# Energy-Aware Multi-Objective Job Shop Scheduling Optimization with Metaheuristics in Manufacturing Industries: A Critical Survey, Results, and Perspectives

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## Abstract

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## 1. Introduction

## 2. Background

#### 2.1. Multi-Objective Optimization

**Definition 1.**

**Definition 2.**

**Definition 3.**

**Definition 4.**

**Definition 5.**

#### 2.2. Metaheuristics and Evolutionary Algorithms

#### 2.3. The JSP Problem

## 3. Literature Survey and Critical Analysis

#### 3.1. Literature Collection and Filtering Methodology

#### 3.2. Taxonomies and Literature Analysis

- Problem features: type of problem, number of objectives, the energy objective, and secondary objectives;
- Constraints and other considerations that have been taken into account in the analyzed works;
- Multi-objective optimizer, including the algorithm in use, compared algorithms, and values of the main parameters.

#### 3.2.1. Taxonomy 1: Problem Features

#### 3.2.2. Taxonomy 2: Constraints and Considerations

- A job can only be assigned to one machine;
- The number of jobs assigned to a machine cannot exceed the net production capacity of the machine;
- The processing time of a batch is equal to the longest time of the jobs on the machine;
- A job cannot start before the previous job is finished on the machine;
- No machine can do more than one job at a time;
- Each operator can only operate one machine at a time;
- Jobs are independent of each other.

- Machines are always available from the start: this first assumption does not hold in many practical circumstances, because not always are all machine available in real environments. This may occur for a manifold of reasons. For example, a machine can be broken, under maintenance, or can be blocked to produce only one type of unit. Surprisingly, all the reviewed papers assumed this start point;
- Once a job is started at a machine, the job cannot be stopped: this second assumption is not always possible either due to breakdowns, production priorities arising during the production cycle, and other assorted reasons. Therefore, in some cases (especially when there are many sub-processes flowing inside the same machine), the production of a unit has to be stopped and does not necessarily resume in the same unit. Possible issues derived from these circumstances during the manufacturing process were considered in [71];
- Each operation should begin immediately after the previous one has been completed: this third assumption is not always the best practice due to production bottlenecks: if a machine has a cycle time higher than other assets, it is a good practice to start the next/previous machine before the other ends. All the papers reviewed made this assumption;
- The production buffer between machines is unlimited: this assumption may hold sometimes, but it is not always true. Now that lean manufacturing is becoming a revolution in factories and that one of its pillars is based on producing only what is indispensable by reducing the length of the batches, assuming unlimited buffers will violate this principle [43];
- Transportation time within the plant and production chain is negligible: this is not always feasible, as the time needed to transport from one part to another one of the productive process can be even higher than that of the productive process itself. Lean manufacturing strives to reduce waste, so improving the product routing inside the factory is important. This constraint will be opposite the route and transport optimization, and its influence in the makespan is mostly considered as negligible. Nevertheless, some works have stepped aside this trend and considered this aspect in the problem formulation [55];
- The change time is negligible: this sixth constraint can be mainly assumed in the production of large batches, but currently, most factories are required to manufacture small batches of products. This entails that tooling changes happen more frequently, so their aggregate impact on production makespans can no longer be neglected [53,55,56,57].

#### 3.2.3. Taxonomy 3: Multi-Objective Optimizer

#### 3.3. Summary of Critical Points Identified in the Literature Analysis

- The first taxonomy given in Section 3.2.1 uncovered that most JSPs solved in the analyzed literature corpus addressed two or three objectives. This conforms to real-world settings, where production scheduling is often driven by a few key performance indicators. Nevertheless, we emphasize that the potential of multi-objective meta-heuristics to seamlessly cope with problems comprising several objectives should be propelled by a real-world need for taking them into consideration. In this regard, most cases reported in the literature posed sophisticated mathematical problem statements without giving an explicit rationale connecting the problem statement itself to real-world circumstances, KPIs, and constraints. This not only hinders the generalization of the studies, but also questions whether the research is truly motivated by real-world problems.
- The formulation of the JSP is based mainly on energy consumption and makespan. This is not an issue, but rather a consequence of the fact that in most practical settings, scheduling in industrial plants is governed mainly by production efficiency, i.e., the production of as much product as possible. The relatively low number of scientific works related to energy-aware production scheduling (slightly above 60 references) is also symptomatic of the fact that it has not been until recently when energy efficiency has become a concerning issue in real-world industries. Several reasons for this growing concern can be speculated around the sharply increasing energy costs, particularly noticeable in certain countries [96]. This fact is encouraging and should catalyze efforts brought to the area surveyed in this work;
- On the negative side, and repeating previous claims, we encountered that most types of JSPs tackled in the analyzed studies were largely specific for the use case under target in the paper, leading to a loose generalization of the results to new real-world setups. Again, this should not be considered an issue if the work at hand confined the conclusions of its experiments to the JSP variant under consideration. However, this was not the case in a subset of the references examined, wherein the novelty of the JSP problem was entangled with the proposal of a novel metaheuristic algorithm without any solid reason. This echoes the longstanding controversy about the role of the metaphor in the design of nature-inspired metaheuristics. We also noted this practice in several works resorting to new biologically inspired solvers over ad hoc JSP formulations, avoiding (1) the inclusion of well-established multi-objective algorithms in the comparisons and (2) the reproducibility of the results of the benchmark leading to the claims about the performance of the new solver. Principled and thorough performance studies should be performed in prospective works to clarify whether the performance of such solvers corresponds to a truly better search capability of their bio-inspired operators;
- When it comes to the realism of the formulated problem, very few papers took into account aspects that are prevalent across the production plants of a diversity of industries, such as waiting times, maintenance cycles, machine downtimes, and other aspects that impact the overall computation of the makespan. The intensity by which the makespan can be affected by not considering these aspects is subject to the use case under consideration. However, the growing capability of modern manufacturing execution systems (MESs) to integrate and handle all sources of information related to the production process should entail more realistic JSP formulations, showing that the makespan computation and the set of imposed constraints can harness the availability of external sources of information. Furthermore, new opportunities for dynamic production scheduling could arise, depending on the rate at which information is updated in the MES;
- Performance comparisons between algorithms should be made incremental. When new algorithms are proposed, they should be evaluated over synthetic JSP instances (i.e., leaving aside conditions/constraints imposed by real settings), so that advances can be validated by the community and improved upon. Our literature analysis revealed that reproducing an article dealing with a real-world scenario with a JSP at its core is hard to achieve. Key information is not provided (in some cases, due to confidentiality clauses), and source codes are not made available. Therefore, one can easily question whether new algorithms are developed ex professo for the use case under analysis, showing off a superior performance over a very scarcely comparableJSP. This could be the reason why Table 2 evinces that almost no multi-objective algorithm that falls out of the metaheuristic mainstream was used in studies published after it was first presented. We definitely envision that the community should report a fair and methodologically principled performance comparison between well-known algorithms over diverse, yet synthetically generated energy-aware JSP problem instances. This study could inform whether there is any value in the set of modern metaheuristic approaches that lie within the boundaries of the aforementioned controversy. Most importantly, by including customized/memetic/hybrid algorithm in the benchmark, such a study would evince whether the customization of metaheuristic algorithms provides any further value beyond solving better specific formulations of the energy-aware JSP.

## 4. Experimental Study

#### 4.1. Problem Statement

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- Energy consumption per time unit:
- –
- machineWorkingEnergy: Total energy consumption by unit time while a machine is working;
- –
- machineIdleEnergy: Total energy consumption by time unit while a machine is in the idle state;
- –
- machineWorkingToStopEnergy: Total energy consumption by time unit while a machine stops from working;
- –
- machineWorkingToIdleEnergy: Total energy consumption by time unit while a machine changes from working to the idle state;

- Machine velocity variables:
- –
- numberOfVelocities: Array of the velocities that a machine can have;

- Velocity energy penalization:
- –
- velocityPenalty: Energy consumption penalization by different velocities;

- Unit time variables:
- –
- machineTimeToIdle: Units of time that a machine needs to change from the idle state to start or from start to idle;
- –
- machineTimeToStop: Units of time that a machine needs to change from the working state to stop or vice versa.

- la04 [98], 5 machines and 10 jobs;
- la10 [98], 5 machines and 15 jobs;
- ft06 [99], 6 machines and 6 jobs;
- orb01 [98], 10 machines and 10 jobs;
- abz5 [100], 10 machines and 10 jobs;
- swv20 [101], 10 machines and 50 jobs;
- ta12 [102], 15 machines and 20 jobs;
- dmu11 [103], 15 machines and 30 jobs;
- yn03 [104], 20 machines and 20 jobs;
- dmu40 [103], 20 machines and 50 jobs;
- ta77 [17], 20 machines and 100 jobs.

#### 4.2. Benchmark and Comparison Methodology

#### 4.2.1. Encoding Strategy

- Makespan array: To fill this array, random integer numbers between one and the total number of available jobs were pushed to it, with the condition that a job number cannot appear more times than the total number of machines to which the the job has been assigned;
- Velocity array: This array contains random integer numbers between one and the number of available velocities;
- Idle array: The contents of this array are random binary numbers.

#### 4.2.2. Multi-Objective Algorithms

#### 4.2.3. Constraints and Considerations

- Machines can be in the idle state, with an associated idle energy consumption;
- Machines can be switched off, with power off and power on energy consumption considered;
- Machines can run at different velocities.

#### 4.2.4. Solution Evaluation

#### 4.2.5. Quality Indicators

- The EP is a measure of the absolute deviation needed to translate each solution in a Pareto front approximation in such a way that it weakly dominates the front used as a reference (it can be the true Pareto front or a subset of it);
- The NHV is computed as 1.0 minus the ratio between the hypervolume of the front to be evaluated and the hypervolume of the reference front. The hypervolume metric calculates the volume (in the space of objectives) covered by members of a given set of non-dominated solutions with respect to a reference point;
- The IGD+ evaluates the convergence performance and the distribution performance of the algorithm by calculating the sum of the minimum distances between each point (individual) on the reference front and the front of solutions obtained by the algorithm.

#### 4.3. Results and Discussion

## 5. Conclusions and Prospective

#### 5.1. Summary of Critical Insights Drawn from the Literature Review

#### 5.2. Summary of Conclusions from the Experimental Results

#### 5.3. Research Directions and Perspectives

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Number of publications per year for the multi-objective JSP problem with energy as one of the targets.

**Figure 7.**Example of an encoded solution to the energy-efficient JSP addressed in the experimental part of this survey.

**Figure 8.**Reference front for the ta12 problem. The different symbols correspond to the contributions of each algorithm.

**Figure 9.**Schedules of the ta12 instance with the extreme solutions (best energy solution and best makespan solution).

**Table 1.**Classification of metaheuristics in nature-inspired and non-nature-inspired techniques, together with some illustrative examples for each of these categories.

Nature-Inspired | Non-Nature-Inspired |
---|---|

• Simulated annealing (SA) | • Tabu search (TS) |

• Swarm Intelligence | • Variable neighborhood search (VNS) |

− Particle swarm optimization (PSO) | • Scatter search (SS) |

− Ant colony optimization (ACO) | • Iterated local search (ILS) |

• Evolutionary computation (EC) | • Guided local search (GLS) |

− Genetic algorithm (GA) | • Path relinking (PR) |

− Evolution strategy (ES) | • Greedy randomized adaptive |

− Genetic programming (GP) | Search procedure (GRASP) |

• Artificial immune system (AIS) |

Year | Reference | Algorithm Used | Initial Algorithm | Algorithms Used for Comparisons |
---|---|---|---|---|

2011 | [94] | SPNE | Dynamic game theory | AL+CGA; PSO+TS; HSISAT |

2013 | [36] | MOACO | ACO | NSGA-II; SPEA-2 |

[70] | IGSAA | SA | - | |

2014 | [82] | BVNSGA-II | NSGA-II | - |

[86] | NSGA-II | NSGA-II | - | |

2015 | [41] | SAA | GA | - |

[69] | Continuous-time MILP | - | - | |

[67] | GD-MOCDE | MOCDE, Gradient descent (DC), | MODE; | |

[68] | ABC | ABC | IGAMU; CSO; SAGA | |

2016 | [37] | MILMO | - | - |

[39] | GAEJP | NSGA-II | NSGA-II; LEKING | |

2017 | [84] | MOGA | Simplex lattice design | NSGA-II; |

[89] | GA-based | GA | - | |

[66] | HMOBSA | MOEAs | NSGA-II; MOEA/D; | |

[89] | Enhanced GA | Standard GA | - | |

[94] | SPNE | DGT | AL+CGA; PSO+TS; HSISAT | |

2018 | [38] | EA-MOA | - | NSGA-II; MOEA/D; DBEA; EADD |

[44] | IGALL | IG | - | |

[46] | SFLA | SFLA | BVNSGA-II | |

[50] | MCEAs | - | NSGA; | |

[57] | Multi-objective DE | - | NSGA-II; AMGA | |

[88] | Bee Colony | Artificial bee colony (ABC) | - | |

[92] | HMOGWO | GWO; GA | NSGA-II; SPEA2; MOGWO; MOGWO1; MOGWO2 | |

[63] | TEPSO | PSO; TABOO | NSGA-II; SPEA2 | |

[64] | NBI | Normal boundary intersection | - | |

[65] | TTLBO | - | IGSA; GA | |

[95] | NSGA-III | NSGA-III | NSGA-III-NIG; EFR-RR; crEA | |

2019 | [40] | MOBSO | Basic BSO | NSGA-II; MOEA/D |

[42] | MDABC | MOEA | NSGAII; EAMOA; CMFOA; MOEA/D; iMOEA/D | |

[43] | EOMO | (MOEA/D). | SPGA-II; NSGA-II; MOEA/D | |

[45] | MOHPIOSA | PIO | NSGA-II | |

[85] | IMOMVO | MOMVO; MOPSO; MOALO; NSGA-II | ||

[71] | MOGSA | MOGA | - | |

[93] | DCRO | CRO | - | |

[56] | MOCGWO | MOG | NSGA-II; NSGA-II + NDM; SPEA2; SPEA2 + NDM; MOCGWO | |

[55] | iMOEA/D | MOEA/d | HMOBSA; NSGA-II | |

[56] | MOCGWO | GWO and CA | NSGA-II; SPEA2; MOCGWO | |

[58] | MOWSA | Whale swarm algorithm | NSGA-II; SPEA2; PAES | |

[61] | COA | NSGA-II; IMEA/D | ||

[91] | ILS | ILS | NSGA-II | |

[54] | New MOGA | MOGA | - | |

[80] | MOGA-LS | ILS; VILS | - | |

2020 | [83] | PH-MOEAD | MOEAD | EMBO; GA; GAR; DPSO; DABC |

[47] | DEMO | - | MODWWO; MPVNS; MOMBO | |

[48] | MHACO | - | NSGA-II; MODEA; SPEA-II | |

[49] | CPLEX (not provided) | - | - | |

[87] | EMA | NSGA-II; NNIA; NSGA-III | ||

[51] | EDA | GA | ||

[52] | Own algorithm | - | - | |

[53] | 2-echelon iMOEA/D | MOEA/D | NSGA-II; MOGLS | |

[90] | HEA | - | NSGA-II; NNIA | |

[59] | iIMOALO | ALO | NSGA-II; MOPSO | |

[60] | NMA | MA | MA | |

[73] | NSGA-II | NSGA-II | SPEA2 | |

[74] | NSGA-II | NSGA-II | - | |

[75] | EE-VBIH; EE-IG; IG-ALL | |||

[76] | MDSS-MOGA-DE | MOABC; MOACO; MOCS | ||

[77] | NSGA-II; SPEA-2 | NSGA-II; SPEA-II | NSGA-II; SPEA-2 | |

[78] | NSGA-II | NSGA-II | ||

[81] | PSO_SWS; PSO_LWR | PSO | PSO_SWS; PSO_LWR; PSO | |

2021 | [72] | HPSO | PSO i | NSGA-II; HPSO-LS |

**Table 3.**Summary of the operators and parameter values set in the multi-objective algorithms considered in our experiments.

NSGA-II | MOEA/D | SMS-EMOA | |||||
---|---|---|---|---|---|---|---|

Parameter | Value | Parameter | Value | Parameter | Value | ||

Selection | Binary tournament | Neighbor selection probability | 0.9 | Selection | Random | ||

Neighbor size | 20 | ||||||

Maximum number of replaced solutions | 2 | ||||||

Aggregation scheme | Tschebyscheff | ||||||

Common Parameters: | |||||||

Population size: 50 individuals | |||||||

Number of function evaluations: $3\times {10}^{5}$ | |||||||

Crossover: 2-parent position exchange in uniformly selected array of the chromosome | |||||||

Crossover probability: 0.9 | |||||||

Mutation: random exchange in uniformly selected array of the chromosome | |||||||

Mutation probability: 1.0 |

**Table 4.**EP median and interquartile range. Dark and light grey background cells highlight the best and second best results, respectively.

SMSEMOA | NSGAII | MOEAD | |
---|---|---|---|

la10 | $2.34e-{01}_{2.2e-01}$ | $1.68e-{01}_{7.1e-02}$ | $9.01e-{01}_{1.6e-01}$ |

ft06 | $3.00e-{01}_{0.0e+00}$ | $3.00e-{01}_{0.0e+00}$ | $1.20e+{00}_{5.0e-01}$ |

orb01 | $3.38e-{01}_{3.5e-01}$ | $2.32e-{01}_{9.9e-02}$ | $1.15e+{00}_{4.1e-01}$ |

swv20 | $7.26e-{01}_{4.1e-01}$ | $4.83e-{01}_{4.2e-01}$ | $7.09e-{01}_{8.5e-01}$ |

ta12 | $1.59e-{01}_{7.2e-02}$ | $1.02e-{01}_{8.0e-02}$ | $3.79e-{01}_{1.8e-01}$ |

dmu11 | $3.71e-{01}_{1.4e-01}$ | $1.78e-{01}_{1.4e-01}$ | $4.14e-{01}_{3.2e-01}$ |

yn03 | $5.35e-{01}_{2.9e-01}$ | $1.97e-{01}_{2.0e-01}$ | $8.66e-{01}_{3.4e-01}$ |

dmu40 | $9.59e+{00}_{7.1e+00}$ | $5.85e+{00}_{3.6e+00}$ | $6.97e+{00}_{8.5e+00}$ |

ta77 | $2.64e+{01}_{9.4e+00}$ | $2.23e+{01}_{7.7e+00}$ | $1.93e+{00}_{1.4e+00}$ |

**Table 5.**NHV median and interquartile range. Dark and light grey background cells highlight the best and second best results, respectively.

SMSEMOA | NSGAII | MOEAD | |
---|---|---|---|

la10 | $3.14e-{01}_{2.0e-01}$ | $2.03e-{01}_{1.3e-01}$ | $8.88e-{01}_{2.2e-01}$ |

ft06 | $1.66e-{01}_{5.7e-02}$ | $1.06e-{01}_{5.4e-02}$ | $1.00e+{00}_{0.0e+00}$ |

orb01 | $5.05e-{01}_{3.2e-01}$ | $2.76e-{01}_{5.9e-02}$ | $1.00e+{00}_{1.0e-01}$ |

swv20 | $7.64e-{01}_{3.9e-01}$ | $4.60e-{01}_{4.4e-01}$ | $7.02e-{01}_{6.2e-01}$ |

ta12 | $1.45e-{01}_{7.0e-02}$ | $7.96e-{02}_{3.5e-02}$ | $3.67e-{01}_{1.8e-01}$ |

dmu11 | $3.79e-{01}_{1.4e-01}$ | $1.41e-{01}_{1.8e-01}$ | $4.03e-{01}_{3.2e-01}$ |

yn03 | $5.21e-{01}_{3.9e-01}$ | $1.62e-{01}_{2.1e-01}$ | $8.62e-{01}_{3.2e-01}$ |

dmu40 | $1.00e+{00}_{0.0e+00}$ | $1.00e+{00}_{0.0e+00}$ | $1.00e+{00}_{0.0e+00}$ |

ta77 | $1.00e+{00}_{0.0e+00}$ | $1.00e+{00}_{0.0e+00}$ | $1.00e+{00}_{0.0e+00}$ |

**Table 6.**GD+ median and interquartile range. Dark and light grey background cells highlight the best and second best results, respectively.

SMSEMOA | NSGAII | MOEAD | |
---|---|---|---|

la10 | $1.78e-{01}_{1.3e-01}$ | $9.89e-{02}_{6.1e-02}$ | $5.54e-{01}_{1.4e-01}$ |

ft06 | $1.03e-{01}_{2.3e-02}$ | $7.72e-{02}_{2.7e-02}$ | $6.89e-{01}_{5.0e-01}$ |

orb01 | $2.90e-{01}_{2.2e-01}$ | $1.56e-{01}_{6.2e-02}$ | $8.27e-{01}_{4.1e-01}$ |

swv20 | $4.97e-{01}_{2.6e-01}$ | $2.78e-{01}_{3.1e-01}$ | $4.44e-{01}_{7.6e-01}$ |

ta12 | $6.01e-{02}_{3.5e-02}$ | $3.45e-{02}_{2.4e-02}$ | $2.08e-{01}_{1.4e-01}$ |

dmu11 | $2.82e-{01}_{1.1e-01}$ | $1.02e-{01}_{1.2e-01}$ | $3.01e-{01}_{2.5e-01}$ |

yn03 | $2.71e-{01}_{3.2e-01}$ | $6.61e-{02}_{1.3e-01}$ | $5.54e-{01}_{3.2e-01}$ |

dmu40 | $9.11e+{00}_{7.1e+00}$ | $5.34e+{00}_{3.5e+00}$ | $6.47e+{00}_{8.5e+00}$ |

ta77 | $2.68e+{01}_{9.3e+00}$ | $2.27e+{01}_{7.8e+00}$ | $1.58e+{00}_{1.8e+00}$ |

NSGAII | MOEAD | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

SMSEMOA | ▽ | – | ▽ | ▽ | – | ▽ | ▽ | ▽ | – | ▲ | ▲ | ▲ | – | ▲ | – | ▲ | – | ▽ |

NSGAII | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | – | ▽ |

NSGAII | MOEAD | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

SMSEMOA | ▽ | ▽ | ▽ | ▽ | ▽ | ▽ | ▽ | – | – | ▲ | ▲ | ▲ | – | ▲ | – | ▲ | – | – |

NSGAII | ▲ | ▲ | ▲ | – | ▲ | ▲ | ▲ | – | – |

NSGAII | MOEAD | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

SMSEMOA | ▽ | ▽ | ▽ | ▽ | – | ▽ | ▽ | ▽ | – | ▲ | ▲ | ▲ | – | ▲ | – | ▲ | – | ▽ |

NSGAII | ▲ | ▲ | ▲ | – | ▲ | ▲ | ▲ | – | ▽ |

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Para, J.; Del Ser, J.; Nebro, A.J.
Energy-Aware Multi-Objective Job Shop Scheduling Optimization with Metaheuristics in Manufacturing Industries: A Critical Survey, Results, and Perspectives. *Appl. Sci.* **2022**, *12*, 1491.
https://doi.org/10.3390/app12031491

**AMA Style**

Para J, Del Ser J, Nebro AJ.
Energy-Aware Multi-Objective Job Shop Scheduling Optimization with Metaheuristics in Manufacturing Industries: A Critical Survey, Results, and Perspectives. *Applied Sciences*. 2022; 12(3):1491.
https://doi.org/10.3390/app12031491

**Chicago/Turabian Style**

Para, Jesus, Javier Del Ser, and Antonio J. Nebro.
2022. "Energy-Aware Multi-Objective Job Shop Scheduling Optimization with Metaheuristics in Manufacturing Industries: A Critical Survey, Results, and Perspectives" *Applied Sciences* 12, no. 3: 1491.
https://doi.org/10.3390/app12031491