Strength Pareto Evolutionary Algorithm Research Articles

Multi-objective mammography unit location–allocation problem: A case study

This work addresses the Multi-Objective Mammography Unit Location–allocation Problem (MOMULAP), aiming to meet three objectives: maximize mammography screening coverage, minimize the total distance traveled weighted by the number of users, and maximize equity in access to mammography screening. We introduce a mixed-integer nonlinear programming (MINLP) formulation to represent the MOMULAP and algorithms based on the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Strength Pareto Evolutionary Algorithm (SPEA2) for treating it. The algorithms were tested with data from seven Brazilian states. In these states, the number of cities ranges from 139 to 853, equipment from 23 to 347 units, and estimated annual demand for screenings from 96,592 to 1,739,085. The solutions provided by this work allow health managers to choose the appropriate location and allocation of the mammography units, considering different objectives.

Design and analysis of solar hybrid combined cooling, heating and power system: A bi-level optimization model

The planning and operation optimization of hybrid combined cooling, heating and power (CCHP) systems is the prerequisite and foundation for its advantages such as economy, energy saving, and high efficiency. This study constructed a bi-level optimization model of a hybrid CCHP system. Firstly, an upper-level capacity planning model of the hybrid CCHP system is constructed considering system economy, energy, and environmental performance. Secondly, a lower-level operation optimization model is proposed, considering the operation and maintenance cost of the system. Thirdly, a multi-objective honey badger algorithm (MOHBA) is developed based on the characteristics of the studied problem and the features of the bi-level optimization model. Finally, the optimization results indicate that the hybrid CCHP can save 32.79 % of the total cost, 49.74 % of primary energy, and 60.18 % of carbon emissions compared to the separation production (SP) system. In addition, compared with improving the strength Pareto evolutionary algorithm (SPEA2), non-dominated sorting genetic algorithm-II (NSGA-II), multi-objective evolutionary algorithm based on decomposition (MOEAD), and multi-objective particle swarm optimization (MOPSO), the proposed MOHBA can provide superior optimization results. The proposed bi-level planning model achieves improved economic, energy, and environmental performance of the hybrid CCHP system compared to the single-level planning model for the given operation modes.

Stock Optimization of Naturally Curved Wood Logs on Freeform Truss Structures

This paper presents an optimization method for incorporating discarded naturally curved wood logs onto a freeform gridshell with a predefined topology. Though still little explored, the research field of reusing structural elements is experiencing increasing attention owing to its significant potential to reduce the environmental impact of building design. However, several constraints must be considered as the optimal structure depends on stock availability and the corresponding geometry and material properties of that given stock. Therefore, the focus is on determining the best configuration of stock elements considering the defined design objectives and constraints. The proposed method is a top-down approach, as the global topology of the structure is predetermined. Multi- objective optimization is conducted using the Strength Pareto Evolutionary Algorithm 2 (SPEA2) and a modified genetic algorithm with permutation encoding in the form of ordered crossover and scramble mutation. Furthermore, this paper introduces a Team-Based Repair (TBR) algorithm that increases the likelihood of each solution being valid for analysis. The performance of the optimization method is demonstrated on a curved gridshell structure, and the effect of the different design objectives and stock sizes on the final design is analyzed and discussed.

Blind Source Separation with Strength Pareto Evolutionary Algorithm 2 (SPEA2) Using Discrete Wavelet Transform

This paper presents a new method for separating the mixed audio signals of simultaneous speakers using Blind Source Separation (BSS). The separation of mixed signals is an important issue today. In order to obtain more efficient and superior source estimation performance, a new algorithm that solves the BSS problem with Multi-Objective Optimization (MOO) methods was developed in this study. In this direction, we tested the application of two methods. Firstly, the Discrete Wavelet Transform (DWT) was used to eliminate the limited aspects of the traditional methods used in BSS and the small coefficients in the signals. Afterwards, the BSS process was optimized with the multi-purpose Strength Pareto Evolutionary Algorithm 2 (SPEA2). Secondly, the Minkowski distance method was proposed for distance measurement by using density information in the discrimination of individuals with raw fitness values for the concept of Pareto dominance. With this proposed method, the originals (original source signals) were estimated by separating the randomly mixed male and two female speech signals. Simulation and experimental results proved that the efficiency and performance of the proposed method can effectively solve BSS problems. In addition, the Pareto front approximation performance of this method also confirmed that it is superior in the Inverted Generational Distance (IGD) indicator.

Adaptive Test Suits Generation for Self-Adaptive Systems Using SPEA2 Algorithm

Self-adaptive systems are capable of reconfiguring themselves while in use to reduce the risks forced by environments for which they may not have been specifically designed. Runtime validation techniques are required because complex self-adaptive systems must consistently offer acceptable behavior for important services. The runtime testing can offer further confidence that a self-adaptive system will continue to act as intended even when operating in unknowable circumstances. This article introduces an evolutionary framework that supports adaptive testing for self-adaptive systems. The objective is to ensure that the adaptive systems continue to operate following its requirements and that both test plans and test cases continuously stay relevant to shifting operational conditions. The proposed approach using the Strength Pareto Evolutionary Algorithm 2 (SPEA2) algorithm facilitates both the execution and adaptation of runtime testing operations.

Software Product Line Maintenance Using Multi-Objective Optimization Techniques

Currently, software development is more associated with families of configurable software than the single implementation of a product. Due to the numerous possible combinations in a software product line, testing these families of software product lines (SPLs) is a difficult undertaking. Moreover, the presence of optional features makes the testing of SPLs impractical. Several features are presented in SPLs, but due to the environment’s time and financial constraints, these features are rendered unfeasible. Thus, testing subsets of configured products is one approach to solving this issue. To reduce the testing effort and obtain better results, alternative methods for testing SPLs are required, such as the combinatorial interaction testing (CIT) technique. Unfortunately, the CIT method produces unscalable solutions for large SPLs with excessive constraints. The CIT method costs more because of feature combinations. The optimization of the various conflicting testing objectives, such as reducing the cost and configuration number, should also be considered. In this article, we proposed a search-based software engineering solution using multi-objective evolutionary algorithms (MOEAs). In particular, the research was applied to different types of MOEA method: the Indicator-Based Evolutionary Algorithm (IBEA), Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D), Non-dominant Sorting Genetic Algorithm II (NSGAII), NSGAIII, and Strength Pareto Evolutionary Algorithm 2 (SPEA2). The results of the algorithms were examined in the context of distinct objectives and two quality indicators. The results revealed how the feature model attributes, implementation context, and number of objectives affected the performances of the algorithms.

An Improved Strength Pareto Evolutionary Algorithm 2 with Adaptive Crossover Operator for Bi-Objective Distributed Unmanned Aerial Vehicle Delivery

With the development of the e-commerce industry, using UAVs (unmanned aerial vehicles) to deliver goods has become more popular in transportation systems. This delivery method can reduce labor costs and improve the distribution efficiency, and UAVs can reach places that are difficult for humans to reach. Because some goods are perishable, the quality of the delivery will have an impact on the customer satisfaction. At the same time, the delivery time should also meet the needs of customers as much as possible. Therefore, this paper takes the distribution distance and customer satisfaction as the objective functions, establishes a bi-objective dynamic programming model, and proposes an improved SPEA2 (strength Pareto evolutionary algorithm 2). The improved algorithm introduces the local search strategy, on the basis of the original algorithm. It conducts a local search for the better non-dominated solutions obtained in each iteration. The new dominated solutions and non-dominated solutions are determined, and the crossover operator is improved, so that the local search ability is improved, on the basis of ensuring its global search ability. The numerical experiment results show that the improved algorithm achieves an excellent performance in three aspects: the Pareto front, generation distance, and spacing, and would have a high application value in UAV cargo delivery and other MOPs (multi-objective optimization problems). The average spacing value of the improved algorithm is more than 20% smaller than SPEA2 + SDE (strength Pareto evolution algorithm 2–shift-based density estimation), which is the second-best algorithm. In the comparison of the average generation distance value, this number reaches 30%.

A metaheuristic-driven physical asset risk management framework for manufacturing system considering continuity measures

To ensure the uninterrupted operation of physical assets, the effective implementation of risk mitigation plans (RMPs) and business continuity plans (BCPs) for critical assets is required. However, manufacturing decision-makers face the challenge of allocating limited resources between RMPs and BCPs while prioritizing sustained success. To address this challenge, a novel approach proposes integrating a metaheuristic algorithm into a risk management framework that considers interconnected risks. The framework utilizes a Bayesian Network (BN) to model interdependencies among critical physical asset risks. It determines the optimal combination of BCPs and RMPs, considering continuity measures and resource limitations. A physical asset risk assessment process evaluates operational and disruption risks based on expected loss and probabilities within the risk network. Given the complexity, the proposed framework incorporates hybrid multi-objective metaheuristic algorithms (e.g., Nondominated Sorting Genetic Algorithm II (NSGA-II), Strength Pareto Evolutionary Algorithm 2 (SPEA2), Multi-Objective Particle Swarm Optimization (MOPSO), and Pareto Envelope-based Selection Algorithm II (PESA-II)) combined with a reinforcement learning approach. A case study of a manufacturing company demonstrates the framework’s applicability and discusses the results. The findings show a significant reduction in the expected loss within the risk network and migration of most physical asset risks from high-risk to acceptable areas. Additionally, a sensitivity analysis examines the available budget, aiding decision-makers in determining the necessary compromise between asset availability and network risk level. In conclusion, the proposed framework empowers decision-makers to allocate resources effectively, prioritize RMPs and BCPs, and ensure continuity for critical physical assets, thereby fostering sustained success in manufacturing systems.

Development of a Bio-inspired Hybrid Decomposition Algorithm Based on Whale and Differential Evolution Strategies for Multiobjective Optimization

A Multiobjective Optimization Problem (MOP) requires the optimization of several objective functions simultaneously, usually in conflict with each other. One of the most efficient algorithms for solving MOPs is MOEA/D (Multiobjective Evolutionary Algorithm Based on Decomposition), which decomposes a MOP into single-objective optimization subproblems and solves them using information from neighboring subproblems. MOEA/D variants with other evolutionary operators have emerged over the years, improving their efficiency in various MOPs. Recently, the IWOA (Improved Whale Optimization Algorithm) was proposed, an optimization algorithm bioinspired by the whale hunting method hybridized with Differential Evolution, which presented excellent results in single-objective optimization problems. This work proposes the MOEA/D-IWOA algorithm, which associates characteristics of the evolutionary operators of the IWOA to MOEA/D. Computational experiments were accomplished to analyze the performance of the MOEA/D-IWOA in benchmark MOPs suites. The results were compared with those obtained by the MOEA/D, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Third Evolution Step of Generalized Differential Evolution (GDE3), Improving the Strength Pareto Evolutionary Algorithm (SPEA2), and Indicator-Based Evolutionary Algorithm (IBEA) algorithms in the Hypervolume and Inverted Generational Distance Plus (IGD+) indicators. The MOEA/D-IWOA proved to be competitive, with a good performance profile, in addition to presenting the best results in some POMs.

A novel Physarum-inspired competition algorithm for discrete multi-objective optimisation problems

Many real-world problems can be naturally formulated as discrete multi-objective optimisation (DMOO) problems. We have proposed a novel Physarum-inspired competition algorithm (PCA) to tackle these DMOO problems. Our algorithm is based on hexagonal cellular automata (CA) as a representation of problem search space and reaction–diffusion systems that control the Physarum motility. Physarum’s decision-making power and the discrete properties of CA have made our algorithm a perfectly suitable approach to solve DMOO problems. Each cell in the CA grid will be decoded as a solution (objective function) and will be regarded as a food resource to attract Physarum. The n-dimensional generalisation of the hexagonal CA grid has allowed us to extend the solving capabilities of our PCA from only 2-D to n-D optimisation problems. We have implemented a novel restart procedure to select the global Pareto frontier based on both personal experience and shared information. Extensive experimental and statistical analyses were conducted on several benchmark functions to assess the performance of our PCA against other evolutionary algorithms. As far as we know, this study is the first attempt to assess algorithms that solve DMOO problems, with a large number of benchmark functions and performance indicators. Our PCA has confirmed our assumption that individual skills of competing Physarum are more efficient in exploration and increase the diversity of the solutions. It has achieved the best performance for the Spread indicator (diversity), similar performance results compared to the strength Pareto evolutionary algorithm (SPEA2) and even outperformed other well-established genetic algorithms.

SPEA2 based on grid density search and elite guidance for multi-objective operation optimization of wastewater treatment process

It is challenging to introduce an optimization method to improve the operation performance of wastewater treatment process (WWTP) on account of its high energy consumption and poor water quality characteristics. In this paper, an improved Strength Pareto Evolutionary Algorithm 2 (SPEA2) based on grid density search and elite guidance (GDSEG-SPEA2) is proposed for multi-objective operation optimization of WWTP. First, the external archive is divided by an improved adaptive grid method to determine the distribution density of the solutions, and a neighborhood circle strategy as well as a mixed perturbation strategy are designed to search the neighborhood of sparse and crowded solutions, resulting in a more uniformly distributed Pareto front. Then, in order to avoid SPEA2 falling into local optimum after adding the neighborhood search strategies, the crossover and mutation operations based on individual information are proposed to generate new individuals. Finally, an elite guidance strategy, in which the poor-performing individuals of the population learn from the best-performing individuals to update their positions, is introduced into the algorithm to improve convergence. The test function verification shows that the proposed algorithm can obtain the Pareto front with better distribution and convergence than other existing algorithms. The operation optimization control experiment of WWTP shows that the proposed algorithm can better purify water quality and reduce more energy consumption on the premise of ensuring that effluent quality meets the discharge standards, which is better than other optimization algorithms in comparison.

A multi-objective Chaos Game Optimization algorithm based on decomposition and random learning mechanisms for numerical optimization

Chaos Game Optimization (CGO) is a heuristic optimization approach that estimates global optima for optimization problems using operators based on chaos theory. This paper first proposes a multi-objective variant of this recent algorithm using decomposition. The proposed algorithm is called Multi-Objective CGO based on Decomposition (MOCGO/D), in which the decomposition step employs a Normalized Boundary Intersection (NBI) technique for decomposing the multi-objective problem into single-objective sub-problems. A novel Random Learning (RL) strategy based on the combination of multiple strategies such as Opposition-based learning, Levy flight operator, Orthogonal learning, and the tangent flight operator, is incorporated in the MOCGO/D to propose an enhanced version called MOCGO/DR algorithm. The RL strategy aims to improve the balance between exploitation and exploration of the conventional CGO, leading to better convergence behavior and avoiding getting trapped in local optima. The first set of experimental results demonstrates that MOCGO/DR can perform better than three other variants of MOCGO, namely archive-based MOCGO (MOCGO/A), crowding-distance based MOCGO (MOCGO/CD) and decomposition-based MOCGO (MOCGO/D) on 62% of test cases. A second set of experiments and evaluation shows that the proposed approach provides better results than well-regarded algorithms, including strength pareto evolutionary algorithm (SPEA2), multiobjective evolutionary algorithm based on decomposition (MOEA/D), multi-objective particle swarm optimization algorithm based on decomposition (MPSO/D), multistage evolutionary algorithm (MSEA), and a fast and elitist multi- objective genetic algorithm (NSGAII) when using performance measures such as GD, IGD, HV, Spacing, Spread, and Hausdorff distance on 65% test cases. This two-stage evaluation was conducted on three different benchmark test sets: the Deb–Thiele–Laumanns–Zitzler (DTLZ) test suite, the Zitzler–Deb–Thiele (ZDT) test suite, and the bias test suite (BT). Overall, the Friedman test results for all performance measures show that MOCGO/DR is demonstrated to be a competitive candidate as a multi-objective optimization algorithm in this space.

Multi-objective optimization of school building envelope for two distinct geometric designs in southern Brazil

The standard Brazilian school projects (EMEIs) were created for the Proinfância [Pro-Childhood] program to respond to the growing national demand for public schools. Unfortunately, the project disregards the Brazilian local climate, leading to an inadequate architectural design, especially in terms of energy performance. Within this context, this research aimed to assess the impact of a new geometric design and envelope proposal on the energy performance of a Brazilian school building. The study object is a standard project (EMEI) of the Proinfância program located in Pelotas, Brazil. Two distinct multi-objective optimizations were performed based on EnergyPlus coupled with the Strength Pareto Evolutionary Algorithm 2 (SPEA2), in which the objective functions were defined to minimize heating and cooling Energy Use Intensity (EUI) for different geometric designs (Base and Linear models). The design variables considered were window-to-wall ratio (WWR); thermal insulation thickness for walls and floor; solar absorptance values for walls and roof; and solar orientation. A total of 74.520 simulations were carried out, and the results indicated that the new geometric design combined with bioclimatic envelope strategies was capable of reducing 52% of the Energy Use Intensity when compared to the standard school project.

Integrating sustainability into production scheduling in hybrid flow-shop environments.

Global energy consumption is projected to grow by nearly 50% as of 2018, reaching a peak of 910.7 quadrillion BTU in 2050. The industrial sector accounts for the largest share of the energy consumed, making energy awareness on the shop floors imperative for promoting industrial sustainable development. Considering a growing awareness of the importance of sustainability, production planning and control require the incorporation of time-of-use electricity pricing models into scheduling problems for well-informed energy-saving decisions. Besides, modern manufacturing emphasizes the role of human factorsin production processes. This study proposes a new approach for optimizing the hybrid flow-shop scheduling problems (HFSP) considering time-of-use electricity pricing, workers' flexibility, and sequence-dependent setup time (SDST). Novelties of this study are twofold: to extend a new mathematical formulation and to develop an improved multi-objective optimization algorithm. Extensive numerical experiments are conducted to evaluate the performance of the developed solution method, the adjusted multi-objective genetic algorithm (AMOGA), comparing it with the state-of-the-art, i.e., strength Pareto evolutionary algorithm (SPEA2), and Pareto envelop-based selection algorithm (PESA2). It is shown that AMOGA performs better than the benchmarks considering the mean ideal distance, inverted generational distance, diversification, and quality metrics, providing more versatile and better solutions for production and energy efficiency.

Prediction and optimization of sustainable fuel cells behavior using artificial intelligence algorithms

The model and optimization of parameters have been performed using a computer intelligence approach in order to provide greater convenience and reduce costs. In this study, the power density and voltage behavior of 13 direct glucose fuel cells (three types: MEA1-MEA4, MEA5-MEA8, and MEA10-MEA14) are modeled through response surface methodology, multi-layer perceptron (MLP), and machine learning (ML). First, the regression coefficients (R2) of the power density RSM model for MEA1-MEA4, MEA5-MEA8, and MEA10-MEA14 are calculated to be 0.99839, 0.99529, and 0.95316, respectively. After that, the best MLP-ANN structure for predicting power density and the voltage of fuel cells is selected with two hidden layers, which have 5, 5 neurons in each hidden layer for MEA1-MEA4, 3, 5 neurons for MEA5-MEA8, and 5, 5 neurons for MEA10-MEA14. Next, multi-objective optimization for power density and the voltage of the fuel cells is performed using three different algorithms: RSM, non-dominated sorting genetic algorithm version 2 (NSGA-II), and the Strength Pareto Evolutionary Algorithm 2 (SPEA2). Finally, the best optimum mode of each type of direct glucose fuel cell is investigated by RSM.

Performance of Six Metaheuristic Algorithms for Multi-Objective Optimization of Nonlinear Inelastic Steel Trusses

This paper presents a multi-objective optimization of steel trusses using direct analysis. The total weight and the inter-story drift or displacements of the structure were two conflict objectives, while the constraints relating to strength and serviceability load combinations were evaluated using nonlinear inelastic and nonlinear elastic analyses, respectively. Six common metaheuristic algorithms such as nondominated sorting genetic algorithm-II (NSGA-II), NSGA-III, generalized differential evolution (GDE3), PSO-based MOO using crowding, mutation, and ε-dominance (OMOPSO), improving the strength Pareto evolutionary algorithm (SPEA2), and multi-objective evolutionary algorithm based on decomposition (MOEA/D) were applied to solve the developed MOO problem. Four truss structures were studied including a planar 10-bar truss, a spatial 72-bar truss, a planar 47-bar powerline truss, and a planar 113-bar truss bridge. The numerical results showed a nonlinear relationship and inverse proportion between the two objectives. Furthermore, all six algorithms were efficient at finding feasible optimal solutions. No algorithm outperformed the others, but NSGA-II and MOEA/D seemed to be better at both searching Pareto and anchor points. MOEA/D was also more stable and yields a better solution spread. OMOPSO was also good at solution spread, but its stability was worse than MOEA/D. NSGA-III was less efficient at finding anchor points, although it can effectively search for Pareto points.

Solving a multiobjective professional timetabling problem using evolutionary algorithms at Mandarine Academy

AbstractIn this paper, we propose a method for solving a real‐world timetabling problem at Mandarine Academy. The primary motivation for this work is to provide an automated professional course scheduling tool to replace the time‐consuming task of manually creating timetables that are constantly incorrect. Following a review of both scientific literature and company requirements, a mathematical model of the problem is provided, which includes 18 constraints (hard/soft) and five objectives, two of which are competing. We test a handful of multi‐objective evolutionary algorithms (MOEA's) starting with the non‐dominated sorting genetic algorithm (NSGA II and NSGA III), the multi‐objective evolutionary algorithm based on decomposition (MOEA/D), the indicator‐based evolutionary algorithm and finally the strength Pareto evolutionary algorithm . Two custom genetic operators (mutation and crossover) are proposed and compared to conventional operators (PMX and swap mutation). To obtain elite configurations, a tuning phase involving all of the aforementioned algorithms is carried out. Experiments were divided by problem size, with three to five objectives tested. Experiments include the use of real‐world data from the company's catalog. This dataset was made available to the scientific community to serve as a testing ground for professional course scheduling, an underexploited field of scheduling. We discuss findings, including a comparison of each algorithm's performance using various metrics, as well as convergence graphs and population evolution.

A strength pareto evolutionary algorithm based on adaptive reference points for solving irregular fronts

Evolutionary algorithms have proven to be extremely effective at tackling multi-objective optimization problems (MOPs). However, when dealing with many-objective optimization problems (MaOPs), their performance frequently degrades, especially when the Pareto marking irregular shapes. The population pressure to choose the Pareto optimal front and address the generalizability of different Pareto front shapes becomes more challenging as the number of objectives increases. We present a strength Pareto evolutionary algorithm based on adaptive reference points (SPEA/ARP) to address this problem. First, the reference points are updated using current and historical population information. The angles between the current demographic information and the predefined uniform reference points are used to select the active reference points, and the adaptive reference points are selected from the historical population information projected onto the reference plane. Second, the fitness function values are applied to classify the environmental selection criteria into two categories: 1) The angle distance scaling function using adaptive reference points is utilized to increase selection pressure, and the diversity of non-dominated solutions is balanced using the angle-based secondary selection technique. 2) Otherwise, the fitness function values are employed to choose the next generation of non-dominated solutions. Third, an aggregate fitness r-value generated by the angle distance scaling function is employed to construct matching pools that produce valid offsprings. Finally, extensive experiments are carried out to demonstrate SPEA/ARP performance by comparing it with six state-of-the-art many-objective evolutionary algorithms on 5-, 10-, 15-objective of 31 benchmark MaOPs. The experiments show that SPEA/ARP outperforms the compared algorithms.

Modeling and optimization of bakery production scheduling to minimize makespan and oven idle time

Makespan dominates the manufacturing expenses in bakery production. The high energy consumption of ovens also has a substantial impact, which bakers may overlook. Bakers leave ovens running until the final product is baked, allowing them to consume energy even when not in use. It results in energy waste, increased manufacturing costs, and CO2 emissions. This paper investigates three manufacturing lines from small and medium-sized bakeries to find optimum makespan and ovens’ idle time (OIDT). A hybrid no-wait flow shop scheduling model considering the constraints that are most common in bakeries is proposed. To find optimal solutions, non-dominated sorting genetic algorithm (NSGA-II), strength Pareto evolutionary algorithm (SPEA2), generalized differential evolution (GDE3), improved multi-objective particle swarm optimization (OMOPSO), and speed-constrained multi-objective particle swarm optimization (SMPSO) were used. The experimental results show that the shortest makespan does not always imply the lowest OIDT. Even the optimized solutions have up to 231 min of excess OIDT, while the makespan is the shortest. Pareto solutions provide promising trade-offs between makespan and OIDT, with the best-case scenario reducing OIDT by 1348 min while increasing makespan only by 61 min from the minimum possible makespan. NSGA-II outperforms all other algorithms in obtaining a high number of good-quality solutions and a small number of poor-quality solutions, followed by SPEA2 and GDE3. In contrast, OMOPSO and SMPSO deliver the worst solutions, which become pronounced as the problem complexity grows.

Competitive and Cooperative-Based Strength Pareto Evolutionary Algorithm for Green Distributed Heterogeneous Flow Shop Scheduling

Competitive and Cooperative-Based Strength Pareto Evolutionary Algorithm for Green Distributed Heterogeneous Flow Shop Scheduling