Abstract
Degree constrained minimum spanning tree (DCMST) refers to constructing a spanning tree of minimum weight in a complete graph with weights on edges while the degree of each node in the spanning tree is no more thand(d≥ 2). The paper proposes an improved multicolony ant algorithm for degree constrained minimum spanning tree searching which enables independent search for optimal solutions among various colonies and achieving information exchanges between different colonies by information entropy. Local optimal algorithm is introduced to improve constructed spanning tree. Meanwhile, algorithm strategies in dynamic ant, random perturbations ant colony, and max-min ant system are adapted in this paper to optimize the proposed algorithm. Finally, multiple groups of experimental data show the superiority of the improved algorithm in solving the problems of degree constrained minimum spanning tree.
Highlights
Minimum spanning tree (MST) is a classic combinatorial optimization problem
It is a problem of so-called degree-constrained minimum spanning tree (DCMST)
Randomized primal method (RPM) [12], which is a dynamic table structure, integrated multistart hill-climbing (MHC) [14], stimulated annealing (SA), and genetic algorithm (GA) [12, 13] and the node weight information as a whole was presented by Knowles to find the optimal solutions of DCMST
Summary
Minimum spanning tree (MST) is a classic combinatorial optimization problem. Many engineering problems in common cases, for example, pipeline, circuit design, and transportation network, can be transformed into minimum spanning tree. For instance, genetic algorithms, simulated annealing algorithm, and ant colony algorithm, have been a research focus to generate acceptable solutions in a valid time Among these modern optimization algorithms, ant colony algorithm comes as a novel bionics algorithm and converges to the shortest path by information transferring and updating among ants. Algorithms that employ multicolony ant algorithm will converge in a shorter period of time compared to those applied with single colony but feature the same ant population in total especially when the problem is in large scale Taking all these factors into account, Mathematical Problems in Engineering the paper proposes a degree-constrained minimum spanning tree based on improved multiant colonies. The tabu list is applied in case of local circling while random disturbance factor is set here to increase the possibility of selection among different paths so as to promote objective and diverse solutions
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