Multi-Objective Evolutionary Optimization Based On Perceiving Pareto Front Characteristics: Theory And Method

Multi-objective optimization problems(MOPs)are ubiquitous in industry production and daily life,such as rescue path planning of robots and optimal scheduling in microgrids.Such MOPs have the typical feature of containing several objective functions which are conflicting with each other.Therefore,there is no solution that makes all the objectives optimal at the same time.In addition,the Pareto fronts of the MOPs,i.e.,the(hyper)surface formed by the optimal solution set of the MOPs in the objective space,exist many complex characteristics,which further increases the difficulty of solving the optimization problems.Multi-objective evolutionary optimization methods have shown clear advantages in solving MOPs.However,these methods do not make full use of the information during evolution to perceive the characteristics of the Pareto front,so as to design specific intelligent optimization strategies.For MOPs whose Pareto fronts' characteristics are discontinuous,convex/concave,or their recombination,the above-mentioned methods have a long way to go.Based on these observations,multi-objective evolutionary optimization based on perceiving Pareto front characteristics for MOPs with complex Pareto fronts is proposed.Firstly,a muti-objective evolutionary optimization method based on perceiving discontinuty of Pareto front is proposed,so as to deal with MOPs with discontinuous Pareto front.This method perceives the discontinuities of the Pareto front based on the crowding distance between individuals and a given threshold.The discontinuous points are adopted to divide the objective space into several grids,and the dominant relationship between the discontinuous points and the grids are determined to demarcate the objective space.The subspace information interaction,the span of the Pareto front in the subspace and the selection conditions of the solution are presented to consider the convergence and distribution performance of the solution set.To verify the effectiveness of the proposed method,the proposed method is applied to 15 test instances,and compared with NSGA-II,RPEA,MOEA/D,MOEA/D-PBI,MOEA/D-STM,and MOEA/D-ACD with the same instances.Experimental results demonstrate that the proposed method can deal well with the optimization problems with discontinuous characteristics of Pareto front.Secondly,a constrained muti-objective evolutionary optimization method based on perceiving discontinuty of Pareto front is proposed to deal with CMOPs with discontinuous Pareto front.The relationship between the angles formed by the discontinuous points and its corresponding direction vectors,and the angles formed by any two adjacent direction vectors,are compared to determine the discontinuous area.The discontinuity of the Pareto front is adopted to trigger the direction vectors adjustment mechanism to adjust the distribution of direction vectors.Besides,the degree of constraint violations has different effects on individuals located on different position in Pareto front.Therefore,the individuals are classified into different types according to constraint violations and perception result.Different constraint strategies are selected for each type of individuals.The above strategies enhance the adaptability of the algorithm in CMOPs.To verify the effectiveness of the proposed method,comparisons are conducted with SPEA2,SMS-EMOA,AR-MOEA,MOEA/D-AWA,i MOEA,Pa RP/EA,CA-MOEA and RVEA-i GNG for 26 constrained test instances,Experimental results show that the proposed method can deal well with the optimization problems with complex characteristics of Pareto frontier caused by constraints.Furthermore,a muti-objective evolutionary optimization method based on perceiving discontinuty and convexity/concavity of Pareto front is proposed to handle the MOPs with discontinuous and convex/concave Pareto front.The angle calculation function(ACF)is adopted to calculate extreme points.The relationship between an individual on the Pareto front and the connecting line/hyperplane of extreme points,as well as the crowding distance of the individuals are adopted to extract information during the evolution.The dichotomy is employed to divide the complex Pareto fronts,and the convex/concave of each sub-front is independently perceived based on the the relative location between the connecting line/hyperplane of extreme points and an individual on the sub-fronts.The syncretic direction point selection strategy of discontinuous and concave-convex is adopted to refine the distribution of direction vectors.This method handles the superimposed characteristics separately,which can greatly reduce the complexity of solving MOPs.To verify the effectiveness of the proposed method,it is compared with a number of commonly used methods,including,SPEA2,SMS-EMOA,AR-MOEA,MOEA/D-AWA,i MOEA,Pa RP/EA,CA-MOEA,and RVEA-i GNG for 31 test instances.The experimental results indicate that the method can obtain the Pareto optimal solution sets with superior performance in the MOPs with multiple characteristics Pareto fronts.Finally,the multi-objective evolutionary optimization method based on perceiving Pareto front characteristics is applied to the operation optimization strategy of integrated coal mine energy system.A mathematical model is formulated and the optimization strategy of integrated coal mine energy system based on perception of Pareto front's characteristics is proposed.In addition,the experimental section,the proposed method is compared with CCMO and CMOEA-MS under three designed representative scenarios.The experimental results show that the optimization operation strategy generated by the proposed method can optimize real-world complex problems with the characteristics of multi-variable,multi-objective and strong constraints simultaneously.To sum up,the above research achievements can not only enrich and deepen the multi-objective evolutionray optimization theories,but also improve the performance of multi-objective evolutionary optimization methods,thereby promoting the application of these theories in real-world applications effectively.It has important values in theory and application.The paper has 49 figures,31 tables,and 97 references.