Studies On Constraint Handling Techniques For Multi-objective Evolutionary Algorithms Based On Cone Decomposition

Constrained multi-objective optimization problems exist extensively in the field of scientific research and engineering practice.Such problems often require more than one objective to be optimized at the same time and need to meet certain constraints due to the influence of various environmental factors.When the number of objectives is greater than or equal to 4,such problems are called constrained many-objective optimization problems.As the number of objectives increases,the existing multi-objective evolutionary algorithms will face some challenging issues,which will affect the convergence and distribution of the population,and drastically increase the computational complexity of the algorithm.Due to the existence of constraints,the algorithm needs to deal with the infeasible solutions generated during the evolution process reasonably,so as to overcome the infeasible region and converge to the global optimum.Compared with the domination-based evolutionary algorithm,the decomposition-based evolutionary algorithm has an obvious advantage in computing efficiency so that it was attracted wide attention and recently a number of many-objective evolution algorithms have borrowed the idea of decomposition to maintain population diversity.However,pure decompositionbased evolutionary algorithm,such as MOEA/D,has potential deficiency which affects the algorithm's performance in terms of convergence and diversity of the population when solving constrained many-objective optimization problems,and the handling of constraints are not reasonable enough.Therefore,this thesis proposes a constrained many-objective evolutionary algorithm based on cone decomposition,which not only decomposes the multi-objective optimization problem into a series of scalar optimization subproblems,but also divides the two-dimensional space formed by the objective and constraint of the subproblem into a series of constraint sublayers.Then,individuals with different degree of constraint violation are assigned to different constraint sublayers,so that effective information of feasible individuals and infeasible individuals is reasonably used to help population evolution,and the constrained many-objective optimization problems is more effectively and efficiently handled.The main research contents are as follows:1)A constrained cone decomposition strategy is proposed,which can be divided into two stages: objective cone decomposition and constraint cone layering.The objective cone decomposition decomposition stage decomposes the constrained multi-objective optimization problem into a series of constrained scalar optimization subproblems,and a unique cone subregion in objective space is allocated for each subproblem.In addition,K-D tree,a special data structure,is adopted to quickly locate the corresponding cone subregion for a given individual.For each subproblem,the two-dimensional space,which is composed of the aggregation objective function value and the degree of constraint violation,is stratified into a series of constraint sublayers by the constraint cone layering stage.2)On the basis of the constrained cone decomposition strategy,a cone layering selection mechanism is proposed.In the selection operation,the individual in different constraint sublayer is selected with different probability to unearth the effective information contained in the infeasible individual,which helps the algorithm to avoid local optimal traps and break through the obstacle constraint conditions,so as to converge to the global optimum.3)On the basis of the constrained cone decomposition strategy,a cone layering update mechanism is proposed.Firstly,the subproblem of the individual is identified by the constrained cone decomposition strategy,and then the subproblem and its neighbor subproblems are updated with this individual.In the process of updating subproblems,the constraint sublayer of the individual is identified,and then different elite preservation strategies are adopted for different constraint sublayers,so as to maximize the use of the effective information contained in all individuals,including infeasible individuals,to help the population evolution.4)Experiments on C-DTLZ series test instances as well as two practical engineering problems were conducted to test the comprehensive performance of the proposed algorithm in terms of is solutions quality and computing efficiency.In addition,several outstanding multiobjective evolutionary algorithms,including domination-based and decomposition-based algorithms,are chosen for performance comparison,so as to verify the effectiveness and efficiency of the proposed algorithm in constrained multi-objective optimization problems.Accorging to the comprehensive experiments on standard test instances and practical engineering problems,the constrained many-objective evolutionary algorithm based on cone decomposition proposed in this thesis can well handle constrained many-objective optimization problems with a good solutions quality as well as a good efficiency.