Eduardo G. Pardo

Variable Formulation Search for the Cutwidth Minimization Problem

Many optimization problems are formulated as min-max problems where the objective function consist of minimizing a maximum value. In this case, it is usual that many solutions of the problem has associated the same value of the objective function. When this happens it is difficult to determine which solution is more promising to continue the search. In this paper we propose a new variant of the Variable Neighbourhood Search methodology to tackle this kind of problems. The new variant, named Variable Formulation Search, makes use of alternative formulations of the problem to determine which solution is more promising when they have the same value of the objective function in the original formulation. We do that in shaking, local search and neighbourhood change steps of the basic Variable Neighbourhood Search. We apply the new methodology to the Cutwidth Minimization Problem. Computational results show that our proposal outperforms previous algorithms in the state of the art in terms of quality and computing time.

Linguistic description of traffic in a roundabout

The linguistic description of a physical phenomenon is a summary of the available information where certain relevant aspects are remarked while other irrelevant aspects remain hidden. This paper deals with the development of computational systems capable to generate linguistic descriptions from images captured by a video camera. The problem of linguistically labeling images in a database is a challenge where still much work remains to be done. In this paper, we contribute to this field using a model of the observed phenomenon that allows us to interpret the content of images. We build the model by combining techniques from Computer Vision with ideas from the Zadehs Computational Theory of Perceptions. We include a practical application consisting of a computational system capable to provide a linguistic description of the behavior of traffic in a roundabout.

Branch and bound for the cutwidth minimization problem

The cutwidth minimization problem consists of finding a linear arrangement of the vertices of a graph where the maximum number of cuts between the edges of the graph and a line separating consecutive vertices is minimized. We first review previous approaches for special classes of graphs, followed by lower bounds and then a linear integer formulation for the general problem. We then propose a branch-and-bound algorithm based on different lower bounds on the cutwidth of partial solutions. Additionally, we introduce a Greedy Randomized Adaptive Search Procedure (GRASP) heuristic to obtain good initial solutions. The combination of the branch-and-bound and GRASP methods results in optimal solutions or a reduced relative gap (difference between upper and lower bounds) on the instances tested. Empirical results with a collection of previously reported instances indicate that the proposed algorithm is able to solve all the small instances (up to 32 vertices) as well as some of the large instances tested (up to 158 vertices) using less than 30 minutes of CPU time. We compare the results of our method with previous lower bounds, and with the best previous linear integer formulation solved using Cplex. Both comparisons favor the proposed procedure.

Variable Neighborhood Search strategies for the Order Batching Problem

The Order Batching Problem is an optimization problem belonging to the operational management aspect of a warehouse. It consists of grouping the orders received in a warehouse (each order is composed by a list of items to be collected) in a set of batches in such a way that the time needed to collect all the orders is minimized. Each batch has to be collected by a single picker without exceeding a capacity limit. In this paper we propose several strategies based on the Variable Neighborhood Search methodology to tackle the problem. Our approach outperforms, in terms of quality and computing time, previous attempts in the state of the art. These results are confirmed by non-parametric statistical tests. HighlightsWe address the Order Batching Problem (OBP).We implement a two-stage Variable Neighborhood Search to tackle the OBP.We develop several mechanisms that can be helpful in similar problem.We additionally propose an improved Combined routing strategy.We perform computational experiments that show the superiority of our proposal.

Parallel variable neighborhood search for the min–max order batching problem

Warehousing is a key part of supply chain management. It primarily focuses on controlling the movement and storage of materials within a warehouse and processing the associated transactions, including shipping, receiving, and picking. From the tactical point of view, the main decision is the storage policy, that is, to decide where each product should be located. Every day a warehouse receives several orders from its customers. Each order consists of a list of one or more items that have to be retrieved from the warehouse and shipped to a specific customer. Thus, items must be collected by a warehouse operator. We focus on situations in which several orders are put together into batches, satisfying a fixed capacity constraint. Then, each batch is assigned to an operator, who retrieves all the items included in those orders grouped into the corresponding batch in a single tour. The objective is then to minimize the maximum retrieving time for any batch. In this paper, we propose a parallel variable neighborhood search algorithm to tackle the so-called min–max order batching problem. We additionally compare this parallel procedure with the best previous approach. Computational results show the superiority of our proposal, confirmed with statistical tests.

General Variable Neighborhood Search for the Order Batching and Sequencing Problem

Abstract Warehousing has been found as an essential issue by the industry in the last few years, being a key part of the supply chain management. It mainly focuses its attention on moving and storing materials in warehouses by performing different activities such as shipping, receiving, and picking operations. The profits obtained by warehouse management systems strongly depends on how customer orders, containing a set of goods, are collected. This picking process consists in collecting goods (items) before shipment to satisfy the orders of the customers. The Order Batching and Sequencing Problem (OBSP) involves the process of collecting orders in a warehouse by grouping orders into batches with a maximum fixed capacity. In the context of the OBSP, each order has a certain due date, i.e., it must be collected before a specific time. Otherwise, it has associated a tardiness penalty. The problem then consists in grouping orders into batches, sequencing the batches and finding a route to collect each batch, in such a way that the total tardiness is minimized. In this paper we propose a heuristic approach based on the Variable Neighborhood Search methodology to address the problem. Additionally, we provide an extensive experimental comparison between our procedure and the best previous method found in the related literature. The experimentation reveals that our algorithm improves the state of the art in both, quality and computing time. This fact is finally confirmed by non-parametric statistical tests.

General Variable Neighborhood Search applied to the picking process in a warehouse

Abstract The order batching problem is a part of the picking process of items in a warehouse. A set of items conform an order and a set of orders conform a batch. The problem consist of grouping the orders received in the warehouse in different batches. Each batch have to be collected by a single picker without exceed a capacity limit. The objective is to minimize the total time needed to collect all the items. In this paper we propose a General Variable Neighborhood Search algorithm to tackle the problem. Our approach outperforms other previous methods in the state of the art.

Embedding signed graphs in the line

Signed graphs are graphs with an assignment of a positive or a negative sign to each edge. These graphs are helpful to represent different types of networks. For instance, they have been used in social networks, where a positive sign in an edge represents friendship between the two endpoints of that edge, while a negative sign represents enmity. Given a signed graph, an important question is how to embed such a graph in a metric space so that in the embedding every vertex is closer to its positive neighbors than to its negative ones. This problem is known as Sitting Arrangement (SA) problem and it was introduced by Kermarrec et al. (Proceedings of the 36th International Symposium on Mathematical Foundations of Computer Science (MFCS), pp. 388–399, 2011). Cygan et al. (Proceedings of the 37th International Symposium on Mathematical Foundations of Computer Science (MFCS), 2012) proved that the decision version of SA problem is NP-Complete when the signed graph has to be embedded into the Euclidean line. In this work, we study the minimization version of SA (MinSA) problem in the Euclidean line. We relate MinSA problem to the well known quadratic assignment (QA) problem. We establish such a relation by proving that local minimums in MinSA problem are equivalent to local minimums in a particular case of QA problem. In this document, we design two heuristics based on the combinatorial structure of MinSA problem. We experimentally compare their performances against heuristics designed for QA problem. This comparison favors the proposed heuristics.

Automatic cognate identification based on a fuzzy combination of string similarity measures

Cognates are words in different languages that have similar spelling and meaning. The identification of cognates is very useful for many different Natural Language Processing tasks, and also in the process of learning a second language. This paper presents a new approach to classify pairs of words into cognates/false friends or not related classes. The proposed approach uses a fuzzy system to combine complementary string similarity measures in order to improve the cognate identification task. The underlying hypothesis is that the combination of different string measures by applying heuristic knowledge, can outperform those measures working separately. The results obtained by the proposed system confirm the previous hypothesis, and furthermore it also outperforms other systems that combine string measures by using a supervised approach. As an additional contribution, we have created a bilingual test data set which include pairs of cognates, false friends and unrelated words in Spanish and English, that is freely available for research purposes.

A variable neighborhood search approach for the crew pairing problem

Abstract In this paper we propose a Variable Neighborhood Search approach for the Crew Pairing Problem. This problem consist in assigning a crew to each of the flights of a flight scheduling, in a predefined time horizon. The main objective of the problem is to minimize the number of cabin crews needed to cover all the flights subject to a set of constraints. These constraints are real-life specifications regulated by airline rules and other operational challenges. In particular we propose a General Variable Neighborhood Search algorithm to tackle the problem and we have tested our approach over a real instance provided by an airline and over an additional set of generated instances. The obtained results have been compared with a previous multi-start approach in the state of the art and with the initial solution provided to the algorithm which, in the case of the real instance, was the solution in use by the airline.