Adaptive Stochastic Ranking Constraint Handling Methods For Evolutionary Optimization

Optimization problem is one kind of common problems in scientific research and engineering practice,which usually contains one or more number of objectives for optimizing.As an intelligent search method, evolutionary algorithm can achieve multiple solutions in one search, which is suitable for solving optimization problem. However, some optimization problems need to deal with many constraints,such as constraints in space, time,physical, economic and so on, when searching the finial solutions. These constraint conditions increase the difficulties of search, so some mechanisms dealing with these constraints are needed to lead direction of search toward the feasible solution region,when using evolutionary algorithm to solve these optimization problems with constraints.In this paper, we discuss methods of dealing with these constraints in evolutionary algorithm, and a novel self-adaptive stochastic ranking processing mechanismis proposed to deal with the constraints of optimization problem.With traditional stochastic ranking processing method, a fixed probability is set up to allow some infeasible solutions to be selected for evolution, which makes useful information in infeasible region be used by algorithm. With consideration for the difference of fitness values, the period of evolutionary process and the speed of generating better individual, a self-adaptive dynamic probability is designed instead of the original fixed probability, which improve the control of searching on infeasible region.By using the novel self-adaptivestochastic ranking processing mechanism,the individuals in infeasible region have larger chance to be selected for evolution in early period of evolutionary process or when individuals replaced frequently or the difference of fitness values is small.At the same time, in order to avoid feasible solutions being replaced by infeasible solutions when using the stochastic ranking processing mechanism, a elite archive is introduced in this paper to reserve a number of best feasible individuals.In this paper, we discuss the self-adaptive stochastic ranking mechanism used in single-objective optimization problem with constraints and multi-objective optimization problem with constraits, and the contributions of this paper are presented as follows:1. A self-adaptive stochastic ranking processing mechanismis proposed for single-objective optimization problem with constraints. The self-adaptive stochastic ranking processing mechanism isintegrated into the traditional evolutionary strategy(?, ?)-ES algorithm to select individuals of next generation from the whole population. As a result, the new proposed algorithm can deal with single-objective optimization problem with constraintswell.2. A self-adaptive stochastic ranking processing mechanismis proposed for multi-objective optimization problem with constraints. The self-adaptive stochastic ranking processing mechanism is integrated into the algorithm MOEA/D-DE when updating population with the new individual. As a result, the improved algorithm can deal with multi-objective optimization problem with constraints.3. The elite archive is introduced in the paper to reserve a number of best feasible individuals for both single-objective optimization problem with constraints and multi-objective optimization problem with constraints. Experiments on several test problems shows that the new algorithm with the mechanism of elite archive can make the algorithm converge toward satisfactory solutions faster and better.4. In this paper, we use the proposed algorithm with self-adaptive stochastic ranking processing mechanism and elite archive to solve some engineering problems, such as speed reducer(gear train) problem and three bar truss structure design problem.Experiment results show that the proposed algorithm is suitable to deal with optimization problem with constraints.