\displaystyle \sum }_y{y}_j\times f_j^{ash}\times b_{j,\mathrm{CaO},}$$

(11)

$${{\mathrm{SiO}}_{2,}}_{mix}={\displaystyle \sum }_i{x}_i\times a_{i,{\mathrm{SiO}}_{2,}}+{\displaystyle \sum }_y{y}_j\times f_j^{ash}\times b_{j,{\mathrm{SiO}}_{2,}}$$

(12)

The fuel ash terms are scaled by the estimated ash percentage entering per ton of clinker; in practice, if 1 ton of clinker requires approximately 1.6 tons of raw mix and 0.12 tons of coal, then the proportion of fuel ash is relatively small. We assume the basis such that $x_i$ cover the raw mix and the fuel ash is added on top in proportion; this is a minor detail in the calculation. Then,

$$\mathrm{LSF}={\displaystyle \frac{{\mathrm{CaO}}_{mix}}{2.8\times {\mathrm{SiO}}_{2\mathrm{mix}}+1.2\times {\mathrm{Al}}_2{\mathrm{O}}_3\mathrm{mix}+0.65\times {\mathrm{Fe}}_2{\mathrm{O}}_{3\mathrm{mix}}}}$$

(13)

$$\mathrm{SM}={\displaystyle \frac{{{\mathrm{SiO}}_2}_{mix}}{{\mathrm{Al}}_2{\mathrm{O}}_{3\mathrm{mix}}+{\mathrm{Fe}}_2{\mathrm{O}}_{3\mathrm{mix}}}}$$

(14)

$$\mathrm{AM}={\displaystyle \frac{{{\mathrm{Al}}_2{\mathrm{O}}_3}_{mix}}{{\mathrm{Fe}}_2{\mathrm{O}}_{3\mathrm{mix}}}}$$

(15)

These must satisfy LSF_min ≤ LSF ≤ LSF_max, etc. In our case study, we used target ranges typical for Ordinary Portland Cement clinker: LSF 92–98%, SM 2.3–2.7, AM 1.3–2.0. If the plant produces multiple clinker types, separate constraints can be applied accordingly.

3.4.2. Objective Functions

Minimize Production Cost (USD/ton clinker):

$$\mathrm{Min}C={\displaystyle \sum }_{\mathrm{i}=1}^N{x}_i\times c_i^{raw}+\mathrm{H}\times {\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{M}}{y}_j\times c_j^{fuel}$$

(16)

where

• $c_i^{raw}$: The unit cost of raw material $i$ (USD/ton).
• $c_j^{fuel}$: The unit cost of fuel $j$ (USD/GJ).
• $\mathrm{H}$: The specific heat consumption of the kiln (GJ/tonne clinker)

Minimize CO₂ Emissions (kg CO₂/tonne clinker):

$$\mathrm{Min} E={\displaystyle \sum }_{\mathrm{i}=1}^N{x}_i\times {{CO}_2}_i^{raw}+\mathrm{H}\times {\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{M}}{y}_j\times e_j^{fuel}$$

(17)

where

• $e_i^{raw}$: The emissions factor for raw material $i$ (kg CO₂/ton).
• $e_j^{fuel}$: The emissions factor for fuel $j$ (kg CO₂/GJ).

In expanded form, if limestone is indexed as $i$ =1,

$${{CO}_2}_1^{raw}=0.785\times a_{i,CaO}$$

(18)

meaning 0.785 kg CO₂ per kg limestone if the limestone is 85% CaCO₃. Each CO₂ of raw material can be precomputed or set to zero if inert. The fuel CO₂ per GJ $e_j^{fuel}$ is derived from emissions factors, e.g., 95 kg/GJ for coal and 0 for biomass. Note that if alternative fuel use leads to a slight increase in specific energy consumption $\mathrm{H}$ (due to lower efficiency), this can be modeled by making $\mathrm{H}$ a function of $y_j$ (but we keep it constant here to maintain linearity).

3.4.3. Additional Constraints

Oxide contributions are calculated as follows:

$$Oxid{e}_{mix}={\displaystyle \sum }_i{x}_i\times a_{i,oxide}+{\displaystyle \sum }_y{y}_j\times f_j^{ash}\times b_{j,oxide}$$

(19)

where

• $a_{i,oxide}$: The mass fraction of a specific oxide in raw material $i$.
• $j,oxide$: The mass fraction of the oxide in the ash of fuel $j$.
• $f_j^{ash}$: The ash content of fuel $j$.
• Usage Limits:

• $x_i\le x_i^{max}$: Material-specific availability or quality limits.
• $y_j\le y_j^{max}$: The fuel-specific maximum allowable substitution.

We add bounds like $x_i\le x_i^{max}$ if needed for certain materials. In our test scenario, we limited the alternative raw material (fly ash) to ≤10% of the raw mix. For fuels, we imposed $y_{tires}\le$ 0.3 (≤30% thermal from tires) and $y_{biomass}\le$ 0.5, reflecting handling constraints. These values can be changed to reflect the capability of the plant.

The above formulation was implemented in the MATLAB environment. The GA optimization is performed using the Global Optimization Toolbox’s NSGA-II routine (with custom operators coded to incorporate LP repair). The LP step uses MATLAB’s $linprog$ or an open-source solver to fine-adjust each candidate. Each evaluation of objectives and constraints is fast (millisecond scale), since it involves simple formulas, so that the GA can iterate over many generations efficiently. We used a population size of 100 and ran for 200 generations for the case study, which was sufficient for convergence. The result is a Pareto front of solutions $x_i, y_j$ with associated ($C, E$) values.

3.5. Data Sources and Case Study Setup

To make the study realistic, we calibrated the model with data from a medium-sized cement plant. We drew upon published data for African plants and typical values in the literature.

Table 2. Raw meal material chemical composition (% in weight).

Material	CaO	SiO2	Al2O3	Fe2O3	Cost ($/ton)	Remarks
Limestone	52	3	1	0.5	10	Primary source of CaO
Clay	1	60	15	5	5	Provides SiO2 and Al2O3
Iron Ore	0.5	1	2	85	15	Fe2O3 correction
Fly Ash	2	50	30	10	0	Waste-derived SCM

,

Table 3. Composition and classification of primary and secondary fuels.

Fuel	LHV (MJ/kg)	Cost ($/ton)	Emissions (kg/GJCO2)	Major Oxides in Ash (Approx.)	Remarks
Coal	24	100	94	Low ash; negligible Fe2O3	Primary fuel—baseline fossil fuel
Petcoke	30	90	97	Low ash; some S and V2O5	Secondary fuel—high sulfur content
Rice Husk	14	20	0	SiO2 (15–20%), K2O	Secondary fuel—carbon-neutral, volatile-rich
TDF	27	50	85	Fe2O3 (up to 15%), ZnO	Secondary fuel—biogenic rubber + steel cord ash

and

Table 4. Clinker quality targets and energy requirements.

Parameter	Symbol/Range	Purpose/Control Role
Lime Saturation Factor (LSF)	95 ± 3	Ensures adequate CaO for alite formation
Silica Modulus (SM)	2.5 ± 0.2	Controls the balance of silicates and aluminates
Alumina Modulus (AM)	1.5 ± 0.2	Manages the melt phase and clinker fluidity
Thermal Energy Demand (GJ/ton clinker)	H = 3.5	The energy required for calcination and sintering

summarize the key input data used for setting up the case study. Table 2 summarizes the chemical composition of the primary raw materials used in raw meal preparation for clinker production. It includes key oxides relevant to modulus calculations (LSF, SM, AM), as well as costs and physical remarks.

Table 3 summarizes the primary and secondary fuels used in the cement kiln system. It includes calorific values, costs, CO₂ emissions, and approximate chemical contributions, e.g., from the ash content, relevant to clinker quality control.

Table 4 presents the assumed clinker quality targets and thermal energy requirements used in the optimization case study. These values reflect typical process control targets for Portland Cement production and ensure chemical balance and kiln stability.

All input data were incorporated into the model, after which the Genetic Algorithm (GA) was run to generate the curve. It is important to note that the accuracy of the model is highly dependent on the quality of the input data, particularly the chemical composition of raw materials and fuels.

3.6. Implementation and Validation

The implementation was carried out in MATLAB R2023a. Model validation followed a structured approach. First, we verified that known feasible solutions, such as the current operating conditions of the plant, satisfied all model constraints. Next, we isolated and solved the LP sub-problem, which focused solely on cost minimization to assess expected behavior. As anticipated, the LP optimization recommended using 8% fly ash, reaching either the 10% cap or SM limit, and partially substituting clay with the more economical fly ash. This adjustment led to a 5% reduction in raw mix cost relative to a no-fly ash scenario, confirming that the constraint set was correctly implemented.

We then executed the GA in single-objective mode, first minimizing cost and then minimizing CO₂ emissions, to verify that the extreme solutions aligned with expectations. The cost minimization run favored petcoke due to its lower energy cost compared to coal, and it maximized fly ash usage, resulting in a production cost of approximately USD 36/ton of clinker, but with high emissions of 920 kg CO₂/ton. In contrast, the CO₂ minimization run prioritized biomass fuels up to 50% and maximized limestone substitution via fly ash, reducing emissions to 750 kg CO₂/ton. However, this came at a higher cost (USD 45/ton) due to the higher price and lower efficiency of biomass and marginally more expensive raw materials. These outcomes confirmed expectations: reducing emissions typically incurs a cost penalty. With the boundary solutions validated, we proceeded to the full multi-objective GA run to explore intermediate scenarios.

The NSGA-II parameters were configured with a crossover rate of 0.8 and a mutation rate of 0.1, employing a real-coded GA. Convergence was achieved around generation 150, as the Pareto front stabilized. To validate selected GA solutions, we cross-checked them using a high-fidelity process simulation implemented in Python (version: Python 3.11.4). This simulation confirmed that the predicted moduli and emissions were consistent with the GA outputs. These results affirm the robustness of the hybrid approach. Overall, the methodology combines detailed chemical and process constraints with evolutionary optimization, offering a robust framework for evaluating the balance between cost and sustainability in cement production. The following section presents the results of this method and discusses their implications.

4. Results and Discussion

4.1. Optimization Results: Cost–Emissions

The GA-LP optimization produced a set of Pareto optimal solutions, each specifying a raw mix (material fractions) and fuel split for the kiln. Figure 2 illustrates the resulting Pareto front, i.e., the curve between production cost and CO₂ emissions per ton of clinker. As expected, the relationship shows an inverse correlation: solutions with lower emissions come at higher costs, and vice versa. Cost-optimal solutions lie toward the right (higher emissions), while emission-optimal solutions are on the left (higher cost). The curve is relatively smooth, indicating a continuous trend without large jumps, which suggests that the model can gradually shift the mix to trade cost for emissions.

The minimum-cost solution, at USD 35.8/ton of clinker and 928 kg CO₂/ton, uses 100% petroleum coke (the cheapest fuel per energy unit) and maximizes low-cost raw materials. Fly ash is used at its 10% cap, clay is increased due to its low cost and silica content, and limestone is minimized (78%) to meet the LSF constraint. The mix includes 10–12% clay and 0.5% iron additive. This configuration reduces costs, but yields high emissions due to the carbon intensity of the petcoke and unavoidable calcination from limestone. All quality constraints are satisfied: LSF sits at the lower bound (92%) and SM at the upper bound (2.7), indicating that the optimizer exploits constraint limits for cost savings. This outcome reflects a purely cost-driven strategy, which is typical of profit-focused operations. Notably, similar behavior was reported by Babazadeh et al. [25] for an Iranian plant, where maximal siliceous fly ash and low-cost fuel drove the LSF to its lower limit, reinforcing the alignment of this result with real-world observations in cost-optimized cement production scenarios.

The minimum CO₂ solution achieves 740 kg CO₂/ton clinker, about 20% lower than the cost-optimal case, but at a higher cost of USD 44.5/ton. This environmentally focused scenario shifts the fuel mix to 50% biomass (maximum allowed), 20% tire-derived fuel, and 30% coal to maintain energy density. Despite a higher limestone content (82%) and an LSF near 97–98%, total emissions drop due to the low CO₂ impact of biomass and partial substitution with tires. The increased limestone is necessary to balance clinker chemistry, compensating for biomass ash composition (rich in silica and alkalis). Iron content is also increased to maintain chemical moduli. The raw mix still includes 10% fly ash, the cap used across all scenarios. The cost increase stems mainly from the lower calorific value of biomass and its assumed cost (USD 20/ton), which, when energy-adjusted, is higher than that of coal. Handling requirements also raise operational costs.

Importantly, this solution maintains clinker quality, with an LSF of 97, an SM of 2.4, and an AM of 1.4, indicating acceptable and possibly slightly harder-burning clinker. These results align with observations by Schneider, Romer, Tschudin and Bolio [54], who noted that high-performance clinker remains achievable under high alternative fuel substitution when raw mix adjustments are made. This result mirrors practice in modern European plants, which achieve similar emissions levels with over 50% alternative fuel substitution, thereby supporting the credibility and practical relevance of the model [54]. Between these extremes, the Pareto front provides a continuum of solutions.

Table 5. Pareto-optimal solution results.

	Raw Mix Composition (%)				Fuel Mix Composition (%)				Cost (USD/ton)	CO2 (kg/ton)	Clinker Quality (LSF, SM, AM)
Solution	Limestone	Clay	Fly Ash	Iron Ore	Coal	Petcoke	Biomass	TDF
A (Low-Cost)	78.0	11.5	10	0.5	0	100	0	0	35.8	928	(92.1, 2.70, 1.30)
B (Balanced)	80.5	9.5	10	0.0	50	0	30	20	39.0	830	(94.5, 2.55, 1.45)

presents the results of two representative Pareto-optimal solutions, labeled Solution A and Solution B, for cement raw mix and fuel blend optimization. Solution A prioritizes cost, while Solution B offers a more balanced approach between cost and CO₂ emissions. All clinker quality metrics (LSF, SM, AM) are within acceptable standards. Our model’s optimized scenario achieves 740 kg CO₂/ton clinker. These results are consistent with benchmarks from modern European cement plants, which report emissions in the range of 750–850 kg CO₂/ton clinker under 50–60% alternative fuel substitution, as documented by Schneider et al. [54].

In Table 5, Solution A represents a near-cost-optimal case that is slightly adjusted, possibly to satisfy an emissions constraint, while Solution B offers a balanced trade-off, delivering notable CO₂ reduction with a modest cost increase. Specifically, Solution B employs 30% biomass and 20% TDF, lowering emissions by approximately 11% compared to Solution A (830 vs. 928 kg CO₂/ton) at a cost of USD 39/ton, which is about 9% higher than that for A. Its raw mix includes slightly more limestone than that of A, compensating for the lower silica contribution from biomass ash compared to petcoke ash. These intermediate solutions demonstrate the value of flexibility in fuel and raw mix strategies. For example, Solution B may appeal to policymakers seeking a compromise between economic and environmental goals, delivering meaningful emissions reductions at acceptable costs. This type of insight is the key strength of multi-objective optimization. Rather than testing a limited set of scenarios, it reveals near-optimal combinations, such as 30% biomass plus 20% TDF, that might otherwise be overlooked in conventional analysis.

The Pareto front in Figure 2 highlights the principle of diminishing returns in emissions reduction. As the curve shifts leftward, it steepens, signaling that the cost per unit of CO₂ saved increases. In our case, reducing emissions from 930 to 850 kg CO₂/ton (a 9% reduction) increases cost modestly by USD 3 (from USD 36 to USD 39), indicating a shallow slope. However, further reduction to 780 kg CO₂/ton (another 8%) raises the cost to USD 42, showing a steeper slope and higher marginal cost. This pattern aligns with industry findings that initial reductions of up to about 20% via alternative fuel substitution are cost-effective, while greater reductions often require more expensive interventions or high-grade biomass. Such information is critical for carbon pricing strategies. For example, a carbon tax of USD 10/ton CO₂ would shift the cost-optimal point leftward until the marginal abatement cost equals the tax. In this case, Solution B, which reduces CO₂ emissions by 100 kg at a USD 3 premium, results in an abatement cost of USD 30/ton justifiable under a USD 30 carbon tax. The model thus offers quantitative support for policy and investment decisions under climate regulations.

4.2. Raw Mix and Fuel Blend Implications

A key outcome is the way in which the raw mix design adjusts dynamically with changes in the fuel mix. Unlike traditional optimization, where the raw mix is optimized independently for cost under fixed fuel conditions, this model captures interactions driven by fuel ash composition. For instance, in high-alternative-fuel scenarios such as Solution B and the low-CO₂ extreme, the Fe₂O₃ contribution from tire-derived fuel (which contains steel) was sufficient to eliminate the need for iron ore. In Solution B, iron ore was excluded (0%), compared to 0.5% in Solution A, reducing both material costs and the AM of the clinker, which the model balanced at 1.45, still within acceptable limits. Biomass also introduces ash components like alkalis that have a lower sulfur content, which can influence kiln chemistry. While our current model did not explicitly constrain alkali levels, this parameter can be integrated to improve operational practicality. Alkali metal oxides such as K₂O and Na₂O are present in clinker due to their presence in trace concentrations in raw materials like clay, shale, and fuels, and especially in alternative fuels such as biomass and RDF, which often contain higher alkali contents. Limiting their combined concentration (K₂O + Na₂O < 0.6%) is essential for several reasons. High alkali levels can contribute to deleterious alkali–silica reactions in concrete when reactive aggregates are used, compromising long-term durability. Additionally, excess alkalis may form low-melting-point compounds, leading to kiln deposit formation, preheater fouling, and operational inefficiencies.

On the fuel side, the optimization produced results that align with practical expectations. Biomass was prioritized for CO₂ reduction until limited by cost or technical constraints, after which the model introduced TDF to maintain the energy balance of the kiln due to its higher calorific value. While allowing 100% biomass would likely push the model toward full substitution, assuming carbon-neutral operational limits makes this unrealistic. The 50% cap reflects practical combustion constraints in large kilns. TDF played a dual role as it provided moderate CO₂ reduction and contributed Fe₂O₃ through its ash, eliminating the need for separate iron ore addition in some solutions. This co-benefit is well documented—used-tire ash is rich in iron and zinc, supporting clinker formation, although excessive zinc can pose coating issues. Similarly, other alternative fuels like spent pot liner (a by-product of aluminum production) can supply functional elements such as fluorine and sodium, which act as mineralizers in small amounts. The results of this study suggest that such interactions between fuel ash and raw mix design can be leveraged in optimization, as demonstrated by the elimination of iron ore when using TDF.

From a cost standpoint, the model reveals savings that may not be immediately intuitive. In Solution A, for example, 100% petcoke emerged as the most cost-effective fuel, with no coal used, indicating that, under the given assumptions, the lower cost of the petcoke per energy unit outweighed any drawbacks. However, in real operations, the high sulfur content in petcoke may incur additional costs, such as the need for extra limestone to control SO₂ emissions or limits tied to product quality. Since our model did not penalize sulfur, it defaulted to full petcoke use. In practice, a plant facing sulfur-related constraints could incorporate them into the model, for example, by setting a cap on total SO₂ emissions. This would force a more balanced fuel mix, potentially including lower-sulfur options like coal or biomass. The model is easily adaptable to include such constraints or additional objectives, such as minimizing SO₂ or NO_x emissions, enabling more comprehensive optimization that is aligned with regulatory and operational priorities.

4.3. Comparison to African Case Studies

It is valuable to compare our optimization results with results from African cement plants implementing similar strategies. In the Nigerian case study (BUA plant) by Joseph and Obodeh [19], the use of 50% agro-waste as an alternative fuel reduced production costs from USD 38.2 to USD 23 per ton, a reported 40% reduction. In our model, increasing alternative fuel usage from 0% to 50% reduced costs from USD 44 to USD 36, an 18% reduction. The greater savings in their case likely reflect assumptions of free and abundant alternative fuels, while our model included a moderate cost and supply cap for biomass. If we assumed zero biomass cost and unlimited availability, our optimization would also shift to maximum alternative fuel use, potentially mirroring their 30–70% savings. Similarly, a South African study by Beltran and Arnesh [42] reported a 16.7% CO₂ reduction using a fuel mix of 20% used oil and some tire-derived fuel.

Our Solution B, with 30% biomass and 20% tires, achieved an 11% reduction. Substituting used oil for biomass in our model would likely yield even lower amounts of CO₂, given its lower carbon intensity than coal. Overall, our findings align in scale with these studies, accounting for scenario-specific assumptions.

A key advantage of the Pareto front is that it offers more profound insight than single-scenario studies. Many published analyses examine only one or two scenarios of alternative fuels or raw mix changes. In contrast, a multi-objective approach systematically explores all scenarios. For example, if a cement plant manager in Africa is cautious about high alternative fuel usage due to operational risks, they could opt for a moderate solution like 20–30% alternative fuel from the Pareto front, and still understand the cost and emissions implications of not going further. Figure 2 illustrates this: the slope at any point on the curve represents the marginal cost of CO₂ abatement in dollars per ton.

While the optimal solution of 30% biomass and 20% TDF substitution achieves favorable economic and environmental outcomes, its generalizability is constrained by regional fuel availability and policy differences. In particular, the model assumes low-cost waste resources that are commonly observed in specific African contexts with donor or government-supported waste valorization. In resource-scarce settings or regions lacking organized biomass supply chains, such substitution ratios may be unfeasible. Moreover, the carbon tax value of USD 30/ton used in the model is based on international assumptions, and exceeds current values implemented in Africa. For example, South Africa applies a carbon tax ranging from USD 8 to USD 15/ton, depending on industry and allowable offsets. Future studies should integrate local market dynamics, carbon pricing frameworks, and fuel logistics to refine scenario applicability.

4.4. Relevance of Multi-Objective Optimization to Sustainable Cement Production

The MOO results highlight several actionable insights for sustainable cement production. A CO₂ emissions reduction of up to 20% is achievable through integrated optimization of raw mix and fuel use, without compromising clinker quality. This result aligns with the findings of Schneider et al. [54], who stated that alternative fuels can be incorporated without affecting clinker performance. This is especially relevant for African plants with older systems and high CO₂ intensity [55,56]. Mutually beneficial scenarios are possible; for example, using 10% fly ash and 15–20% tire-derived fuel can reduce both production costs and CO₂ emissions by about 5%. These cost-effective measures should be prioritized, particularly in regions where fly ash or low-cost waste fuels, e.g., rice husk and used oil, are readily available, as shown in Joseph and Obodeh’s study at the BUA plant in Nigeria [19]. While higher levels of alternative fuel use may raise costs slightly (e.g., USD 3/ton for 50% alternative fuel), modest carbon credits (around USD 5/tCO₂) or improved waste supply infrastructure could offset these increases and support cleaner operations at minimal overall cost [37,57]. Intermediate solutions like 30% biomass and 20% tires are feasible today; extreme options may need retrofits (e.g., precalciner). Some plants already see operational benefits from tire use, such as improved kiln stability [21]. All solutions maintain the LSF, SM, and AM within acceptable limits. The model pushes boundaries, but such an operation is manageable with modern quality control tools, which are increasingly available in African plants [18]. The hybrid GA-LP model is fast and adaptable, making it suitable as a decision-support tool across multiple plants to guide investments in alternative fuel and raw material use [10,19]. The results and the relevance of this optimization framework to sustainable cement production in Africa are presented in Figure 3, Figure 4, Figure 5 and Figure 6.

Figure 3 shows the proportion of each fuel type and compares fuel compositions in the main scenarios. From the figure, it can be observed that Solution A (cost-optimal) uses 100% petcoke (a fossil fuel), which has the lowest cost but the highest emissions. Solution B (balanced trade-off) incorporates 30% biomass, 20% TDF, and 50% Coal. This hybrid mix balances costs and emissions effectively. In the low-CO₂ solution, biomass dominates the fuel mix at 50%, displacing most petcoke and coal, reducing fossil fuel use significantly.

These configurations highlight how fuel blending affects sustainability outcomes through the strategic blending of available fuels. Increasing biomass and RDF use reduces fossil fuel dependence and emissions, but may affect flame temperature and operational constraints, which are relevant for kiln control and retrofitting discussions.

Figure 4 compares the raw mix composition between Solution A and Solution B. The figure shows corresponding changes in the raw mix design, highlighting differences in raw mix usage, particularly the elimination of iron additive in Solution B. It reveals that in Solution B, the iron additive is eliminated due to the Fe₂O₃ contribution from tire ash, demonstrating the interaction between fuel ash chemistry and raw mix formulation.

This co-benefit reduces material costs and subtly alters clinker moduli. There is a clear interaction between fuel ash and raw mix, allowing the system to economize on raw materials and reduce emissions from carbonates, e.g., limestone.

Figure 5 quantifies the cumulative cost and emissions of moving through the solution space, showing how each added solution contributes incrementally to the total cost and emissions. This dual-axis line graph compares the total cost and CO₂ emissions across progressive solutions (A → Low-CO₂). It helps to visualize the incremental impact of moving along the Pareto front and helps to evaluate the system-wide implications of transitioning toward cleaner configurations.

As CO₂ decreases, the cumulative cost increases. The increase is nearly linear at first, but becomes steeper between Intermediate and Low-CO₂. This figure can help stakeholders to visualize the total system burden of each shift, which is crucial for investment planning and lifecycle assessment. It highlights that incremental decarbonization is economical, but aggressive shifts require financial incentives.

Figure 6 presents a sensitivity analysis showing how production cost increases nonlinearly as the biomass share in the fuel mix increases from 0% to 50%. It highlights that below 30%, the increase in production cost is moderate. The curve helps to identify economically viable substitution levels under fuel cost and supply constraints.

Substitution levels beyond 30% incur nonlinear cost penalties exceeding USD 48/ton at 50% biomass, which is essential for plants constrained by fuel supply or capital. While biomass is carbon-neutral, its lower calorific value and higher moisture content reduce its combustion efficiency. Plants must weigh these factors, especially if biomass supply is limited or seasonal.

A key innovation of this study is the explicit integration of fuel ash chemistry into the raw mix optimization process. Unlike traditional models that optimize fuel and raw materials separately, our model directly integrates the oxide contribution of fuel ash into the raw mix formulation, enabling more accurate control of clinker quality indices such as the LSF, SM, and AM under real kiln conditions. This integration ensures that the final clinker composition remains within quality specifications even when high shares of alternative fuels are used. Such coupling is essential in real-world applications, where ash content can significantly influence kiln feed chemistry and clinker mineralogy, especially under high-substitution scenarios. By embedding ash-driven adjustments directly into the optimization logic, the model aligns more closely with operational realities and sets a methodological advancement over prior decoupled approaches.

Although the model supports high levels of alternative fuel substitution, its practical implementation in African cement plants may face technical and infrastructural constraints. Many facilities lack precalciners, automated dosing systems, or robust fuel handling infrastructure, which limits their ability to handle high-moisture or variable-fraction biomass. A detailed risk assessment of equipment modifications, such as retrofitting feed systems or adding combustion controls, is therefore essential. Moreover, the current model assumes that fuels are already pretreated; in reality, the cost and energy required for shredding, drying, and homogenizing waste fuels should be included. Future extensions of this work will incorporate these retrofit risks and preprocessing costs into the optimization model to better reflect the whole system.

4.5. Sensitivity Analysis

This section evaluates how changes in key input parameters, the biomass price, and the LSF target affect clinker production costs, emissions, and fuel use. It assesses the robustness of the optimized clinker production strategy by simulating how performance shifts under realistic operational and economic scenarios.

• Baseline scenario. The reference clinker production case assumes the optimized mix (LSF 0.92) and current fuel prices, yielding a production cost of roughly USD 45/t and CO₂ emissions of 910 kg/t (typical for modern kilns). The share of alternative fuels, like biomass and TDF, is about 50% in this study. These values serve as the point of comparison for all perturbations.
• Increased biomass price. Raising the biomass price, by 20% for example, makes biofuel substitution less attractive. In our model, the biomass share falls sharply (the alternative fuel share drops from 50% to 20%), with coal and TDF filling the gap. As a result, the production cost rises to about USD 50/t (11%), reflecting that fuel accounts for 40% of the cement cost, and CO₂ emissions increase to roughly 960 kg/t. The higher use of fossil fuels increases emissions by 5–10% compared to the baseline. Thus, expensive biomass leads to more fuel switching, less biomass, more coal/TDF, higher costs, and higher CO₂ emissions.
• Reduced biomass price. Conversely, a lower biomass cost encourages greater substitution. The biomass share increases the alternative fuel share to 70%, reducing reliance on coal/TDF. The production cost falls to about USD 42/t (–7%), and CO₂ emissions decrease to 880 kg/t. In this scenario, the marginal fuel savings and higher biogenic share cut CO₂ emissions by a few percent. Thus, cheaper biomass allows for more fuel switching, reducing costs and emissions relative to the baseline case.
• Higher LSF (limestone purity). Increasing the target LSF by 5%, e.g., from about 0.92 to 0.97, forces more limestone and less clay in the raw mix. This raises the calcination load, so CO₂ emissions climb by roughly 33 kg/t (3.6%). The raw material cost impact is modest; if limestone is slightly cheaper than clay, the effect on the total cost is small, in the range of a few percent. In our analysis, the cost changes by only USD–1/t to USD 46/t. The alternative fuel share remains at 50%, i.e., the fuel mix is unchanged, but the higher LSF means a slightly higher kiln output per clay input.
• Lower LSF. Reducing the LSF target by 5%, e.g., to 0.87, has the opposite effect: more clay is used, lowering the levels of CaO from limestone. CO₂ emissions drop by 33 kg/t (3.6%). The raw material cost impact is again small, at a few percent; in this study, the cost is USD 44–46/t, offsetting slightly higher clay costs. The alternative fuel share stays near 50%. Thus, a lower limestone fraction (lower LSF) yields a modest emissions benefit at a slight cost penalty.

Governing Equations for Sensitivity Analysis

For clarity, the cost and emissions equations introduced initially in Section 3 (Equations (1) and (2) are restated here to support the sensitivity scenarios that follow.

• Cost Equation:

$$\mathrm{C}={\displaystyle \sum }_{i=1}^N{x}_i\times c_i^{raw}+{\displaystyle \sum }_{j=1}^{M}H\times y_j\times c_j^{fuel}$$

(20)

• Emissions Equation:

$$E={\displaystyle \sum }_{\mathrm{i}=1}^N{x}_i\times {{\mathrm{CO}}_2}_i^{raw}+{\displaystyle \sum }_{j=1}^{M}H\times y_j\times {{\mathrm{CO}}_2}_j^{fuel}$$

(21)

• LSF Sensitivity Estimate:

For an approximate 5% change in the LSF, the CO₂ emissions vary as follows: $△E_{LSF=\pm 33 Kg {CO}_2/ton clinker}$, based on an increase or decrease in the limestone content and its calcination CO₂.

Table 6. Impact of biomass cost and LSF target on clinker production metrics.

Scenario	LSF Target	Alternative Fuel Share (%)	Fuel Cost (USD/t Clinker)	CO2 (kg/t Clinker)
Baseline (optimized mix)	0.92	50	45	910
+20% biomass price	0.92	20	50	960
−20% biomass price	0.92	70	42	880
+5% LSF target	0.97	50	44	943
−5% LSF target	0.87	50	46	877

presents the impact of changes in biomass price and the LSF target on four clinker production metrics: cost, CO₂ emissions, alternative fuel share, and LSF value. This offers a quick reference for interpreting multi-objective considerations under different operational scenarios.

The table shows how key parameter changes affect clinker production performance:

• Biomass Cost Sensitivity:

• An increased cost reduces the alternative fuel share and increases both costs and emissions.
• A reduced cost enhances alternative fuel substitution, lowering both emissions and costs.

• LSF Target Sensitivity:

• A higher LSF increases emissions due to more limestone and calcination.
• A lower LSF reduces emissions modestly, with minor cost impacts.

• Trade-Off Summary:

• Emissions variation range: ±33 kg CO₂/ton (±3.6%).
• Cost variation: ±$3–5/ton clinker.
• The alternative fuel share is most affected by biomass pricing, ranging from 20 to 70%.

These results provide a quantitative foundation for adaptive decision-making in sustainable cement production, demonstrating how economic and quality-driven adjustments affect CO₂ emissions and costs under realistic operating conditions. These sensitivity results help to identify the robustness of the optimized clinker mix under varying economic and material quality assumptions.

The sensitivity analysis in Figure 7 presents a comprehensive view of how the clinker production cost, CO₂ emissions, alternative fuel share, and LSF target respond to changes in the biomass price and quality standards. This plot shows variation in the cost, CO₂ emissions, alternative fuel share, and LSF target across five modeled scenarios.

The sensitivity analysis confirms that clinker production performance is highly responsive to biomass cost and LSF targets. Fuel economics, particularly biomass pricing, exert the most decisive influence on both environmental and economic outcomes, while quality constraints like the LSF affect emissions more than cost. The results underscore the value of a multi-objective optimization approach in guiding adaptive, data-driven decisions. Cement producers can use this model not only to assess feasible production strategies under changing market or regulatory pressures, but also to align operational priorities with long-term decarbonization goals.

5. Conclusions

This study proposed a novel hybrid GA–LP optimization model to optimize raw mix design and alternative fuel blending in cement production. The integrated approach effectively balances production cost and CO₂ emissions while ensuring clinker quality through chemical modulus constraints. The hybrid framework leverages the strength of GA for multi-objective search and the accuracy of LP to enforce strict feasibility, particularly in maintaining compliance with kiln feed and clinker property requirements. The core innovation lies in the explicit incorporation of fuel ash chemistry into the raw mix adjustment process, a methodological advancement that distinguishes this work from previous optimization models, which have often treated fuel and raw mix design independently. This allows for more realistic modeling of ash–oxide interactions and offers a practical decision-support tool for cement plants transitioning to high usage rates of waste-derived fuels. Also, this integrated formulation enables more accurate and feasible optimization outcomes, especially under scenarios of high alternative fuel substitution.

The optimization results show a clear cost–emissions trade-off, with the Pareto front offering decision-makers a range of solutions. For instance, a 20% CO₂ reduction from the baseline (928 kg to 740 kg/ton clinker) is feasible with a modest increase in cost (from USD 36 to USD 45/ton clinker). Such results are consistent with industrial findings and reflect real-world plant conditions, as demonstrated by the case study grounded in African cement operations. Sensitivity analysis confirms that biomass pricing significantly influences fuel strategy and emissions, while changes in LSF targets affect clinker chemistry more than the overall cost. These insights will allow plant operators to adapt their strategies dynamically based on economic or regulatory shifts.

Despite its strengths, the model has limitations. First, it assumes fixed input parameters, such as fuel and raw material compositions, prices, and calorific values, which may vary in practice. Second, the model currently treats kiln energy consumption (H) as a constant, not accounting for temperature effects or incomplete combustion of low-grade fuels. Future research should address these limitations by (i) incorporating uncertainty and stochastic elements into input variables, and (ii) extending the model to dynamic multi-period planning under market fluctuations. Also, while the GA–LP model demonstrates strong simulation-based performance, experimental validation using plant-level data such as clinker strength or free CaO content was not conducted. Future studies are encouraged to validate the model with operational data to enhance its real-world applicability.