Aimed at improving the insufficient search ability of constraint differential evolution with single constraint handling technique when solving complex optimization problem, this paper proposes a constraint differentia...Aimed at improving the insufficient search ability of constraint differential evolution with single constraint handling technique when solving complex optimization problem, this paper proposes a constraint differential evolution algorithm?based on ensemble of constraint handling techniques and multi-population?framework, called ECMPDE. First, handling three improved variants of differential evolution algorithms are dynamically matched with two constraint handling techniques through the constraint allocation mechanism. Each combination includes three variants with corresponding constraint handling technique?and these combinations are in the set. Second, the population is divided into three smaller subpopulations and one larger reward subpopulation. Then a combination with three constraint algorithms is randomly selected from the set, and the three constraint algorithms are run in three sub-populations respectively. According to the improvement of fitness value, the optimal constraint?algorithm is selected to run on the reward sub-population, which can share?information and close cooperation among populations. In order to verify the effectiveness of the proposed algorithm, 12 standard constraint optimization problems?and 10 engineering constraint optimization problems are tested. The experimental results show that ECMPDE is an effective algorithm for solving constraint optimization problems.展开更多
The particle swarm optimization(PSO)algorithm is an established nature-inspired population-based meta-heuristic that replicates the synchronizing movements of birds and sh.PSO is essentially an unconstrained algorithm...The particle swarm optimization(PSO)algorithm is an established nature-inspired population-based meta-heuristic that replicates the synchronizing movements of birds and sh.PSO is essentially an unconstrained algorithm and requires constraint handling techniques(CHTs)to solve constrained optimization problems(COPs).For this purpose,we integrate two CHTs,the superiority of feasibility(SF)and the violation constraint-handling(VCH),with a PSO.These CHTs distinguish feasible solutions from infeasible ones.Moreover,in SF,the selection of infeasible solutions is based on their degree of constraint violations,whereas in VCH,the number of constraint violations by an infeasible solution is of more importance.Therefore,a PSO is adapted for constrained optimization,yielding two constrained variants,denoted SF-PSO and VCH-PSO.Both SF-PSO and VCH-PSO are evaluated with respect to ve engineering problems:the Himmelblau’s nonlinear optimization,the welded beam design,the spring design,the pressure vessel design,and the three-bar truss design.The simulation results show that both algorithms are consistent in terms of their solutions to these problems,including their different available versions.Comparison of the SF-PSO and the VCHPSO with other existing algorithms on the tested problems shows that the proposed algorithms have lower computational cost in terms of the number of function evaluations used.We also report our disagreement with some unjust comparisons made by other researchers regarding the tested problems and their different variants.展开更多
工程和科学领域中的优化问题常常具有大量的约束限制,称为约束优化问题.这类问题要求算法有能力在可行域中寻找问题的最优解.本文针对约束优化问题提出一种集成多策略的差分进化算法(Differential Evolution with Ensemble Multi-Strate...工程和科学领域中的优化问题常常具有大量的约束限制,称为约束优化问题.这类问题要求算法有能力在可行域中寻找问题的最优解.本文针对约束优化问题提出一种集成多策略的差分进化算法(Differential Evolution with Ensemble Multi-Strategies,EMSDE).首先,提出一种用于约束优化的参数自适应策略,利用归一化罚函数作为权重引导参数自适应地生成.其次,结合约束和动态罚函数法设计一种新的约束处理技术.最后,采用CEC2017约束优化基准函数来测试EMSDE和7种经典的约束优化算法.实验结果表明,相比7种经典的算法,EMSDE算法具有很强的竞争力.展开更多
文摘Aimed at improving the insufficient search ability of constraint differential evolution with single constraint handling technique when solving complex optimization problem, this paper proposes a constraint differential evolution algorithm?based on ensemble of constraint handling techniques and multi-population?framework, called ECMPDE. First, handling three improved variants of differential evolution algorithms are dynamically matched with two constraint handling techniques through the constraint allocation mechanism. Each combination includes three variants with corresponding constraint handling technique?and these combinations are in the set. Second, the population is divided into three smaller subpopulations and one larger reward subpopulation. Then a combination with three constraint algorithms is randomly selected from the set, and the three constraint algorithms are run in three sub-populations respectively. According to the improvement of fitness value, the optimal constraint?algorithm is selected to run on the reward sub-population, which can share?information and close cooperation among populations. In order to verify the effectiveness of the proposed algorithm, 12 standard constraint optimization problems?and 10 engineering constraint optimization problems are tested. The experimental results show that ECMPDE is an effective algorithm for solving constraint optimization problems.
基金The authors thank the Higher Education Commission,Pakistan,for supporting this research under the project NRPU-8925(M.A.J.and H.U.K.),https://www.hec.gowpk/。
文摘The particle swarm optimization(PSO)algorithm is an established nature-inspired population-based meta-heuristic that replicates the synchronizing movements of birds and sh.PSO is essentially an unconstrained algorithm and requires constraint handling techniques(CHTs)to solve constrained optimization problems(COPs).For this purpose,we integrate two CHTs,the superiority of feasibility(SF)and the violation constraint-handling(VCH),with a PSO.These CHTs distinguish feasible solutions from infeasible ones.Moreover,in SF,the selection of infeasible solutions is based on their degree of constraint violations,whereas in VCH,the number of constraint violations by an infeasible solution is of more importance.Therefore,a PSO is adapted for constrained optimization,yielding two constrained variants,denoted SF-PSO and VCH-PSO.Both SF-PSO and VCH-PSO are evaluated with respect to ve engineering problems:the Himmelblau’s nonlinear optimization,the welded beam design,the spring design,the pressure vessel design,and the three-bar truss design.The simulation results show that both algorithms are consistent in terms of their solutions to these problems,including their different available versions.Comparison of the SF-PSO and the VCHPSO with other existing algorithms on the tested problems shows that the proposed algorithms have lower computational cost in terms of the number of function evaluations used.We also report our disagreement with some unjust comparisons made by other researchers regarding the tested problems and their different variants.
文摘工程和科学领域中的优化问题常常具有大量的约束限制,称为约束优化问题.这类问题要求算法有能力在可行域中寻找问题的最优解.本文针对约束优化问题提出一种集成多策略的差分进化算法(Differential Evolution with Ensemble Multi-Strategies,EMSDE).首先,提出一种用于约束优化的参数自适应策略,利用归一化罚函数作为权重引导参数自适应地生成.其次,结合约束和动态罚函数法设计一种新的约束处理技术.最后,采用CEC2017约束优化基准函数来测试EMSDE和7种经典的约束优化算法.实验结果表明,相比7种经典的算法,EMSDE算法具有很强的竞争力.
