Mathematics

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46 pages, 62628 KB

Open AccessArticle

A Multi-Strategy and Business Analysis Strategy-Enhanced Most Valuable Player Algorithm for Global Optimization and Corporate Bankruptcy Prediction

by Zheming Zhang and Hui Zhang

Mathematics 2026, 14(16), 2863; https://doi.org/10.3390/math14162863 - 7 Aug 2026

Viewed by 339

Abstract

The Most Valuable Player Algorithm (MVPA) is a recently developed metaheuristic optimizer with a simple competition-based framework; however, its search capability is limited by insufficient information interaction and weak diversity maintenance. To address these issues, this study proposes a Multi-Strategy Enhanced Most Valuable [...] Read more.

The Most Valuable Player Algorithm (MVPA) is a recently developed metaheuristic optimizer with a simple competition-based framework; however, its search capability is limited by insufficient information interaction and weak diversity maintenance. To address these issues, this study proposes a Multi-Strategy Enhanced Most Valuable Player Algorithm (MSEMVPA). Three complementary strategies are developed: an Adaptive Historical Differential Competition Strategy (AHDCS) that introduces historical search information and adaptive differential guidance to enhance exploration, an Adaptive Multi-Elite Reorganization Strategy (AMERS) that integrates diverse elite information to improve exploitation, and a Business Analysis Strategy (BAS) that reconstructs inferior individuals to maintain population diversity. The proposed MSEMVPA is evaluated on the CEC2017 benchmark suite through comparative experiments, ablation studies, convergence analysis, statistical tests, and computational complexity analysis. Furthermore, MSEMVPA is employed to optimize a multilayer perceptron model for enterprise bankruptcy prediction. Experimental results demonstrate that MSEMVPA achieves improved optimization accuracy and robustness compared with the original MVPA and several competitive algorithms. The results indicate that the proposed multi-strategy framework provides an effective approach for enhancing MVPA and solving complex optimization problems. Full article

(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)

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33 pages, 382 KB

Open AccessArticle

DBLS-SP: A Dynamic Balanced Local Search with Solution Pool for the Vehicle Routing Problem with Simultaneous Pickup and Delivery and Time Windows

by Meng Wang

Mathematics 2026, 14(15), 2781; https://doi.org/10.3390/math14152781 - 4 Aug 2026

Viewed by 332

Abstract

This paper studies the Vehicle Routing Problem with Simultaneous Pickup and Delivery and Time Windows (VRPSPDTW). The problem arises from reverse logistics, last-mile distribution, and circular logistics, where vehicles must serve delivery and pickup demands while respecting vehicle capacity and customer time-window constraints. [...] Read more.

This paper studies the Vehicle Routing Problem with Simultaneous Pickup and Delivery and Time Windows (VRPSPDTW). The problem arises from reverse logistics, last-mile distribution, and circular logistics, where vehicles must serve delivery and pickup demands while respecting vehicle capacity and customer time-window constraints. This work develops DBLS-SP. The method combines an improved insertion-based initialization procedure, a repair-oriented dynamic scoring strategy, ejection-based reinsertion, multi-armed-bandit control of the route-inheritance ratio, vehicle-layer archive-guided route descent, and quality-first nearest-neighbor pool replacement. Computational experiments on the Wang–Chen (WC) and JD Logistics (JD) benchmark instances show that DBLS-SP obtains the best algorithmic solution on 67 of 68 WC instances and the best or tied-best objective value on 16 of 20 JD instances. The ablation study confirms the contribution of the main components, and the proposed reduction strategy removes more infeasible paths than the original reduction rule while preserving feasibility. Full article

(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)

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43 pages, 25846 KB

Open AccessArticle

An Economic Investment Strategy: Enhanced Golden Sine Optimization Algorithm for Global Optimization and Practical Engineering Applications

by Zheming Zhang and Hui Zhang

Mathematics 2026, 14(13), 2445; https://doi.org/10.3390/math14132445 - 7 Jul 2026

Viewed by 263

Abstract

Cloud task scheduling is a critical optimization problem in cloud computing environments, aiming to allocate computational tasks to appropriate virtual machines while reducing execution time, balancing resource load, and minimizing scheduling cost. However, due to the high dimensionality, nonlinear characteristics, and complex constraints [...] Read more.

Cloud task scheduling is a critical optimization problem in cloud computing environments, aiming to allocate computational tasks to appropriate virtual machines while reducing execution time, balancing resource load, and minimizing scheduling cost. However, due to the high dimensionality, nonlinear characteristics, and complex constraints of cloud scheduling scenarios, traditional optimization methods often struggle to obtain high-quality solutions efficiently. To address these challenges, this paper proposes a Multi-strategy Improved Golden Sine Optimization Algorithm (MIGoldSA) for global optimization and cloud task scheduling problems. First, an adaptive chaotic opposition initialization strategy is incorporated to improve the distribution quality and diversity of the initial population. Second, a dynamic elite-guided sine evolution strategy is designed to reduce the dependence on a single best individual and improve the coordination between global exploration and local exploitation. Third, an Economic Investment Strategy is introduced to adaptively allocate search efforts according to the optimization potential of individuals. To verify the effectiveness of MIGoldSA, extensive experiments are conducted on the IEEE CEC2017 and CEC2022 benchmark suites and compared with nine advanced optimization algorithms. The results show that MIGoldSA obtains the best or tied-best mean fitness values on 60 out of 84 benchmark cases, accounting for 71.43% of all test cases. In the Wilcoxon signed-rank test, MIGoldSA achieves 662 wins, 57 ties, and 37 losses among 756 pairwise comparisons, corresponding to an overall win rate of 87.57% and a non-inferiority rate of 95.11%. In addition, the Friedman mean ranks of MIGoldSA are 1.47, 2.00, 3.98, and 4.17 under the four benchmark settings, which are reduced by 85.26%, 79.94%, 45.25%, and 42.32%, respectively, compared with the original GoldSA. Furthermore, the proposed algorithm is applied to cloud task scheduling problems under different task scales. The experimental results show that MIGoldSA maintains competitive time-cost performance and achieves clear reductions in load cost, price cost, and comprehensive scheduling cost. Compared with the original GoldSA, the normalized comprehensive scheduling cost is reduced by approximately 9–14% in small-scale scenarios and approximately 18–21% in large-scale scenarios. Meanwhile, the normalized load cost and price cost are reduced by about 18–25% and 10–18%, respectively, and the time cost shows an approximately 8–12% reduction in large-scale scheduling scenarios. These quantitative results demonstrate that MIGoldSA can improve the optimization accuracy, statistical robustness, and overall scheduling cost efficiency of the original GoldSA on most tested problems. Full article

(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)

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57 pages, 9900 KB

Open AccessArticle

Quantum Computing and Adaptive Mechanism-Based Bounty Hunter Optimizer for Numerical Optimization and Bankruptcy Prediction

by Haoyuan He and Mingyang Yu

Mathematics 2026, 14(13), 2362; https://doi.org/10.3390/math14132362 - 2 Jul 2026

Viewed by 324

Abstract

To improve the optimization performance of the original Bounty Hunter Optimizer (BHO) in complex search environments, this paper proposes a quantum computing and adaptive mechanism-based BHO, named QCAMBHO. The proposed algorithm integrates three complementary strategies: quantum-computing-enhanced initialization, adaptive Lévy flight, and an adaptive [...] Read more.

To improve the optimization performance of the original Bounty Hunter Optimizer (BHO) in complex search environments, this paper proposes a quantum computing and adaptive mechanism-based BHO, named QCAMBHO. The proposed algorithm integrates three complementary strategies: quantum-computing-enhanced initialization, adaptive Lévy flight, and an adaptive differential operator. These mechanisms are designed to improve population diversity, strengthen global exploration, and enhance later-stage exploitation. The performance of QCAMBHO is evaluated on the CEC2017 and CEC2022 benchmark test suites. Experimental results show that QCAMBHO achieves competitive or superior optimization performance compared with several advanced algorithms in terms of convergence accuracy, stability, and robustness. Ablation experiments further confirm the positive contribution of each strategy and the synergistic effect of their integration. To examine its practical applicability, QCAMBHO is further used to optimize the key parameters of Kernel Extreme Learning Machine (KELM), and a QCAMBHO-KELM model is constructed for enterprise bankruptcy prediction. The results show that QCAMBHO-KELM achieves better overall classification performance than BHO-KELM and other comparison models across multiple evaluation metrics, including accuracy, Matthews correlation coefficient, sensitivity, specificity, precision, recall, and F1-score. These findings indicate that QCAMBHO not only provides an effective optimizer for complex numerical problems but also offers a promising decision-support tool for improving the accuracy and reliability of enterprise bankruptcy early warning. Full article

(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)

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64 pages, 137860 KB

Open AccessArticle

An Artistic Image Segmentation Method Using an Art-Design-Inspiration-Driven Ivy Algorithm

by Xiaoning Wang, Fan Liu, Xianmeng Zhao and Hui Zhang

Mathematics 2026, 14(9), 1546; https://doi.org/10.3390/math14091546 - 2 May 2026

Cited by 1 | Viewed by 435

Abstract

To overcome the limitations of the original Ivy Algorithm (IVYA), including insufficient population diversity, limited step-size adaptability, and premature convergence, this paper proposes a multi-strategy enhanced Ivy optimization algorithm (MEIVYA). The proposed method integrates chaotic population initialization, adaptive growth-rate regulation, and an elite-guided [...] Read more.

To overcome the limitations of the original Ivy Algorithm (IVYA), including insufficient population diversity, limited step-size adaptability, and premature convergence, this paper proposes a multi-strategy enhanced Ivy optimization algorithm (MEIVYA). The proposed method integrates chaotic population initialization, adaptive growth-rate regulation, and an elite-guided cooperative search strategy to improve global exploration, local exploitation, and convergence stability. Experimental results on the CEC2014 and CEC2017 benchmark suites show that MEIVYA achieves competitive convergence accuracy, robustness, and stability compared with several state-of-the-art metaheuristic algorithms. In addition, MEIVYA is applied to multi-threshold image segmentation based on the Otsu criterion, where it produces clearer segmentation structures and better visual quality. The results demonstrate that MEIVYA is an effective and robust approach for both numerical optimization and artistic image segmentation. Full article

(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)

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18 pages, 2046 KB

Open AccessFeature PaperArticle

Genetic Programming with Adaptive Population Restructuring for Dynamic Flexible Job Shop Scheduling

by Masayuki Urabe, Tomohiro Hayashida and Shinya Sekizaki

Mathematics 2026, 14(6), 1000; https://doi.org/10.3390/math14061000 - 16 Mar 2026

Viewed by 522

Abstract

In the dynamic flexible job shop scheduling problem (DFJSP) where the environment changes irregularly, priority rules are used to calculate priorities for each job and machine, determining the processing order. To achieve efficient scheduling, it is necessary to select appropriate priority rules that [...] Read more.

In the dynamic flexible job shop scheduling problem (DFJSP) where the environment changes irregularly, priority rules are used to calculate priorities for each job and machine, determining the processing order. To achieve efficient scheduling, it is necessary to select appropriate priority rules that match the problem’s characteristics whenever the environment changes. To address such problems, Genetic Programming (GP) has been proposed to derive mathematically expressed priority rules. Various GP-based methods exist, among which Population-based Fluctuation GP (PF-GP) is an efficient technique that reuses individuals adapted to problem characteristics. However, optimizing the DFJSP using PF-GP requires significant computational cost. Therefore, methods have been developed to adaptively change the population size for more efficient resource utilization. This paper modifies the adaptive population size change into a population growth method designed to balance scheduling performance and computational efficiency in the DFJSP. By applying this proposed method to various scheduling problems, this paper investigates its effectiveness. Furthermore, this paper compares population growth methods and demonstrates that the proposed method addresses conventional issues in existing population adjustment techniques, enabling the more efficient utilization of computational resources. Full article

(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)

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28 pages, 567 KB

Open AccessFeature PaperArticle

A Simulated Annealing and Variable Neighborhood Search Hybrid for Sequencing Interrelated Activities

by Gintaras Palubeckis, Alfonsas Misevičius and Zvi Drezner

Mathematics 2026, 14(2), 282; https://doi.org/10.3390/math14020282 - 12 Jan 2026

Viewed by 751

Abstract

Determining an appropriate sequence of interrelated activities is one of the keys to developing a complex product. One of the approaches used to sequence activities consists of solving the feedback length minimization problem (FLMP). Several metaheuristic algorithms for this problem have been reported [...] Read more.

Determining an appropriate sequence of interrelated activities is one of the keys to developing a complex product. One of the approaches used to sequence activities consists of solving the feedback length minimization problem (FLMP). Several metaheuristic algorithms for this problem have been reported in the literature. However, they suffer from high computational costs when dealing with large-scale problem instances. To address this research gap, we propose a fast hybrid heuristic for the FLMP, which integrates the simulated annealing (SA) technique with the variable neighborhood search (VNS) method. The local search component of VNS relies on a fast insertion neighborhood exploration procedure performing only

O (1)

operations per move. Using rigorous statistical tests, we show that the SA-VNS hybrid is superior to both SA and VNS applied individually. We experimentally compare SA-VNS against the insertion-based simulated annealing (ISA) heuristic, which is the state-of-the-art algorithm for the FLMP. The results demonstrate the clear superiority of SA-VNS over ISA. The SA-VNS hybrid technique produces equally good or better results across all tested problem instances. In particular, SA-VNS is able to find better solutions than ISA on all instances of size 150 or more. Moreover, SA-VNS requires two orders of magnitude less CPU time than the ISA algorithm. Thus, SA-VNS achieves excellent performance regarding solution quality and running time. Full article

(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)

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7 pages, 290 KB

Open AccessFeature PaperArticle

Determining the Best Algorithm for the Knapsack Problem with Forfeits

by Peter Cadiz, Yun Lu, Myung Soon Song and Francis J. Vasko

Mathematics 2026, 14(1), 143; https://doi.org/10.3390/math14010143 - 30 Dec 2025

Cited by 1 | Viewed by 1013

Abstract

In 2024, four papers that presented four different solution approaches for the knapsack problem with forfeits (KPF) appeared in the OR literature. However, none of these four solution approaches compared their performance to the other three on a standard set of 120 KPF [...] Read more.

In 2024, four papers that presented four different solution approaches for the knapsack problem with forfeits (KPF) appeared in the OR literature. However, none of these four solution approaches compared their performance to the other three on a standard set of 120 KPF test instances. In this short paper, both empirically and statistically, these four KPF solution approaches are compared. Furthermore, by using the solutions from the best method (HESM) among the four to initialize Gurobi, bounded solutions are obtained. For the 120 KPF test instances, this simple hybrid approach resulted in solutions that, on average, were guaranteed to be within 7% of the optimums. This type of guarantee does not exist for other KPF solution methods in the literature. It is very important for operations research (OR) practitioners that need to ensure the value of their solutions to management to have some guarantee of the quality of these solutions. Full article

(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)

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39 pages, 7243 KB

Open AccessArticle

Binary Chaotic White Shark Optimizer for the Unicost Set Covering Problem

by Pablo Zúñiga-Valenzuela, Broderick Crawford, Felipe Cisternas-Caneo, Eduardo Rodriguez-Tello, Ricardo Soto, José Barrera-Garcia and Fernando Lepe-Silva

Mathematics 2025, 13(13), 2175; https://doi.org/10.3390/math13132175 - 3 Jul 2025

Cited by 1 | Viewed by 1507

Abstract

The Unicost Set Covering Problem (USCP), an NP-hard combinatorial optimization challenge, demands efficient methods to minimize the number of sets covering a universe. This study introduces a binary White Shark Optimizer (WSO) enhanced with V3 transfer functions, elitist binarization, and chaotic maps. To [...] Read more.

The Unicost Set Covering Problem (USCP), an NP-hard combinatorial optimization challenge, demands efficient methods to minimize the number of sets covering a universe. This study introduces a binary White Shark Optimizer (WSO) enhanced with V3 transfer functions, elitist binarization, and chaotic maps. To evaluate algorithm performance, we employ the Relative Percentage Deviation (RPD), which measures the percentage difference between the obtained solutions and optimal values. Our approach achieves outstanding results on six benchmark instances: WSO-ELIT_CIRCLE delivers an RPD of 0.7% for structured instances, while WSO-ELIT_SINU attains an RPD of 0.96% in cyclic instances, showing empirical improvements over standard methods. Experimental results demonstrate that circle chaotic maps excel in structured problems, while sinusoidal maps perform optimally in cyclic instances, with observed improvements up to 7.31% over baseline approaches. Diversity and convergence analyses show structured instances favor exploitation-driven strategies, whereas cyclic instances benefit from adaptive exploration. This work establishes WSO as a robust metaheuristic for USCP, with applications in resource allocation and network design. Full article

(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)

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21 pages, 4080 KB

Open AccessFeature PaperArticle

M-Learning: Heuristic Approach for Delayed Rewards in Reinforcement Learning

by Cesar Andrey Perdomo Charry, Marlon Sneider Mora Cortes and Oscar J. Perdomo

Mathematics 2025, 13(13), 2108; https://doi.org/10.3390/math13132108 - 27 Jun 2025

Viewed by 1716

Abstract

The current design of reinforcement learning methods requires extensive computational resources. Algorithms such as Deep Q-Network (DQN) have obtained outstanding results in advancing the field. However, the need to tune thousands of parameters and run millions of training episodes remains a significant challenge. [...] Read more.

The current design of reinforcement learning methods requires extensive computational resources. Algorithms such as Deep Q-Network (DQN) have obtained outstanding results in advancing the field. However, the need to tune thousands of parameters and run millions of training episodes remains a significant challenge. This document proposes a comparative analysis between the Q-Learning algorithm, which laid the foundations for Deep Q-Learning, and our proposed method, termed M-Learning. The comparison is conducted using Markov Decision Processes with the delayed reward as a general test bench framework. Firstly, this document provides a full description of the main challenges related to implementing Q-Learning, particularly concerning its multiple parameters. Then, the foundations of our proposed heuristic are presented, including its formulation, and the algorithm is described in detail. The methodology used to compare both algorithms involved training them in the Frozen Lake environment. The experimental results, along with an analysis of the best solutions, demonstrate that our proposal requires fewer episodes and exhibits reduced variability in the outcomes. Specifically, M-Learning trains agents 30.7% faster in the deterministic environment and 61.66% faster in the stochastic environment. Additionally, it achieves greater consistency, reducing the standard deviation of scores by 58.37% and 49.75% in the deterministic and stochastic settings, respectively. The code will be made available in a GitHub repository upon this paper’s publication. Full article

(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)

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29 pages, 4179 KB

Open AccessArticle

Solving the Economic Load Dispatch Problem by Attaining and Refining Knowledge-Based Optimization

by Pravesh Kumar and Musrrat Ali

Mathematics 2025, 13(7), 1042; https://doi.org/10.3390/math13071042 - 23 Mar 2025

Cited by 8 | Viewed by 1660

Abstract

The Static Economic Load Dispatch (SELD) problem is a paramount optimization challenge in power engineering that seeks to optimize the allocation of power between generating units to meet imposed constraints while minimizing energy requirements. Recently, researchers have employed numerous meta-heuristic approaches to tackle [...] Read more.

The Static Economic Load Dispatch (SELD) problem is a paramount optimization challenge in power engineering that seeks to optimize the allocation of power between generating units to meet imposed constraints while minimizing energy requirements. Recently, researchers have employed numerous meta-heuristic approaches to tackle this challenging, non-convex problem. This work introduces an innovative meta-heuristic algorithm, named “Attaining and Refining Knowledge-based Optimization (ARKO)”, which uses the ability of humans to learn from their surroundings by leveraging the collective knowledge of a population. The ARKO algorithm consists of two distinct phases: attaining and refining. In the attaining phase, the algorithm gathers knowledge from the population’s top candidates, while the refining phase enhances performance by leveraging the knowledge of other selected candidates. This innovative way of learning and improving with the help of top candidates provides a robust exploration and exploitation capability for this algorithm. To validate the efficacy of ARKO, we conduct a comprehensive evaluation against eleven other established meta-heuristic algorithms using a diverse set of 41 test functions of the CEC-2017 and CEC-2022 test suites, and then, three real-life applications also verify its practical ability. Subsequently, we implement ARKO to optimize the SELD problem considering several instances. The examination of the numerical and statistical results confirms the remarkable efficiency and potential practical ability of ARKO in complex optimization tasks. Full article

(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)

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30 pages, 2330 KB

Open AccessArticle

A New Hybrid Improved Kepler Optimization Algorithm Based on Multi-Strategy Fusion and Its Applications

by Zhenghong Qian, Yaming Zhang, Dongqi Pu, Gaoyuan Xie, Die Pu and Mingjun Ye

Mathematics 2025, 13(3), 405; https://doi.org/10.3390/math13030405 - 26 Jan 2025

Cited by 3 | Viewed by 3440

Abstract

The Kepler optimization algorithm (KOA) is a metaheuristic algorithm based on Kepler’s laws of planetary motion and has demonstrated outstanding performance in multiple test sets and for various optimization issues. However, the KOA is hampered by the limitations of insufficient convergence accuracy, weak [...] Read more.

The Kepler optimization algorithm (KOA) is a metaheuristic algorithm based on Kepler’s laws of planetary motion and has demonstrated outstanding performance in multiple test sets and for various optimization issues. However, the KOA is hampered by the limitations of insufficient convergence accuracy, weak global search ability, and slow convergence speed. To address these deficiencies, this paper presents a multi-strategy fusion Kepler optimization algorithm (MKOA). Firstly, the algorithm initializes the population using Good Point Set, enhancing population diversity. Secondly, Dynamic Opposition-Based Learning is applied for population individuals to further improve its global exploration effectiveness. Furthermore, we introduce the Normal Cloud Model to perturb the best solution, improving its convergence rate and accuracy. Finally, a new position-update strategy is introduced to balance local and global search, helping KOA escape local optima. To test the performance of the MKOA, we uses the CEC2017 and CEC2019 test suites for testing. The data indicate that the MKOA has more advantages than other algorithms in terms of practicality and effectiveness. Aiming at the engineering issue, this study selected three classic engineering cases. The results reveal that the MKOA demonstrates strong applicability in engineering practice. Full article

(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)

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13 pages, 1770 KB

Open AccessArticle

Prediction of Carbon Emissions Level in China’s Logistics Industry Based on the PSO-SVR Model

by Liang Chen, Yitong Pan and Dongqing Zhang

Mathematics 2024, 12(13), 1980; https://doi.org/10.3390/math12131980 - 26 Jun 2024

Cited by 16 | Viewed by 2493

Abstract

Adjusting the energy structure of various industries is crucial for achieving China’s carbon peak and carbon neutrality goals. Given the significant proportion of carbon emissions from the logistics industry in the tertiary sector, the research on predicting the carbon emissions of the logistics [...] Read more.

Adjusting the energy structure of various industries is crucial for achieving China’s carbon peak and carbon neutrality goals. Given the significant proportion of carbon emissions from the logistics industry in the tertiary sector, the research on predicting the carbon emissions of the logistics industry is of great significance for China to achieve its “Dual carbon” target. In this paper, the gray relational analysis (GRA) methodology is adopted to screen the influencing factors of carbon emissions in the logistics industry firstly. Then, the particle swarm optimization (PSO) algorithm was used to optimize the penalty coefficientand kernel function range parameter of the support vector regression (SVR) model (i.e. PSO- SVR model). The data from 2000 to 2021 regarding carbon emissions and related influencing factors in China’s logistics industry are analyzed, and the mean absolute percentage error (MAPE) of the PSO-SVR model is 0.82%, which shows that the proposed PSO-SVR model in this paper is effective. Finally, instructive suggestions are provided for China to achieve the “Dual Carbon” goal and upgrading of the logistics industry. Full article

(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)

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21 pages, 1929 KB

Open AccessArticle

An Agile Adaptive Biased-Randomized Discrete-Event Heuristic for the Resource-Constrained Project Scheduling Problem

by Xabier A. Martin, Rosa Herrero, Angel A. Juan and Javier Panadero

Mathematics 2024, 12(12), 1873; https://doi.org/10.3390/math12121873 - 16 Jun 2024

Cited by 3 | Viewed by 2371

Abstract

In industries such as aircraft or train manufacturing, large-scale manufacturing companies often manage several complex projects. Each of these projects includes multiple tasks that share a set of limited resources. Typically, these tasks are also subject to time dependencies among them. One frequent [...] Read more.

In industries such as aircraft or train manufacturing, large-scale manufacturing companies often manage several complex projects. Each of these projects includes multiple tasks that share a set of limited resources. Typically, these tasks are also subject to time dependencies among them. One frequent goal in these scenarios is to minimize the makespan, or total time required to complete all the tasks within the entire project. Decisions revolve around scheduling these tasks, determining the sequence in which they are processed, and allocating shared resources to optimize efficiency while respecting the time dependencies among tasks. This problem is known in the scientific literature as the Resource-Constrained Project Scheduling Problem (RCPSP). Being an NP-hard problem with time dependencies and resource constraints, several optimization algorithms have already been proposed to tackle the RCPSP. In this paper, a novel discrete-event heuristic is introduced and later extended into an agile biased-randomized algorithm complemented with an adaptive capability to tune the parameters of the algorithm. The results underscore the effectiveness of the algorithm in finding competitive solutions for this problem within short computing times. Full article

(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)

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19 pages, 665 KB

Open AccessArticle

A Learnheuristic Algorithm Based on Thompson Sampling for the Heterogeneous and Dynamic Team Orienteering Problem

by Antonio R. Uguina, Juan F. Gomez, Javier Panadero, Anna Martínez-Gavara and Angel A. Juan

Mathematics 2024, 12(11), 1758; https://doi.org/10.3390/math12111758 - 5 Jun 2024

Cited by 3 | Viewed by 2688

Abstract

The team orienteering problem (TOP) is a well-studied optimization challenge in the field of Operations Research, where multiple vehicles aim to maximize the total collected rewards within a given time limit by visiting a subset of nodes in a network. With the goal [...] Read more.

The team orienteering problem (TOP) is a well-studied optimization challenge in the field of Operations Research, where multiple vehicles aim to maximize the total collected rewards within a given time limit by visiting a subset of nodes in a network. With the goal of including dynamic and uncertain conditions inherent in real-world transportation scenarios, we introduce a novel dynamic variant of the TOP that considers real-time changes in environmental conditions affecting reward acquisition at each node. Specifically, we model the dynamic nature of environmental factors—such as traffic congestion, weather conditions, and battery level of each vehicle—to reflect their impact on the probability of obtaining the reward when visiting each type of node in a heterogeneous network. To address this problem, a learnheuristic optimization framework is proposed. It combines a metaheuristic algorithm with Thompson sampling to make informed decisions in dynamic environments. Furthermore, we conduct empirical experiments to assess the impact of varying reward probabilities on resource allocation and route planning within the context of this dynamic TOP, where nodes might offer a different reward behavior depending upon the environmental conditions. Our numerical results indicate that the proposed learnheuristic algorithm outperforms static approaches, achieving up to

25 %

better performance in highly dynamic scenarios. Our findings highlight the effectiveness of our approach in adapting to dynamic conditions and optimizing decision-making processes in transportation systems. Full article

(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)

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