Solving problems with a mix of hard and soft constraints using modified infeasibility driven evolutionary algorithm (IDEA-M)

Most optimization problems in the field of engineering design involve constraints. These constraints are often due to statutory requirements (e.g. safety, physical laws, user requirements/functionality) and/or limits imposed on time and resources. Population based stochastic optimization algorithms are a preferred choice for solving design optimization problems due to their ability to deal with nonlinear black-box functions. Having a good constraint handling technique embedded within the algorithm is imperative for its good performance. With the final aim of achieving feasible optimum solutions, feasibility first techniques, i.e., those which prefer feasible solutions over infeasible, have been commonly used in the past. However, in recent studies more emphasis has been laid on intelligent use of infeasible solutions (instead of their indiscreet rejection) during the course of optimization; particularly because optimum solutions often lie on the constraint boundary. The preservation of good infeasible solutions in the population is likely to improve the convergence in constricted or disconnected feasible regions. In addition, it provides a set of marginally infeasible solutions for trade-off considerations. However, in the case of a problem consisting of a mix of hard (non-negotiable) and soft (negotiable) constraints, such trade-off solutions are practically useful if they violate the soft constraints only. In this paper, previously introduced Infeasibility Driven Evolutionary Algorithm (IDEA) is modified to deliver solutions which strictly satisfy the hard constraints and offer tradeoff solutions with respect to the soft constraints. The performance of the algorithm is demonstrated on three benchmark problems.