Evolutionary algorithm with parallel evaluation strategy of feasible and infeasible solutions considering total 
constraint violation 

Abstract

A new genetic algorithm to search for Pareto-optimal solutions in multi-objective problems with constraints is proposed. 
This algorithm employs the parallel evaluation strategy in which feasible and infeasible solutions are preserved in 
separate populations. Feasible solutions are ranked in accordance with the ordinary non-dominated ranking method. On the 
other hands, infeasible solutions are ranked based on their objective functions and total constraint violation. The total 
constraint violation is treated as the (M+1)-th evaluation function in addition to M original objective functions used for 
ranking infeasible solutions. This non-dominated ranking considering both objective functions and total constraint violation 
is expected to remove infeasible solutions with large constraint violations and preserve useful solutions. Through the present 
numerical tests, the proposed algorithm without tunable parameters outperforms the existing genetic algorithms considering 
either objective functions or constraint violations in multi-objective problems with active constraints. Additionally, the 
proposed algorithm shows better performance than the genetic algorithm using the penalty approach considering the sum of 
objective functions and total constraint violation. The improvement of Pareto-optimal solution search capability is accomplished 
by preserving infeasible solutions near the true Pareto-optimal front restricted by active constraints.