Research On Multiobjective Intelligent Algorithm Based On Elite Set Selection And Expansion Strategy

Optimization problems are the main concern in scientific research and engineering design,most of which feature multiple objectives that are contradictory to and restrained by eachother. The performance improvement of one sub-objective will necessarily leads to theperformance degradation of at least another one sub-objective. Different fromSingle-objective Optimization Problem, Multi-objective Optimization Problem (MOP) has noabsolute or sole optimal solution but a optimal solution set, the elements in which are calledPareto optimal solutions. The elements of solution set are incomparable with each other interms of all objectives. Intelligent Optimization Algorithms is a random search algorithmcame up with through simulating certain natural phenomenon or process, featuringembarrassingly parallel, self-learning, self-organizing and self-adaptation, which provide anew method for solving complex optimization problems. Genetic Algorithm, DifferenceAlgorithm and Particle Swarm Optimization in Intelligent Optimization Algorithms, withconstantly-evolutionary overall searching method throng potential solutions constitutingpopulations, act very suitably as the solution for multi-objective optimization problems, andattract extensive attention from experts and scholars from home and abroad. This paper is tostudy the solutions of multi-objective optimization problem based on the aforesaid threeIntelligent Optimization Algorithms. An important issue in this paper is about how todesignate an algorithm with higher search efficiency and stronger robustness througheffective combination of relevant Intelligent Optimization Algorithms, evolutionary strategiesand Multi-objective optimization techniques so as to improve the quality of problem solutions.Main contents and innovative ideas in this paper are summarized as follows:(1) Elite retention mechanism can effectively prevent optimal individual loss problemincurred by random factors during evolutionary process and ensure global convergence of thealgorithm. The two implementation methods of elite retention mechanism are improved andexpanded, and region-based (μ+λ) selection method as well as external archive set withself-update mechanism are put forward, which are adopted in specific algorithm design;(2) A multi-objective evolutionary algorithm based on gradient cross distribution indexand layer strategy is put forward regarding the fact that the searching capability of thesimulated binary crossover operator in classical multi-objective evolutionary algorithmNSGA-II has relatively smaller impact on searching efficiency and that elite retentionmechanism is not robust enough to influence the population diversity. The algorithm, throughanalyzing the characteristics of cross distribution index contained in simulated binary crossover operators and using time-related logistic function, can designated it into gradientcross distribution index changing from small to large along with evolutionary generation.According to the experiment, this gradient cross distribution index can improve the algorithmperformance, enhance convergence efficiency and keep the population diversity; with regardto the deficiencies in elite retention mechanism of NSGA-II algorithm, an elite retentionmechanism based on layer strategy is proposed by adopting the region-based (μ+λ) selectionmethod, in which blank-coverage at part of Pareto optimal frontier is effectively avoided andthe population diversity is kept by selecting elitists with partition-based scanning to the targetspace. The result of numerical simulation experiment proves that, for most test functions ofZDT series, the algorithm in this paper demonstrates better performance than NSGA-IIalgorithm.(3) To effectively balance convergence rate and diversity, which is a contradictory unity,maintains as the everlasting issue of multi-objective optimization problem. This paperintroduces Differential Evolution Algorithm to increase the optimization speed ofmulti-objective optimization algorithm. The designated rank mutation and crowding distancebased minimum excluded choices contribute to keeping the population diversity. According tothe non-inferiority grade of populations and individuals in evolutionary process, the algorithmselects mutation strategy self-adaptively, improving the mutation operation of differentialevolution; to realize the individual selection of the next generation by adopting elite retentionmechanism with minimum excluded choices improves the selecting operation of differentialevolution; zoom factor F of controlled variable difference vector and crossover probabilityCR are designed into linear decreasing function related to evolutionary generation. Numericalsimulation is carried out to standard test functions and the results are compared with classicalmulti-objective evolutionary algorithm, which shows good results in both approximation anduniformity of the solution sets with good stability. It’s a practical and effective method forsolving multi-objective optimization problems.(4) This paper studies the solutions of multi-objective optimization problem by usingparticle swarm optimization, and applies external archive set with self-update mechanism tothe design of elite retention mechanism, thus coming up with a Multiple Objective ParticleSwarm Optimization based on external archive collection and self-adaptive propagation. Thisalgorithm, regarding the easy tendency of local optimum, poor convergence precision anddifficult determination of global optimal particle etc. when applying particle swarmoptimization to solving multi-objective optimization problem, provides corresponding improvement strategies, specifically showing as:①using opposition based learning strategyto generate initial solution and improve the quality of initial population solution regardingparticle swarm’s sensitivity to initial solution;②using adaptive inertia weight and speededadjustment strategy to increase early global searching ability of algorithm and to strengthenthe algorithm’s late local fine search ability;③using different reproduction strategy toimprove the quantity and quality of non-dominated solutions in external archive set accordingto the quantity of non-dominated solutions in external archive set;④non-dominated solutionsthat has smaller convergence distance and larger crowding distance with current participleswill be selected as global optimal particles;⑤using hill climbing algorithm of local search toupdate individual optimal particles when the individual optimal particles of several successivegenerations are not promoted; the result of numerical simulation experiment shows that theperformance of this algorithm is better than or equal to the that of others.