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Multiple-class multidimensional knapsack optimisation problem and its solution approaches
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DOI：10.1016/j.knosys.2018.11.006.png)
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The knapsack problem is well known in the field of combinatorial optimisation. In this paper, we propose a novel multiple-class multidimensional knapsack optimisation problem (MCMKOP) in which the aim is to minimise the total cost of the chosen knapsacks created by a set of knapsack classes. This scenario has a host of practical applications. As MCMKOP is a new combinatorial optimisation problem, we analyse its complexity and prove that it is NP-hard. Because of the high computational complexity of MCMKOP, three heuristic approaches are proposed. The first is a genetic algorithm (GA), the second is a specialised simulated annealing (SA) technique, and the third is a hybrid algorithm (HSAGA) that combines the GA and SA approaches to overcome their respective limitations and integrate their advantages. The commercial exact solvers CPLEX and Gurobi were also applied to MCMKOP. The performance of the proposed heuristics, CPLEX, and Gurobi was evaluated using 144 randomly generated test instances. The experimental results show that HSAGA gives better solutions than both the SA and GA methods, and outperformed CPLEX and Gurobi on 122 problems out of 144 test instances. The results of a paired-t test also indicate that HSAGA works considerably better than the other four algorithms on all datasets, with maximum gaps between HSAGA and GA, SA, CPLEX, and Gurobi of 95.96, 90.9, 88.9, and 96.16, respectively. (C) 2018 Elsevier B.V. All rights reserved.
Keyword:
Combinatorial optimisation
Multiple-class multidimensional knapsack problem (MCMKOP)
Genetic algorithm
Simulated annealing algorithm
Hybrid simulated annealing genetic algorithm (HSAGA)
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