Studies On Evolutionary Constraint Optimization Based On Cone Decomposition

In practical work and daily life,constrained optimization problems are very common.Compared with the unconstrained optimization problems,both the objective function and constraint violation are needed to be optimized.Constrained optimization problems can be further divided into constrained single-objective optimization problems and constrained multi-objective optimization problems according to the number of objectives.Constrained multi-objective optimization problems are harder to solve due to multiple objective functions.Moreover,Evolutionary Algorithms are able to obtain the solution set of impressive quality when solve unconstraint optimization problems but need extra constraint-handling techniques to deal with constraints.Due to various complex constraints,the constraint optimization problems have become a hot research topic in the field of evolutionary computation.Only by balancing the objective functions and constraints conditions can the quality of solution set be guaranteed.The current researches do not use the information of infeasible solutions to help the feasible solutions to search in the direction of better objective value.The traditional constraint-handling techniques generally separate the objective functions and the constraint conditions to process.Such techniques may make the algorithms fall into local optimal traps.For constraint single-objective optimization problems,a cone-layering constraint-handling technique is designed and for constraint multi-objective optimization problems,a collaborative cone-layering constraint-handling technique is designed.Based on these two techniques,a constraint-layering differential evolution algorithm(CLDE)for constrained singleobjective optimization and a collaborative constraint-layering multi-objective evolutionary algorithm(CCLMOEA)for constrained multi-objective optimization are proposed,respectively.The main research work of this paper is summarized as follows:1)A cone-layering constraint-handling technique for single-objective evolutionary algorithms is proposed,which decomposes the two-dimensional plane of the objective and the constraint violation in a bias way to obtain a series of cone constraint layers.The bias decomposition way allows the algorithm to save more individuals with smaller constraint violation degree,which is more beneficial to search for the global optimal feasible solution.The dual population model is introduced,including conical subpopulation and feasi-ble subpopulation,which evolve together by directing each other to converge to the global optimum better.This technique employs the single-objective cone-layering selection and update mechanism to assist the population to evolve.The selection mechanism uses conical area tournament method to select first parent to produce the promising child.The update mechanism employs different rules to update the conical subpopulation according to the constraint layer where the child lies.2)A collaborative cone-layering constraint-handling technique for multi-objective evolutionary algorithms is proposed,which contains objective cone decomposition strategy,constraint cone layering strategy and dominance-based document strategy.The technique firstly decomposes the multi-objective optimization problem into a series of singleobjective subproblems,and partition the plane of the constraint violation degree and the aggregation objective value.The dominance-based document is also be employed to cooperate with the decomposed population to solve the problems with irregular fronts better.This technique utilizes the multi-objective cone-layering selection and update mechanism to make the population and the archive evolve in a cooperative manner.The selection mechanism employs different probability to select parents from different constraint layers and archive to produce the promising offspring.When a solution is generated,the update mechanism needs to identified the subproblem of the individual firstly,and then the offspring is used to update the population with different strategies according to the constraint sublayer where it lies.If the offspring do not update the population successfully,it is used to update the document for maximizing of utilizing the offspring information.3)On 24 standard test instances and practical engineering problems such as welded beams design in constrained single-objective optimization,CLDE based on the cone-layering constraint-handling technique is comprehensively evaluated,compared with the other popular algorithms such as CMODE(Combining Multiobjective and Differential Evolution).The experiments results reveal that CLDE can produce solutions which are significantly competitive with other popular approaches.And the computational efficiency is good,which is roughly twice that of CMODE.4)The performance of CCLMOEA based on collaborative cone-layering constraint-handling technique is evaluated comprehensively on C-DTLZ series standard test cases and practical engineering problems such as water resource planning for constrained multi-objective optimization.compared with the other popular algorithms,including C-TAEA(Two-Archive Evolutionary Algorithms for Constrained Multi-Objective Optimizations)which possesses great performance.The experimental results show that CCLMOEA can obtain the most excellent solution sets in general and the computational efficiency of CCLMOEA is obviously superior.On the standard test cases of 15 objective,the computational efficiency of CCLMOEA is about 40 to 70 times that of C-TAEA.