A hybrid genetic algorithm for the degree-constrained minimum spanning tree problem

• Published in: Soft computing (Berlin, Germany) Vol. 24; no. 3; pp. 2169 - 2186
• Main Authors: Singh, Kavita, Sundar, Shyam
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2020; Springer Nature B.V
• Subjects: Artificial Intelligence; Computational Intelligence; Constraints; Control; Engineering; Genetic algorithms; Graph theory; Heuristic; Heuristic methods; Integers; Mathematical Logic and Foundations; Mechatronics; Methodologies and Application; Mutation; Optimization; Random variables; Robotics; Search methods; Search process; Local search; Steady-state genetic algorithm; Problem-specific crossover operator; Replacement strategy; Spanning tree; Degree-constrained
• ISSN: 1432-7643; 1433-7479
• DOI: 10.1007/s00500-019-04051-x

Given an undirected, connected, edge-weighted graph G and a positive integer d , the degree-constrained minimum spanning tree (dc-MST) problem aims to find a minimum spanning tree T on G subject to the constraint that each vertex is either a leaf vertex or else has degree at most d in T , where d is a given positive integer. The dc-MST is NP -hard problem for d ≥ 2 and finds several real-world applications. This paper proposes a hybrid approach ( H SSGA) combining a steady-state genetic algorithm and local search strategies for the this problem. An additional step (based on perturbation strategy at a regular interval of time) in the replacement strategy is applied in order to maintain diversity in the population throughout the search process. On a set of available 107 benchmark instances, computational results show the superiority of our proposed H SSGA in comparison with the state-of-the-art metaheuristic techniques.