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Keywords = multi-demand multidimensional knapsack problem

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26 pages, 2233 KB  
Article
Exploring the Impact of Local Operator Configurations in the Multi-Demand Multidimensional Knapsack Problem
by José García, Ivo Cattarinich, Paola Moraga and Hernan Pinto
Appl. Sci. 2025, 15(4), 2059; https://doi.org/10.3390/app15042059 - 16 Feb 2025
Cited by 2 | Viewed by 948
Abstract
The Multi-demand Multidimensional Knapsack Problem (MDMKP) is a challenging combinatorial task due to its capacity and demand constraints. Local search operators play a key role in metaheuristics when navigating such complex solution spaces, yet their impact on MDMKP performance has received limited attention. [...] Read more.
The Multi-demand Multidimensional Knapsack Problem (MDMKP) is a challenging combinatorial task due to its capacity and demand constraints. Local search operators play a key role in metaheuristics when navigating such complex solution spaces, yet their impact on MDMKP performance has received limited attention. In this work, we investigate four local operator configurations—Add, Drop, Swap, and All Operator—within the Whale Optimization Algorithm framework. Our approach integrates these operators to broaden search coverage and refine candidate solutions. This design aims to enhance solution quality by balancing exploration and exploitation across multiple dimensions of the MDMKP. Experimental results on benchmark instances with different sizes (n=100,250, and 500) show that the All Operator configuration consistently achieves better maximum and average values. In large-scale instances (n = 500), the “All Operator” configuration achieves an average maximum value of 107,967, which is approximately 1.4% higher than the 106,490 achieved by the “Add Operator” and about 0.2% higher than the 107,771 obtained by the “Swap Operator”, while significantly outperforming the “Drop Operator” (average maximum of 99,164). Statistical tests confirm its advantage over the other configurations, suggesting that combining multiple local operators can significantly strengthen performance in high-dimensional and constraint-heavy settings like the MDMKP. Full article
(This article belongs to the Special Issue Novel Research and Applications on Optimization Algorithms)
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20 pages, 415 KB  
Article
Binarization Technique Comparisons of Swarm Intelligence Algorithm: An Application to the Multi-Demand Multidimensional Knapsack Problem
by José García, Paola Moraga, Broderick Crawford, Ricardo Soto and Hernan Pinto
Mathematics 2022, 10(17), 3183; https://doi.org/10.3390/math10173183 - 3 Sep 2022
Cited by 3 | Viewed by 1930
Abstract
In order to minimize execution times, improve the quality of solutions, and address more extensive target situations, optimization techniques, particularly metaheuristics, are continually improved. Hybridizing procedures are one of these noteworthy strategies due to their wide range of applications. This article describes a [...] Read more.
In order to minimize execution times, improve the quality of solutions, and address more extensive target situations, optimization techniques, particularly metaheuristics, are continually improved. Hybridizing procedures are one of these noteworthy strategies due to their wide range of applications. This article describes a hybrid algorithm that combines the k-means method to produce a binary version of the cuckoo search and sine cosine algorithms. The binary algorithms are applied on the NP-hard multi-demand multidimensional knapsack problem. This problem is of particular interest because it has two types of constraints. The first group of constraints is related to the capacity of the knapsacks, and a second type is associated with the demand that must be met. Experiments were undertaken to acquire insight into the contribution of the k-means technique and the local search operator to the final results. Additionally, a comparison is made with two other types of binarization, the first based on a random method and the second based on the percentile concept. The results reveal that the k-means hybrid algorithm consistently provides superior results in most cases studied. In particular, incorporating the local search operator improved the results by an average of 0.23%. On the other hand, when comparing the results with 100 items and 30-30 restrictions, k-means was 1.06% better on average than the random operator. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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