The clustered shortest-path tree problem (CluSPTP) is an extension of the classical single-source shortest-path problem, in which, given a graph with the set of nodes partitioned into a predefined, mutually exclusive and exhaustive set of clusters, we are looking for a shortest-path spanning tree from a given source to all the other nodes of the graph, with the property that each cluster should induce a connected subtree. CluSPTP belongs to the class of generalized combinatorial optimization problems, and, in general, is proved to be a non-deterministic polynomial time hard (NP-hard) problem. In this paper, we propose a novel genetic algorithm (GA), which is designed to fit the challenges of the investigated problem. The main features of our GA are: the use of an innovative representation scheme that allows us to define meaningful genetic operators and the use of a hybrid initial population. Extensive computational results are reported and discussed for two sets of instances: euclidean and non-euclidean. The performance of the proposed algorithm was evaluated on six types of benchmark euclidean instances available in the literature and on six types of non-euclidean instances obtained from the corresponding euclidean ones. The obtained results show an improvement with respect to existing methods from the literature, both in terms of the quality of the achieved solutions and the computation times necessary to obtain them. They demonstrate that our genetic algorithm outperforms all the existing methods from the literature, providing for all the existing benchmark instances the optimal solutions in all 30 independent trials.

Several iterative processes have been defined by researchers to approximate the fixed points of various classes operators. In this paper we present, by using the basins of attraction for the roots of some complex polynomials, an empirical comparison of some iteration procedures for fixed points approximation of Newton’s iteration operator. Some numerical results are presented. The Matlab m-files for generating the basins of attraction are presented, too.

This paper deals with the two-stage transportation problem with fixed charges, denoted by TSTPFC. We propose a fast solving method, designed for parallel environments, that allows solving real-world applications efficiently. The proposed constructive heuristic algorithm is iterative and its primary feature is that the solution search domain is reduced at each iteration. Our achieved computational results were compared with those of the existing solution approaches. We tested the method on two sets of instances available in literature. The outputs prove that we have identified a very competitive approach as compared to the methods than one can find in literature.

This paper deals with a complex optimization problem, more specifically the two-stage transportation problem with fixed costs. In our investigated transportation problem, we are modeling a distribution network in a two-stage supply chain. The considered two-stage supply chain includes manufacturers, distribution centers, and customers, and its principal feature is that in addition to the variable transportation costs, we have fixed costs for the opening of the distribution centers, as well as associated with the routes. In this paper, we describe a different approach for solving the problem, which is an effective hybrid genetic algorithm. Our proposed hybrid genetic algorithm is constructed to fit the challenges of the investigated supply chain network design problem, and it is achieved by incorporating a linear programming optimization problem within the framework of a genetic algorithm. Our achieved computational results are compared with the existing solution approaches on a set of 150 benchmark instances from the literature and on a set of 50 new randomly generated instances of larger sizes. The outputs proved that we have developed a very competitive approach as compared to the methods that one can find in the literature.

This paper concerns the two-stage transportation problem with fixed charges associated to the routes and proposes an efficient multi-start Iterated Local Search (ILS) procedure for the total distribution costs minimization. Our heuristic approach constructs an initial solution, uses a local search procedure to increase the exploration, a perturbation mechanism and a neighborhood operator in order to diversify the search. Computational experiments were performed on two sets of instances: one that consists of 20 benchmark instances available in the literature and a second one that contains 10 new randomly generated larger instances. The achieved computational results prove that our proposed solution approach is highly competitive in comparison with the existing approaches from the literature.