Improved Constraint Handling Technique for Multi-Objective Optimization with Application to Two Fermentation Processes

Abstract

Constraints besides bounds are often present in multi-objective optimization (MOO) problems for chemical engineering applications; these arise from mass and energy balances, equipment limitations, and operational requirements. Penalty function and feasibility approaches are popular constraint-handling techniques for solving constrained MOO problems by stochastic global optimization techniques such as genetic algorithms and differential evolution. This chapter briefly reviews selected applications of these constraint-handling approaches in chemical engineering. In the penalty function approach, solutions are penalized based on constraint violations; its performance depends on the penalty factor, which necessitates selection of a suitable value for the penalty factor for different problems. Generally, the feasibility approach is good for solving problems with inequality constraints due to their large feasible regions. It gives higher priority to a feasible solution over an infeasible solution, but this limits the diversity of search. Feasible search space is extremely small for problems with equality constraints, and so the feasibility approach may not be effective for handling this type of constraint. Adaptive relaxation of constraints in conjunction with the feasibility approach addresses this issue by relaxing feasible search space dynamically. This approach has been found to be better and effective for solving single-objective optimization problems with equality and inequality constraints by stochastic global optimization techniques. In this chapter, a modified adaptive relaxation with feasibility approach is explored for solving constrained MOO problems by stochastic optimizers, and its performance is compared with that of feasibility approach alone. For this, the modified adaptive relaxation with feasibility approach is incorporated in the multi-objective differential evolution algorithm, and tested on two benchmark functions with equality constraints. Finally, multi-objective differential evolution with the proposed constraint handling approach is applied to optimize two fermentation processes for multiple objectives. © 2013 John Wiley & Sons, Ltd.