A Hybrid Algorithm of Ant Colony and Benders Decomposition for Large-Scale Mixed Integer Linear Programming

Abstract

The mixed integer linear programming (MILP) has been widely applied in many fields such as supply chain management and robot control, while how to develop a more efficient algorithm to solve large-scale MILP is still in discussion. This study addresses a hybrid algorithm of the ant colony and Benders decomposition to improve the efficiency. We firstly introduce the design of our algorithm, in which the Benders algorithm decomposes the MILP into a master problem and a slack problem, the ant colony algorithm generates initial solutions for the master problem, and heuristic rules obtain feasible solutions for the slack problem. Then, the computational experiments are carried out to verify efficiency, with a benchmark test and some medium-large scale examples. Compared with other algorithms like CPLEX, GUROBI, and traditional ACA, our algorithm shows a better performance with a 0.3%–4.0% optimality gap, as well as a significant decrease of 54.3% and 33.6% on average in the CPU time and iterations, respectively. Our contribution is to provide a low-workload, time-saving, and high-accuracy hybrid algorithm to solve MILP problems with a large amount of variables, which can be widely used in more commercial solvers and promote the utilization of the artificial intelligence.