Ant System for the k-Cardinality Tree Problem

Abstract

Abstract. This paper gives an algorithm for finding the minimum weight tree having k edges in an edge weighted graph. The algorithm combines a search and optimization technique based on pheromone with a weight based greedy local optimization. Experimental results on a large set of problem instances show that this algorithm matches or surpasses other algorithms including an ant colony optimization algorithm, a tabu search algorithm, an evolutionary algorithm and a greedy-based algorithm on all but one of the 138 tested instances.

A new hybrid evolutionary algorithm for the huge k -cardinality tree problem

“…We applied our algorithm to 12 of the edge-weighted graphs from the benchmark set by Blum and Blesa [4], and compared the results to the current state-of-the-art algorithm for this benchmark set, that is, an ant colony optimization approach (denoted by ACO) by Bui and Sundarraj [10]. The results are shown in Tables 2 to 13.…”

“…However, the interest in heuristics was quickly lost and research focused on the development of more appealing metaheuristics [6]. Among these, the different versions of variable neighborhood search (VNS) proposed in [27] can be regarded as state-of-the-art for the benchmark instance set proposed in the same paper, and the ant colony optimization (ACO) approach proposed in [10] is currently state-of-the-art for the benchmark instance set proposed in [4]. Much less research efforts were directed at the node weighted KCT problem.…”

LS(Graph): a constraint-based local search for constraint optimization on trees and paths

“…Most of these COT/COP problems are NP-hard. They are often approached by dedicated algorithms including exact methods, such as the Lagrangian-based heuristic [7], the ILP-based algorithm using directed cuts [25], the Lagrangian-based branch and bound in [15], and the vertex labeling algorithm from [30]; there are also meta-heuristic algorithms such as a hybrid evolutionary algorithm [19], ant colony optimization [21], and local search [20]. These techniques exploit the structure of the constraints and the objective functions but are often difficult to extend or reuse.…”

Combining Ant Colony Optimization with Dynamic Programming for Solving the k-Cardinality Tree Problem

“…The edge-weighted version of the KCT problem was first tackled by exact approaches [14,8,17] and heuristics [12,11,8]. Soon, the research focused on the development of more appealing metaheuristics: two evolutionary computation approaches [1,4], three tabu search methods [2,15,4], different variations of variable neighborhood search (VNS) [18] and two ant colony optimization (ACO) approaches [7,4]. Two sets of benchmark instances exist: one was introduced for the empirical evaluation of the VNS-based approaches in [18], and the other one for the metaheuristics proposed in [4].…”

“…Two sets of benchmark instances exist: one was introduced for the empirical evaluation of the VNS-based approaches in [18], and the other one for the metaheuristics proposed in [4]. The variable neighborhood decomposition search (VNDS) algorithm proposed in [18] is the state-of-the-art method for the first set, and the ACO algorithm proposed in [7] is so for the second set.…”