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On Solving 0/1 Multidimensional Knapsack Problem with a Genetic Algorithm Using a Selection Operator Based on K-Means Clustering Principle

Laabadi Soukaina, Naimi Mohamed, Amri Hassan El, Achchab Boujemâa

Foundations of Computing and Decision Sciences

2022

Vol. 47, No. 3

247--269

The growing need for profit maximization and cost minimization has made the optimization field very attractive to both researchers and practitioners. In fact, many authors were interested in this field and they have developed a large number of optimization algorithms to solve either academic or real-life problems. Among such algorithms, we cite a well-known metaheuristic called the genetic algorithm. This optimizer tool, as any algorithm, suffers from some drawbacks; like the problem of premature convergence. In this paper, we propose a new selection strategy hoping to avoid such a problem. The proposed selection operator is based on the principle of the k-means clustering method for the purpose of guiding the genetic algorithm to explore different regions of the search space. We have elaborated a genetic algorithm based on this new selection mechanism. We have then tested our algorithm on various data instances of the 0/1 multidimensional knapsack problem. The obtained results are encouraging when compared with those reached by other versions of genetic algorithms and those reached by an adapted version of the particle swarm optimization algorithm.

Supplementary crossover operator for genetic algorithms based on the center-of-gravity paradigm

Angelov P.

Control and Cybernetics

2001

Vol. 30, no 2

159-176

A supplementary crossover operator for genetic algorithms (GA) is proposed in the paper. It performs specific breeding between the two fittest parental chromosomes. The new child chromosome is based on the center of gravity (CoG) paradigm, taking into account both the parental weights (measured by their fitness) and their actual value. It is designed to be used in combination with other crossover and mutation operators (it applies to the best fitted two parental chromosomes only) both in binary and real-valued (evolutionary) GA. Analytical proof of its ability to improve the result is provided for the simplest case of one variable and when the elitist selection strategy is used. The new operator is validated with a number of usually used numerical test functions as well as with a practical example of supply air temperature and flow rate scheduling in a hollow core ventilated slab thermal storage system. The tests indicate that it improves results (the speed of convergence as well as the final result) without a significant increase in computational expenses.