Iterative semi-continuous relaxation heuristics for the multiple-choice multidimensional knapsack problem

2012 ◽  
Vol 39 (1) ◽  
pp. 32-41 ◽  
Author(s):  
Igor Crévits ◽  
Saïd Hanafi ◽  
Raïd Mansi ◽  
Christophe Wilbaut
Keyword(s):  
Knapsack Problem ◽  
Multiple Choice ◽  
Multidimensional Knapsack Problem ◽  
Multidimensional Knapsack ◽  
Continuous Relaxation

scholarly journals Simulated Annealing Algorithm for the Multiple Choice Multidimensional Knapsack Problem

2021 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Simulated Annealing ◽  
Open Source ◽  
Knapsack Problem ◽  
Simulated Annealing Algorithm ◽  
Multiple Choice ◽  
Optimal Solutions ◽  
Multidimensional Knapsack Problem ◽  
Multidimensional Knapsack ◽  
Benchmark Instances ◽  
Annealing Algorithm

The multiple choice multidimensional knapsack problem (MCMK) is a harder version of the 0/1 knapsack problem, and is ever more complex than the 0/1 multidimensional knapsack problem. In MCMK, there are several groups of items. The objective is to maximize the value (profit) by choosing exactly 1 item from each group such that all the constraints are satisfied. It is difficult and NP-hard even to find a solution that does not violate all constraints. In this work, we present a simulated annealing based algorithm with open source C++ code to find good solutions to the multidimensional multiple choice knapsack problem. In all of the benchmark instances we used, the algorithm is able to find optimum (or close) solutions, thereby proving that the algorithm is suitable for solving larger instances for which optimal solutions are unknown.

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