The multiple-choice multidimensional knapsack problem (MMKP) is a well-known NP-hard that has many real-time applications. However, owing to its complexity, finding computationally efficient solutions for the MMKP remains challenging task. In this study, we propose Modified Artificial Bee Colony algorithm (MABC) solve MMKP. MABC employs surrogate relaxation, Hamming distance, and tabu list enha...

We study the interval knapsack problem (I-KP), and the interval multiple-choice knapsack problem (I-MCKP), as generalizations of the classic 0/1 knapsack problem (KP) and the multiple-choice knapsack problem (MCKP), respectively. Compared to singleton items in KP and MCKP, each item i in I-KP and I-MCKP is represented by a ([ai, bi], pi) pair, where integer interval [ai, bi] specifies the possi...

The multidimensional multiple-choice knapsack problem (MMKP) is an extension of the 0-1 knapsack problem. The core concept has been used to design efficient algorithms for the knapsack problem but the core has not been developed for the MMKP so far. In this paper, we develop an approximate core for the MMKP and utilize it to solve the problem exactly. Computational results show that the algorit...

This paper presents a heuristic to solve the Multidimensional Multiple-choice Knapsack Problem (MMKP), a variant of the classical 0–1 Knapsack Problem. We apply a transformation technique to map the multidimensional resource consumption to single dimension. Convex hulls are constructed to reduce the search space to find the near-optimal solution of the MMKP. We present the computational complex...

RÉSUMÉ : We consider two variants of knapsack problems with setups arising as subproblems in a DantzigWolfe decomposition approach to more complex combinatorial optimization problems. In the multiple-class binary knapsack problem with setups, items are partitioned into classes whose use implies a setup cost and associated capacity consumption. Item weights are assumed to be a multiple of their ...

After the seminal books by Martello and Toth (1990) Kellerer, Pferschy, Pisinger (2004), knapsack problems became a classical rich research area in combinatorial optimization. The purpose of this survey, which is structured two parts, to cover developments that appeared field after publication latter volume. Part I devoted whose goal optimally assign items single knapsack. Besides (binary, subs...