Set-based Many-objective Evolutionary Optimization Algorithms

Multi-objective optimization problems (MOPs) are very common and importantin real-word applications. Problems with more than three objectives are defined asmany-objective optimization problems (MaOPs). They are very difficult to solve. Atpresent, strategies for solving MaOPs are hot topics in the community of evolutionaryoptimization. Wherein, set-based evolutionary optimization algorithms by using theperformance of sets are effective ways to solve MaOPs. In addition, from theperspective of a decision-maker, its aim is to get a number of solutions interested bythe decision-maker. In view of this, the thesis studies set-based evolutionaryoptimization algorithms by integrating a decision-maker’s preferences for solvingMaOPs, including building the model of this kind of optimization problems,designing evolutionary strategies, and conducting a series of comparative analysis.First, aiming at the difficulty in solving a many-objective optimization problem,a set-based many-objective evolutionary algorithm which integrates adecision-maker’s preferences is presented. In this method, each objective function ofthe original optimization problem is transformed into a desirability function based onthe preference areas given by the decision-maker. The optimization problem is furthertransformed into a bi-objective optimization one by taking such indicators ashyper-volume and the decision-maker’s satisfaction as two new objectives in which aset formed by multiple solutions of the original optimization problem is as the newdecision variable. The transformed bi-objective optimization problem is solved byusing a set-based evolutionary optimization algorithm to obtain a Pareto optimal setwhich meets the decision-maker’s preferences and balances the convergence and thedistribution. The proposed method is applied to four benchmark many-objectiveoptimization problems and compared with the other methods. The experimentalresults show its advantages.Then, for solving the above transformed bi-objective optimization problem, aset-based evolutionary genetic algorithm is presented. The crossover operator inside aset is designed based on the simplex method. The mutation operator of a set ispresented to obey the Gaussion distribution and changes with the decision-maker’spreferences. The crossover operator between sets is developed by using the entropy ofa set to maintain the diversity of the population. The proposed method is applied tofive benchmark many-objective optimization problems, and compared with the otherfour methods. The experimental results empirically demonstrate its effectiveness. Similarly, inspired by the above research, another set-based evolutionary geneticalgorithm for solving the transformed bi-objective optimization problem is presented.The adaptive crossover operator inside a set is designed by using the indicators ofparents to control the probability and magnitude of the crossover operator. The PSObased mutation strategy of a set is presented by using the global and the local optimalsolutions. The proposed method is applied to five benchmark many-objectiveoptimization problems, and compared with the other three methods. The experimentalresults empirically demonstrate its effectiveness.Finally, for the many-objective optimization problem, an indicator-basedmany-objective particle swarm optimizaiton is presented. In this method, the decisionvariable is a set including multiple solutions of the original optimization problem. Theoriginal optimization problem is converted to a bi-objective optimization problem bytaking hyper-volume and the spread as the new objectives. Sets are regarded asparticles and a method for updating the particles based on particle swarm optimizationis developed. In addition, a method for choosing the optimal particle set is designedby taking advantage of indicators. It can achieve the interaction among sets withoutincreasing the computational complexity. Solutions in a set are also regarded asparticles. The position of a particle is updated by using information of the optimalreference point of each set so as to guide particles to converge towards Pareto optimalsolutions as soon as possible. The merits of the proposed algorithm are experimentaldemonstrated by applying it to scalable benchmark many-objective optimizationproblems.All these three kinds of set-based genetic algorithms in this thesis not only offereffective ways to solve many-objective optimization problems, but also enrichtheoretical and application research.