Recent advances in algorithms for the multidimensional multiple choice knapsack problems have enabled us to solve rather large problem instances. However, these algorithms are evaluated with very limited benchmark instances. In this study, we propose new methods to systematically generate comprehensive benchmark instances. Some instances with special correlation properties between parameters ar...

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...

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...

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...

The paper focuses on composing of discrete information units (items) into information complexes in hypertext systems. We consider basic operations (analysis, comparison, approximation, aggregation), combinatorial models (multicriteria ranking, knapsack problem with compatibility of items, multiple choice problem, morphological clique problem). Combinatorial information design on the base of mor...

It is well-known that the multiple knapsack problem is NP-hard, and does not admit an FPTAS even for the case of two identical knapsacks. Whereas the 0-1 knapsack problem with only one knapsack has been intensively studied, and some effective exact or approximation algorithms exist. A natural approach for the multiple knapsack problem is to pack the knapsacks successively by using an effective ...

This paper presents a new heuristic algorithm for the MultipleChoice Multi-Dimension Knapsack Problem (MMKP) in PRAM model. MMKP is a variant of the classical 0-1 knapsack problem, has a knapsack with multidimensional capacity constraints, groups of items, each item having a utility value and multidimensional resource constraints. The problem is to maximize the total value of the items in the k...