José A. Iranzo

An efficient evolutionary algorithm for the ring star problem

This paper addresses the ring star problem (RSP). The goal is to locate a cycle through a subset of nodes of a network aiming to minimize the sum of the cost of installing facilities on the nodes on the cycle, the cost of connecting them and the cost of assigning the nodes not on the cycle to their closest node on the cycle. A fast and efficient evolutionary algorithm is developed which is based on a new formulation of the RSP as a bilevel programming problem with one leader and two independent followers. The leader decides which nodes to include in the ring, one follower decides about the connections of the cycle and the other follower decides about the assignment of the nodes not on the cycle. The bilevel approach leads to a new form of chromosome encoding in which genes are associated to values of the upper level variables. The quality of each chromosome is evaluated by its fitness, by means of the objective function of the RSP. Hence, in order to compute the value of the lower level variables, two optimization problems are solved for each chromosome. The computational results show the efficiency of the algorithm in terms of the quality of the solutions yielded and the computing time. A study to select the best configuration of the algorithm is presented. The algorithm is tested on a set of benchmark problems providing very accurate solutions within short computing times. Moreover, for one of the problems a new best solution is found. 2013 Elsevier B.V. All rights reserved.

Algorithms for the quickest path problem and the reliable quickest path problem

The quickest path problem consists of finding a path in a directed network to transmit a given amount of items from an origin node to a destination node with minimal transmission time, when the transmission time depends on both the traversal times of the arcs, or lead time, and the rates of flow along arcs, or capacity. In telecommunications networks, arcs often also have an associated operational probability of the transmission being fault free. The reliability of a path is defined as the product of the operational probabilities of its arcs. The reliability as well as the transmission time are of interest. In this paper, algorithms are proposed to solve the quickest path problem as well as the problem of identifying the quickest path whose reliability is not lower than a given threshold. The algorithms rely on both the properties of a network which turns the computation of a quickest path into the computation of a shortest path and the fact that the reliability of a path can be evaluated through the reliability of the ordered sequence of its arcs. Other constraints on resources consumed, on the number of arcs of the path, etc. can also be managed with the same algorithms.

An improved evolutionary algorithm for the two-stage transportation problem with fixed charge at depots

This paper addresses a two-stage transportation problem with a fixed charge at depots. The goal is to determine the best way of delivering a commodity from a set of plants to a set of customers with known demand using a set of potential depots as intermediate transshipment points, while minimizing the overall costs incurred. These costs refer to fixed costs arising from using the depots and to variable shipping costs. To solve the problem, a hybrid evolutionary algorithm is developed which combines the control by the chromosomes of which depots to open with the use of optimization techniques to associate a feasible solution to each chromosome. The computational results show the efficiency of the algorithm in terms of the quality of the solutions yielded and the computing time.

The energy-constrained quickest path problem

This paper addresses a variant of the quickest path problem in which each arc has an additional parameter associated to it representing the energy consumed during the transmission along the arc while each node is endowed with a limited power to transmit messages. The aim of the energy-constrained quickest path problem is to obtain a quickest path whose nodes are able to support the transmission of a message of a known size. After introducing the problem and proving the main theoretical results, a polynomial algorithm is proposed to solve the problem based on computing shortest paths in a sequence of subnetworks of the original network. In the second part of the paper, the bi-objective variant of this problem is considered in which the objectives are the transmission time and the total energy used. An exact algorithm is proposed to find a complete set of efficient paths. The computational experiments carried out show the performance of both algorithms.

MEALS: A multiobjective evolutionary algorithm with local search for solving the bi-objective ring star problem☆

In this paper we develop a hybrid metaheuristic for approaching the Pareto front of the bi-objective ring star problem. This problem consists of finding a simple cycle (ring) through a subset of nodes of a network. The aim is to minimize both the cost of connecting the nodes in the ring and the cost of allocating the nodes not in the ring to nodes in the ring. The algorithm preserves the general characteristics of a multiobjective evolutionary algorithm and embeds a local search procedure which deals with multiple objectives. The encoding scheme utilized leads to solving a Traveling Salesman Problem in order to compute the ring associated with the chromosome. This allows the algorithm to implicitly discard feasible solutions which are not efficient. The algorithm also includes an ad-hoc initial population construction which contributes to diversification. Extensive computational experiments using benchmark problems show the performance of the algorithm and reveal the noteworthy contribution of the local search procedure.

Dealing with residual energy when transmitting data in energy-constrained capacitated networks

Abstract This paper addresses several problems relating to the energy available after the transmission of a given amount of data in a capacitated network. The arcs have an associated parameter representing the energy consumed during the transmission along the arc and the nodes have limited power to transmit data. In the first part of the paper, we consider the problem of designing a path which maximizes the minimum of the residual energy remaining at the nodes. After formulating the problem and proving the main theoretical results, a polynomial time algorithm is proposed based on computing maxmin paths in a sequence of non-capacitated networks. In the second part of the paper, the problem of obtaining a quickest path in this context is analyzed. First, the bi-objective variant of this problem is considered in which we aim to minimize the transmission time and to maximize the minimum residual energy. An exact polynomial time algorithm is proposed to find a minimal complete set of efficient solutions which amounts to solving shortest path problems. Second, the problem of computing an energy-constrained quickest path which guarantees at least a given residual energy at the nodes is reformulated as a variant of the energy-constrained quickest path problem. The algorithms are tested on a set of benchmark problems providing the optimal solution or the Pareto front within reasonable computing times.

A matheuristic for the two-stage fixed-charge transportation problem

Abstract This paper addresses the two-stage fixed-charge transportation problem which involves the distribution of a commodity from plants to customers through intermediate depots, while minimizing the overall costs incurred. There are two costs associated with each arc: a fixed cost for the use of the arc, and a variable cost proportional to the number of units sent along the arc. First, we prove some theoretical properties which extend well-known results of the fixed-charge transportation problem. Then, we present a matheuristic that uses an evolutionary algorithm and exploits these properties to guide the algorithm towards better solutions. The chromosome of the evolutionary algorithm controls the arcs that can be used in the delivery. Its fitness is computed as the objective function value of a feasible solution of the problem, which is obtained by applying optimization techniques. The computational results show the effectiveness of the algorithm.

An Evolutionary Algorithm for the Biobjective Capacitated m-Ring Star Problem

This paper addresses the biobjective capacitated m-ring star problem. The problem consists of finding a set of m simple cycles rings through a subset of nodes of a network. The network consists of a distinguished node called the depot and two different kinds of nodes, the customers and the transition points. Each ring contains the depot, a number of customers and some transition points. The customers not in any ring are directly connected to nodes in the rings. The rings must be node-disjoint and the total number of customers in a ring or connected to a ring is limited by the capacity of the ring. The aim is to minimize two objective functions, one referring to the cost due to the links of the rings and the other referring to the cost of allocating customers to nodes in the ring. An evolutionary algorithm is developed to approximate the Pareto front. The algorithm combines standard characteristics of evolutionary algorithms with the use of a heuristic to construct feasible solutions to the problem. A computational experiment is carried out using benchmark instances to show the performance of the algorithm.