A hybrid of Nested Partition, Binary Ant System, and Linear Programming for the multidimensional knapsack problem

This work presents a hybrid algorithm of Nested Partition (NP), Binary Ant System (BAS), and Linear Programming (LP) to solve the multidimensional knapsack problem (MKP). The hybrid NP+BAS+LP algorithm takes advantage of the global search strategies of the NP algorithm; the ability of BAS to quickly generate good solutions and incorporates information obtained from solving a LP relaxation of the MKP to help guide the search. It thus incorporates both the lower bounds (LB), found by the BAS, and the upper bounds (UB), found by solving the relaxed LP, into the search by embedding both in the NP framework. An adjustable computation budget is implemented where the number of samples increases if the LB and the UB point to different promising subregions. The proposed hybrid is compared to state-of-the-art solution techniques and is found to be one of the best algorithms in terms of the quality of solutions obtained and CPU time requirements.