Exploiting Trade-Off Criteria to Improve the Efficiency of Genetic Multi-Objective Optimisation Algorithms
Viviane De Buck, Philippe Nimmegeers, Ihab Hashem, Carlos André Muñoz López, Jan Van Impe
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.