Hybrid tabu search – strawberry algorithm for multidimensional knapsack problem

Abstract

Multidimensional Knapsack Problem (MKP) has been widely used to model real-life combinatorial problems. It is also used extensively in experiments to test the performances of metaheuristic algorithms and their hybrids. For example, Tabu Search (TS) has been successfully hybridized with other techniques, including particle swarm optimization (PSO) algorithm and the two-stage TS algorithm to solve MKP. In 2011, a new metaheuristic known as Strawberry algorithm (SBA) was initiated. Since then, it has been vastly applied to solve engineering problems. However, SBA has never been deployed to solve MKP. Therefore, a new hybrid of TS-SBA is proposed in this study to solve MKP with the objective of maximizing the total profit. The Greedy heuristics by ratio was employed to construct an initial solution. Next, the solution was enhanced by using the hybrid TS-SBA. The parameters setting to run the hybrid TS-SBA was determined by using a combination of Factorial Design of Experiments and Decision Tree Data Mining methods. Finally, the hybrid TS-SBA was evaluated using an MKP benchmark problem. It consisted of 270 test problems with different sizes of constraints and decision variables. The findings revealed that on average the hybrid TS-SBA was able to increase 1.97% profit of the initial solution. However, the best-known solution from past studies seemed to outperform the hybrid TS-SBA with an average difference of 3.69%. Notably, the novel hybrid TS-SBA proposed in this study may facilitate decisionmakers to solve real applications of MKP. It may also be applied to solve other variants of knapsack problems (KPs) with minor modifications