Binary metaheuristic algorithms for 0–1 knapsack problems: Performance analysis, hybrid variants, and real-world application

Abstract

This paper examines the performance of three binary metaheuristic algorithms when applied to two distinct knapsack problems (0–1 knapsack problems (KP01) and multidimensional knapsack problems (MKP)). These binary algorithms are based on the classical mantis search algorithm (MSA), the classical quadratic interpolation optimization (QIO) method, and the well-known differential evolution (DE). Because these algorithms were designed for continuous optimization problems, they could not be used directly to solve binary knapsack problems. As a result, the V-shaped and S-shaped transfer functions are used to propose binary variants of these algorithms, such as binary differential evolution (BDE), binary quadratic interpolation optimization (BQIO), and binary mantis search algorithm (BMSA). These binary variants are evaluated using various high-dimensional KP01 examples and compared to several classical metaheuristic techniques to determine their efficacy. To enhance the performance of those binary algorithms, they are combined with repair operator 2 (RO2) to offer better hybrid variants, namely HMSA, HQIO, and HDE. Those hybrid algorithms are evaluated using several medium- and large-scale KP01 and MKP instances, as well as compared to other hybrid algorithms, to demonstrate their effectiveness. This comparison is conducted using three performance metrics: average fitness value, Friedman mean rank, and computational cost. The experimental findings demonstrate that HQIO is a strong alternative for solving KP01 and MKP. In addition, the proposed algorithms are applied to the Merkle-Hellman Knapsack Cryptosystem and the resource allocation problem in adaptive multimedia systems (AMS) to illustrate their effectiveness when applied to optimize those real applications. The experimental findings illustrate that the proposed HQIO is a strong alternative for handling various knapsack-based applications.

Keywords

• Knapsack problems
• Repair operator 2
• Metaheuristic algorithms
• Merkle–Hellman knapsack cryptosystem