Hybrid Multi-Objective Combinatorial Optimization Technique with Improved Compatibility between GA and Gradient-Based Local Search

Abstract

*† This paper presents a hybrid multi-objective algorithm and demonstrates the algorithm’s ability to find solutions for a constrained multi-objective mixed discrete non-linear programming problem. The hybrid algorithm uses a Genetic Algorithm as a global search tool with a gradient based Sequential Quadratic Programming algorithm for local search in a way that seems to overcome the demerits of these two algorithms when used independently. The approach here addresses some of the issues that current state-ofthe-art optimization techniques face. Handling constraints is a primary concern for most of the global optimization algorithms that seek to address mixed discrete non-linear programming problem. In general, hybrid optimization algorithms tend to outperform their individual counterparts. Often, the enhanced performance of the hybrid approach leverages the computational efficiency of the gradient-based search and the design space exploration of the global search. The approach used here adds to the expected improvements along with a mechanism to address mixed discrete, nonlinear problems with the global search and to address strict constraint enforcement with the local search. Hybridizing two algorithms has proven to outperform their individual counterparts. However, not much is exploited from the process of hybridizing two algorithms other than the computational efficiency of the gradient-based algorithm and exploring capability of the global search algorithms. The work here presents a compatible hybridization between GA and SQP with improved information sharing between the two algorithms. The hybrid approach first solves a set of test problems to demonstrate its abilities and shortcomings; then the hybrid approach solves a greener aircraft design problem posed as a mixed discrete non-linear programming problem. The results of the greener aircraft design problem present the trade-offs that exist between the various environmental, economic and the performance metrics.