A Genetic Algorithm Meta-Heuristic for a Generalized Quadratic Assignment Problem

TL;DR

This paper introduces a genetic algorithm heuristic combined with local search to effectively solve the complex generalized quadratic assignment problem, demonstrating superior performance over existing methods.

Contribution

It develops a novel genetic algorithm with local search for GQAP, addressing multiple constraints and comparing results with established solvers.

Findings

GA heuristic outperforms MPL/CPLEX in solution quality

Local search improves final solution quality

Effective for different GQAP instances

Abstract

The generalized quadratic assignment problem (GQAP) is one of the hardest problems to solve in the operations research area. The GQAP addressed in this work is defined as the task of minimizing the assignment and transportation costs of assigning a set of facilities to a set of locations. The facilities have different space requirements, and the locations have different space capacities. Multiple facilities can be assigned to each location if the space capacity is not violated. In this work, three instances of GQAP in different situations are presented. Then, a genetic algorithm is developed to solve the GQAP instances. Finally, the local neighborhood search with the steepest descend strategy is constructed and applied to the final solution obtained by the GA, and the final solution is compared with the best solution found by MPL/CPLEX software and reference papers. The results show that the developed GA heuristic is effective for solving the GQAP.