Non-dominated Ranked Genetic Algorithm for Solving Constrained Multi-objective Optimization Problems

Evolutionary algorithms are becoming increasingly valuable in solving large-scale, realistic engineering multiobjective optimization problems, which typically require consideration of conflicting and competing design issues. A criticism of Evolutionary Algorithms might be the lack of efficient and robust generic methods to handle constraints. The most widespread approach for constrained search problems is to use penalty methods, because of their simplicity and ease of implementation. Penalty function is generic and applicable to any type of constraint (linear or nonlinear). Nonetheless, the most difficult aspect of the penalty function approach is to find appropriate penalty parameters. In this paper, a method combining the new Non-dominated Ranked Genetic Algorithm (NRGA), with a parameterless penalty approach are exploited to devise the search to find Pareto optimal set of solutions, alleviate the above difficulties. The parameterless penalty approach that does not require any penalty parameter where penalty parameters assignment among feasible and infeasible solutions are made with a view to provide a search direction towards the feasible region. The new Parameterless Penalty and the Non-dominated Ranked Genetic Algorithm (PP-NRGA) continuously find better Pareto optimal set of solutions. This new algorithm have been evaluated by solving five test problems, reported in the multi-objective evolutionary algorithm (MOEA) literature. Performance comparisons based on quantitative metrics for accuracy, coverage, and spread are presented.