Multidimensional Knapsack Problem: A Fitness Landscape Analysis

Abstract

Fitness landscape analysis techniques are used to better understand the influence of genetic representations and associated variation operators when solving a combinatorial optimization problem. Five representations are investigated for the multidimensional knapsack problem. Common mutation operators, such as bit-flip mutation, are employed to generate fitness landscapes. Measures such as fitness distance correlation and autocorrelation are applied to examine the landscapes associated with the tested genetic encodings. Furthermore, additional experiments are made to observe the effects of adding heuristics and local optimization to the representations. Encodings with a strong heuristic bias are more efficient, and the addition of local optimization techniques further enhances their performance.

Performance Study of Cultural Algorithms Based on Genetic Algorithm with Single and Multi Population for the MKP

“…As mentioned earlier, the MKP is a well-known nondeterministic-polynomial time-hard combinatorial optimization problem, with a wide range of applications (Tavares et al, 2008). The classical 0-1 knapsack problem is one of the most studied optimization and involves the selection of a subset of available items having maximum profit so that the total weight of the chosen subset does not exceed the knapsack capacity.…”

“…Multidimensional Knapsack Problem (MKP) is a well-known nondeterministic-polynomial time-hard combinatorial optimization problem, with a wide range of applications, such as cargo loading, cutting stock problems, resource allocation in computer systems, and www.intechopen.com economics (Tavares et al, 2008). MKP has received wide attention from the operations research community, because it embraces many practical problems.…”

“…Yet another research utilizes adaptive GA for 0/1 Knapsack problems where special consideration is given to the penalty function where constant and self-adaptive penalty functions are adopted (Zoheir, 2002). Fitness landscape analysis techniques are used to better understand the properties of different representations that are commonly adopted when evolutionary algorithms are applied to MKP (Tavares et al, 2008). Other investigation utilizes multiple representations in a GA for the MKP (Representation-Switching GA) know as RSGA (Fukunaga, 2009).…”

CHAMP: Creating heuristics via many parameters for online bin packing

“…We also conducted, and present here, a fitness landscape analysis (Wright, 1932;Tavares et al, 2008) to better understand the performance of the proposed algorithm in relation with the policy matrix representation. To the best of our knowledge, this is the first study on fitness landscape analysis on the search space of online bin-packing policies.…”

A Genetic Algorithm Approach for the TV Self-Promotion Assignment Problem

“…We have noticed that the simplified problem is a binary programming problem that has similarities with other known combinatorial optimization problems, such as the multiple knapsack problem (see e.g. [3,4]). …”