Balancing Survival of Feasible and Infeasible Solutions in Constraint Evolutionary Optimization Algorithms

Real-world optimization problems often involve constraints that relate to viability of implementing a solution. To solve such problems efficiently, a good constraint handling method is indispensable for an optimization algorithm. Population-based optimization algorithms allow a flexible way to handle constraints by making a careful comparison between feasible and infeasible solutions present in the population. A previous approach, which emphasized feasible solutions infinitely more than the infeasible solutions, has been popularly applied for more than one-and-half decade, mostly with real-parameter genetic algorithms (RGAs). Despite its popular use, the idea was criticized for its extreme selection pressure against infeasible solutions. Since optimal solutions often lie on the constraint boundaries, survival of certain infeasible solutions close to critical constraint boundaries should help RGA's recombination and mutation operators to produce near-optimal solutions. In this paper, we extend the earlier parameter-less constraint handling approach so as to strike a balance between survival of feasible and infeasible solutions in a GA population. The balance is controlled through an additional parameter that could be pre-specified or adaptively updated as the algorithm progresses. A parametric study is conducted to determine an appropriate value which works the best on most problems of this study. A significant improvement in performance is observed for the commonly-used g-series test problem suite and a real-world application problem (welded beam design). The approach is generic and can be easily extended to other real-parameter evolutionary algorithms, multi-objective and other advanced optimization tasks.