Exploiting Trade-Off Criteria to Improve the Efficiency of Genetic Multi-Objective Optimisation Algorithms

Abstract

The highly competitive nature of the chemical industry requires the optimisation of the design and exploitation of (bio-)chemical processes with respect to multiple, often conflicting objectives. Genetic algorithms are widely used in the context of multi-objective optimisation due to their overall straightforward implementation and numerous other advantages. NSGA-II, one of the current state-of-the-art algorithms in genetic multi-objective optimisation has, however, two major shortcomings, inherent to evolutionary algorithms: 1) the inability to distinguish between solutions based on their mutual trade-off and distribution; 2) a problem-irrelevant stopping criterion based on a maximum number of iterations. The former results in a Pareto front that contains redundant solutions. The latter results in an unnecessary high computation time. In this manuscript, a novel strategy is presented to overcome these shortcomings: t-domination. t-domination uses the concept of regions of practically insignificant trade-off (PIT-regions) to distinguish between solutions based on their trade-off. Two solutions that are located in each other’s PIT-regions are deemed insignificantly different and therefore one can be discarded. Additionally, extrapolating the concept of t-domination to two subsequent solution populations results in a problem-relevant stopping criterion. The novel algorithm is capable of generating a Pareto front with a trade-off-based solution resolution and displays a significant reduction in computation time in comparison to the original NSGA-II algorithm. The algorithm is illustrated on benchmark scalar case studies and a fed-batch reactor case study.