The classical 0-1 knapsack problem is one of the more studied combinatorial optimization problem which belong to the NP class of algorithms. A number of its generalized forms have been addressed by various researchers using different designing techniques. In this paper, we design and analyze the Multiple Knapsack Problems (MKP) by using genetic algorithms. A modified Genetic Algorithm (mGA) is developed with the key focus on efficient encoding scheme for binary string representation and a competent dynamic programming based method for initial population generation. Furthermore transposition is applied in mGA instead of crossover for maintaining the population diversity. Performance analysis of the mGA, justifies our claims that the population incorporates adequate quality and diversity to reach a near optimal solution and transposition reduces the overall computation time.
Abstract-The Generalized Travelling Salesman Problem (GTSP) is a special instance of the well-known travelling salesman problem which belongs to NP-hard class of problems. In the GTSP problem which is being addressed in this research we split the set of nodes (e.g. cities) into non-overlapping subsets; where the optimal solution is a minimum cost tour visiting exactly one node from each subset. In this paper a genetic algorithm with new and innovative way of generating initial population is presented. Concepts like cluster segmentation, partially greedy crossover, greedy insert mutation and enhanced swap mechanisms are also introduced. An initial analysis of the proposed algorithm shows enhanced results in terms of optimality and computational time as compared to existing approaches.Index Terms-Generalized travelling salesman problem, genetic algorithms, greedy insert mutation, partially greedy crossover.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.