GKNAP: A Java and C++ package for solving the multidimensional knapsack problem
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The 0/1 multidimensional (multi-constraint) knapsack problem is the 0/1 knapsack problem with m constraints. It is a strongly NP-hard problem, and might be difficult to solve using exact methods like branch and bound and dynamic programming, especially when the number of variables is large. We present a genetic algorithm for the multidimensional knapsack problem with Java and C++ code that is able to solve publicly available instances in a very short computational duration. Our algorithm uses iteratively computed Lagrangian multipliers as constraint weights to augment the greedy algorithm for the multidimensional knapsack problem and uses that information in a greedy crossover in a genetic algorithm. The algorithm uses several other hyperparameters which can be set in the code to control convergence. Our algorithm improves upon the algorithm by Chu and Beasley (Chu & Beasley, 1998) in that it converges to optimum or near optimum solutions much faster.
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