On the Feasibility Problem of Penalty-Based Evolutionary Algorithms for Knapsack Problems

Abstract

Constrained optimization problems can be tackled by evolutionary algorithms using penalty functions to guide the search towards feasibility. The core of such approaches is the design of adequate penalty functions. All authors, who designed penalties for knapsack problems, recognized the feasibility problem, i.e. the final population contains unfeasible solutions only. In contrast to previous work, this paper explains the origin of the feasibility problem. Using the concept of fitness segments, a computationally easy analysis of the fitness landscape is suggested. We investigate the effects of the initialization routine, and derive guidelines that ensure resolving the feasibility problem. A new penalty function is proposed that reliably leads to a final population containing feasible solutions, independently of the initialization method employed.