A Binary Differential Evolution with Adaptive Parameters Applied to the Multiple Knapsack Problem

André, Leanderson; Parpinelli, Rafael Stubs

doi:10.1007/978-3-319-13650-9_6

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…The Island-inspired Genetic Algorithm [17] is a metaheuristic that uses one population of individuals as islands (island-model GA). This approach uses only one population where each individual is considered to be an island itself.…”

Section: B Island-inspired Genetic Algorithmmentioning

confidence: 99%

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The Multiple Knapsack Problem Approached by a Binary Differential Evolution Algorithm with Adaptive Parameters

André¹,

Parpinelli²

2015

Polibits

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In this paper the well-known 0-1 Multiple Knapsack Problem (MKP) is approached by an adaptive Binary Differential Evolution (aBDE) algorithm. The MKP is a NP-hard optimization problem and the aim is to maximize the total profit subjected to the total weight in each knapsack that must be less than or equal to a given limit. The aBDE self adjusts two parameters, perturbation and mutation rates, using a linear adaptation procedure that changes their probabilities at each generation. Results were obtained using 11 instances of the problem with different degrees of complexity. The results were compared using aBDE, BDE, a standard Genetic Algorithm (GA) and its adaptive version (aGA), and an island-inspired Genetic Algorithm (IGA) and its adaptive version (aIGA). The results show that aBDE obtained better results than the other algorithms. This indicates that the proposed approach is an interesting and a promising strategy to control the parameters and for optimization of complex problems.Index Terms-Adaptive parameter control, binary differential evolution, multiple knapsack problem, evolutionary computation. I. INTRODUCTIONT HE 0-1 Multiple Knapsack Problem (MKP) is a binary NP-hard combinatorial optimization problem that consists in given a set of items and a set of knapsacks, each item with a mass and a value, determine which item to include in which knapsack. The aim is to maximize the total profit subjected to the total weight in each knapsack that must be less than or equal to a given limit.Different variants of the MKP can be easily adapted to real problems, such as, capital budgeting, cargo loading and others [1]. Hence, the optimization of resource allocation is one major concern in several areas of logistics, transportation and production [2]. In this way, the search for efficient methods to achieve such optimization aims to increase profits and reduce the use of raw materials.According to the size of an instance (number of items and number of knapsacks) of the MKP, the search space can become too large to apply exact methods. Hence, a large number of heuristics and metaheuristics have been applied to the MKP. Some examples are the modified binary Manuscript

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Section: B Island-inspired Genetic Algorithmmentioning

confidence: 99%

“…The trial vector is recombined with individual i accordingly to the crossover rate (line 8-13). Finally, it is applied the bit-flip mutation using its probability (line [15][16][17][18].…”

Section: B Island-inspired Genetic Algorithmmentioning

confidence: 99%

The Multiple Knapsack Problem Approached by a Binary Differential Evolution Algorithm with Adaptive Parameters

André¹,

Parpinelli²

2015

Polibits

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Adaptation of Binary Pigeon-Inspired Algorithm for Solving Multidimensional Knapsack Problem

Bolaji¹,

Babatunde

Shola

2017

Advances in Intelligent Systems and Computing

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A Modified Binary Pigeon-Inspired Algorithm for Solving the Multi-dimensional Knapsack Problem

Bolaji

Okwonu

Shola

et al. 2020

Journal of Intelligent Systems

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AbstractThe pigeon-inspired optimization algorithm is a category of a newly proposed swarm intelligence-based algorithm that belongs to the population-based solution technique. The MKP is a class of complex optimization problems that have many practical applications in the fields of engineering and sciences. Due to the practical applications of MKP, numerous algorithmic-based methods like local search and population-based search algorithms have been proposed to solve the MKP in the past few decades. This paper proposes a modified binary pigeon-inspired optimization algorithm named (Modified-BPIO) for the 0 - 1 multidimensional knapsack problem (MKP). The utilization of the binary pigeon-inspired optimization (BPIO) for solving the multidimensional knapsack problem came with huge success. However, it can be observed that the BPIO converges prematurely due to lost diversity during the search activities. Given the above, the crossover operator is integrated with the landmark component of the BPIO to improve the diversity of the solution space. The MKP benchmarks from the Operations Research (OR) library are utilized to test the performance of the proposed binary method. Experimentally, it is concluded that the proposed Modified-BPIO has a better performance when compared with the BPIO and existing state-of-the-arts that worked on the same MKP benchmarks.

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A Binary Differential Evolution with Adaptive Parameters Applied to the Multiple Knapsack Problem

Cited by 3 publications

References 13 publications

The Multiple Knapsack Problem Approached by a Binary Differential Evolution Algorithm with Adaptive Parameters

The Multiple Knapsack Problem Approached by a Binary Differential Evolution Algorithm with Adaptive Parameters

Adaptation of Binary Pigeon-Inspired Algorithm for Solving Multidimensional Knapsack Problem

A Modified Binary Pigeon-Inspired Algorithm for Solving the Multi-dimensional Knapsack Problem

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