Edna Ayako Hoshino

A branch-and-cut-and-price approach for the capacitated m-ring-star problem

The capacitated m-ring-star problem is a variant of the classical one-depot capacitated vehicle routing problem in which a customer is either on a route or is connected to another customer or to some Steiner point present in a route. We develop a new exact algorithm for this problem using a branch-and-cut-and-price approach and compare its performance with that of a branch-and-cut algorithm proposed earlier in the literature. Computational results show that the new algorithm outperforms the branch-and-cut one in many instance classes.

A branch-and-price approach for the partition coloring problem

This work proposes a new integer programming model for the partition coloring problem and a branch-and-price algorithm to solve it. Experiments are reported for random graphs and instances originating from routing and wavelength assignment problems arising in telecommunication network design. We show that our method largely outperforms previously existing approaches.

Column Generation Algorithms for the Capacitated m-Ring-Star Problem

In this paper we propose an integer programming formulation for the capacitated m-ring-star problem ( ) based on a set coveringmodel and develop an exact branch-and-price( ) algorithm to solve it exactly. The is a variant of the classical one-depot capacitated vehicle routing problem in which a customer is either on a route or is connected to another customer or to some connection pointpresent in a route. The set of potential connection points and the number mof vehicles are given a priori. Routing and connection costs are also known and the goal is to minimize the sum of routing and connection costs. To our knowledge, the only exact approach for the is a branch-and-cut( ) proposed in [2]. Extensive experimentation reported here shows that our algorithm is competitive with the algorithm. This performance was achieved after a profound investigation of the alternatives for column generation relaxation and a careful implementation of the pricing algorithm.

A Branch-and-Cut-and-Price Approach for the Capacitated m-Ring-Star Problem

Abstract The Capacitated m-ring-star Problem is a variant of the classical one-depot capacitated vehicle routing problem in which a customer is either on a route or is connected to another customer or to some Steiner point present in a route. We develop a new exact algorithm for this problem using a branch-and-cut-and-price approach and compare its performance with that of a branch-and-cut algorithm proposed earlier in the literature. Computational results show that the new algorithm outperforms the branch-and-cut one in many instance classes.

The Ring Tree Facility Location Problem

Abstract In this work we discuss a facility location variant of the capacitated ring tree problem. The new model generalizes vehicle routing problems and Steiner tree problems, yielding applicability in telecommunication and transportation networks. In this ring tree facility location problem (RTFLP) two layers of networks have to be designed to connect two different types of customers to a central depot. The first, or inner layer, consists of cycles that intersect in the depot and collect all type 2 customers, and some of the type 1 customers. An outer layer is represented by a forest that contains the remaining type 1 customers such that each tree shares exactly one vertex with the inner layer. Capacity bounds apply to the number of connected substructures emanating from the depot, the number of customers in each of these so-called ring trees, and in each tree of the forest. Additional optional Steiner vertices can be used to reduce the overall costs, which are layer-dependent edge costs and facility location costs at the vertices in which the two layers coincide. Our contribution is the introduction of the RTFLP, the development of two mathematical formulations, and preliminary computational results for the first RTFLP test set derived from instances from the literature.

Algorithms for Computing the Family-Free Genomic Similarity Under DCJ

The genomic similarity is a large-scale measure for comparing two given genomes. In this work we study the (NP-hard) problem of computing the genomic similarity under the DCJ model in a setting that does not assume that the genes of the compared genomes are grouped into gene families. This problem is called family-free DCJ similarity. Here we propose an exact ILP algorithm to solve it, we show its APX-hardness, and we present three combinatorial heuristics, with computational experiments comparing their results to the ILP. Experiments on simulated datasets show that the proposed heuristics are very fast and even competitive with respect to the ILP algorithm for some instances.

Pricing strategies for capacitated ring-star problems based on dynamic programming algorithms

Abstract The Capacitated m-Ring-Star Problem ( crsp ) is the problem of designing a set of rings that pass through a central depot and through some transition points and/or customers, and then assigning each nonvisited customer to a visited point or customer. The number of customers visited and connected to a ring is bounded by an upper limit: the capacity of the ring. The objective is to minimize the total routing cost plus assignment costs. The problem has several applications in telecommunication network design and transportation planning. In addition, closely related versions to the crsp involving different graph topologies and objective functions have been recently studied by several authors. The recent literature shows that effective methods for solving these class of difficult optimization problems are based on the combination of column-and-cut generation techniques. In particular, the effectiveness of these methods strongly depend on the qualities and complexities of the associated pricing problems. In this paper, we investigate different pricing strategies based on dynamic programming algorithms for the crsp that can also be adapted to deal with different graph topologies. We describe a general bounding procedure based on column-and-cut generation that is used to test the effectiveness of the different pricing strategies. We report an extensive computational analysis on crsp benchmark instances from the literature and on newly generated instances for its generalization to the multi-depot case, the Multi-Depot Ring-Star Problem ( mdrsp ). The results obtained show the effectiveness of the pricing strategies proposed and that tight lower bounds can be computed for instances involving up to 431 nodes.

Heuristic approaches to the Distinguishing Substring Selection Problem

Abstract The Distinguishing Substring Selection Problem aims to find a target string close to all strings in a given set of good strings and far enough of strings in another set of bad strings. This problem has applications in bioinformatics and it is related to the closest substring problem and other string selection problems. In this work, we investigate two heuristics for the problem based on rounding procedures and variable neighborhood search approaches. Both heuristics consider the solution of the linear relaxation of an integer programming formulation for the problem as an initial solution. We conducted computational experiments in three groups of instances. The rounding procedure provides good solutions and the VNS improves these results using different rounding procedures as neighborhood structures. To the best of our knowledge, this is the first paper that provides computational results for the problem.

Computing the family-free DCJ similarity

BackgroundThe genomic similarity is a large-scale measure for comparing two given genomes. In this work we study the (NP-hard) problem of computing the genomic similarity under the DCJ model in a setting that does not assume that the genes of the compared genomes are grouped into gene families. This problem is called family-free DCJ similarity.ResultsWe propose an exact ILP algorithm to solve the family-free DCJ similarity problem, then we show its APX-hardness and present four combinatorial heuristics with computational experiments comparing their results to the ILP.ConclusionsWe show that the family-free DCJ similarity can be computed in reasonable time, although for larger genomes it is necessary to resort to heuristics. This provides a basis for further studies on the applicability and model refinement of family-free whole genome similarity measures.

The minimum cut cover problem

Abstract We studied the minimum cut cover problem that consists in finding a minimum cardinality family of cuts C of a graph G such that each edge of G belongs to at least one cut C ∈ C . This problem is NP -hard and arises in fault testing and diagnosis, pattern recognition, and biological identification. We propose here a new integer programming formulation and a new exact algorithm for the problem. We also proposed a simple heuristic and made empirical experiments to compare it with those reported in the literature. It is an ongoing work. The preliminary results show that the dual bounds provided by the new formulation are tighter than those obtained using the earlier one and the primal bounds given by our heuristic are near optimal for the small instances and tighter than other reported in the literature.