Evaluating the impact of different types of crossover and selection methods on the convergence of 0/1 Knapsack using Genetic Algorithm

TL;DR

This paper evaluates how different crossover and selection methods in Genetic Algorithms affect convergence speed in solving the 0/1 knapsack problem, finding the most efficient combination for faster solutions.

Contribution

It systematically compares various crossover and selection methods in Genetic Algorithms specifically for the 0/1 knapsack problem, identifying the most effective combination.

Findings

One point crossover with tournament selection yields the fastest convergence.

Different method combinations significantly affect the efficiency of solving 0/1 knapsack.

The study provides insights into optimizing Genetic Algorithm parameters for combinatorial problems.

Abstract

Genetic Algorithm is an evolutionary algorithm and a metaheuristic that was introduced to overcome the failure of gradient based method in solving the optimization and search problems. The purpose of this paper is to evaluate the impact on the convergence of Genetic Algorithm vis-a-vis 0/1 knapsack. By keeping the number of generations and the initial population fixed, different crossover methods like one point crossover and two-point crossover were evaluated and juxtaposed with each other. In addition to this, the impact of different selection methods like rank-selection, roulette wheel and tournament selection were evaluated and compared. Our results indicate that convergence rate of combination of one point crossover with tournament selection, with respect to 0/1 knapsack problem that we considered, is the highest and thereby most efficient in solving 0/1 knapsack.