Research On Multi-strategy Differential Evolution Algorithm For Mixed-variable Optimization Problems

In scientific research and engineering practice,there are many complex optimization problems that are nonlinear,multimodal,discontinuous,nonconvex,non-integrable,non-differentiable,feasible domain disconnected,and decision variables containing both continuous and discrete variables,such as pressure vessel design problems,welded beam design problems,and disc brake design problems.These problems can be collectively referred to as mixed-variable optimization problems.According to the number of objectives to be optimized,they can be divided into Single-objective Mixed-variable Optimization Problems（MVOPs）and Multi-objective Mixed-variable Optimization Problems（MO-MVOPs）.For these problems,traditional optimization methods are often unable to solve them effectively,and evolutionary algorithms can solve such problems effectively.Although Differential Evolution（DE）,a classical evolutionary algorithm,has a strong competitive ability in continuous optimization problems,it cannot solve complex mixed-variable optimization problems because DE was originally designed only for solving problems with only continuous variables.In this thesis,we investigate the shortcomings of the DE algorithm in solving mixed-variable optimization problems so that the DE algorithm can solve complex MVOPs and MO-MVOPs more efficiently.First,by analyzing the characteristics and solution difficulties of such problems,a single-objective DE algorithm based on multi-strategy collaboration,MCDE_mv,is designed to solve MVOPs.MCDE_mv uses a mixed-variable co-evolutionary scheme that allows the algorithm to solve mixed-variable optimization problems.In addition,a multi-strategy co-evolutionary approach and a statistical-based local search method are used to further improve the accuracy of the algorithm.The results on the relevant test functions and two real MVOPs demonstrate the effectiveness of the algorithm.Second,an improved multi-objective DE algorithm based on Pareto domination,MO-MCDE_mv,is designed to solve MO-MVOPs.The algorithm makes important improvements to the selection of optimal individuals in the multi-strategy co-evolutionary approach and the local search method based on MCDE_mv,so that the algorithm can be applied to solve multi-objective optimization problems.Experimental results on two types of multi-objective test functions and two real MO-MVOPs show that the algorithm is effective.Finally,in order to further improve the performance of solving MO-MVOPs,a reinforcement learning-based multi-strategy multi-objective DE algorithm,RLMMDE,is designed.The algorithm uses a classical reinforcement learning technique,Q-Learning,to complete the design of the multi-strategy multi-objective DE algorithm.A reference point adaptive activation mechanism is designed to control the reference point adaptive adjustment by borrowing the properties of reinforcement learning.In addition,a new reference point adaptive method is designed to dynamically adjust the reference points to improve the generality and robustness of the algorithm.Experimental results on several different types of multi-objective test functions and two real MO-MVOPs show that the algorithm is more competitive compared to other advanced algorithms.