Juan Javier González Barbosa

A Survey of Decomposition Methods for Multi-objective Optimization

The multi-objective optimization methods are traditionally based on Pareto dominance or relaxed forms of dominance in order to achieve a representation of the Pareto front. However, the performance of traditional optimization methods decreases for those problems with more than three objectives to optimize. The decomposition of a multi-objective problem is an approach that transforms a multi-objective problem into many single-objective optimization problems, avoiding the need of any dominance form. This chapter provides a short review of the general framework, current research trends and future research topics on decomposition methods.

Spanish Natural Language Interface for a Relational Database Querying System

The fast growth of Internet is creating a society where the demand on information storage, organization, access, and analysis services is continuously growing. This constantly increases the number of inexperienced users that need to access databases in a simple way. Together with the emergence of voice interfaces, such a situation foretells a promising future for database querying systems using natural language interfaces. We describe the architecture of a relational database querying system using a natural language (Spanish) interface, giving a brief explanation of the implementation of each of the constituent modules: lexical parser, syntax checker, and semantic analyzer.

An ant colony system algorithm to solve routing problems applied to the delivery of bottled products

This work presents a methodology of solution for the well-known vehicle routing problem (VRP) based on an ant colony system heuristic algorithm (ACS), which is applied to optimize the delivery process of RoSLoP (Routing-Scheduling-Loading Problem) identified in the company case of study. A first version of this algorithm models six variants of VRP and its solution satisfies the 100% of demands of the customers. The new version of the algorithm can solve 11 variants of VRP as a rich VRP. Experiments were carried out with real instances. The new algorithm shows a saving of two vehicles with regard to the first version, reducing the operation costs of the company. These results prove the viability of using heuristic methods and optimization techniques to develop new software applications.

A distributed metaheuristic for solving a real-world scheduling-routing-loading problem

In this paper a real and complex transportation problem including routing, scheduling and loading tasks is presented. Most of the related works only involve the solution of routing and scheduling, as a combination of up to five different types of VRPs (Rich VRP), leaving away the loading task, which are not enough to define more complex real-world cases. We propose a solution methodology for transportation instances that involve six types of VRPs, a new constraint that limits the number of vehicles that can be attended simultaneously and the loading tasks. They are solved using an Ant Colony System algorithm, which is a distributed metaheuristic. Results from a computational test using real-world instances show that the proposed approach outperforms the transportation planning related to manual designs. Besides a well-known VRP benchmark was solved to validate the approach.

An Ant Colony Algorithm for Improving Ship Stability in the Containership Stowage Problem

This paper approaches the containership stowage problem. It is an NP-hard minimization problem whose goal is to find optimal plans for stowing containers into a containership with low operational costs, subject to a set of structural and operational constraints. In this work, we apply to this problem an ant-based hyperheuristic algorithm for the first time, according to our literature review. Ant colony and hyperheuristic algorithms have been successfully used in others application domains. We start from the initial solution, based in relaxed ILP model; then, we look for the global ship stability of the overall stowage plan by using a hyperheuristic approach. Besides, we reduce the handling time of the containers to be loaded on the ship. The validation of the proposed approach is performed by solving some pseudo-randomly generated instances constructed through ranges based in real-life values obtained from the literature.

On the Exact Solution of VSP for General and Structured Graphs: Models and Algorithms

In this chapter the vertex separation problem (VSP) is approached. VSP is NP-hard with important applications in VLSI, computer language compiler design, and graph drawing, among others. In the literature there are several exact approaches to solve structured graphs and one work that proposes an integer linear programming (ILP) model for general graphs. Nevertheless, the model found in the literature generates a large number of variables and constraints, and the approaches for structured graphs assume that the structure of the graphs is known a priori. In this work we propose a new ILP model based on a precedence representation scheme, an algorithm to identify whether or not a graph has a Grid structure, and a new benchmark of scale-free instances. Experimental results show that our proposed ILP model improves the average computing time of the reference model in 79.38 %, and the algorithm that identifies Grid-structured graphs has an effectiveness of 100 %.

Integer Linear Programming Formulation and Exact Algorithm for Computing Pathwidth

Computing the Pathwidth of a graph is the problem of finding a linear ordering of the vertices such that the width of its corresponding path decomposition is minimized. This problem has been proven to be NP-hard. Currently, some of the best exact methods for generic graphs can be found in the mathematical software project called SageMath. This project provides an integer linear programming model (IPSAGE) and an enumerative algorithm (EASAGE), which is exponential in time and space. The algorithm EASAGE uses an array whose size grows exponentially with respect to the size of the problem. The purpose of this array is to improve the performance of the algorithm. In this chapter we propose two exact methods for computing pathwidth. More precisely, we propose a new integer linear programming formulation (IPPW) and a new enumerative algorithm (BBPW). The formulation IPPW generates a smaller number of variables and constraints than IPSAGE. The algorithm BBPW overcomes the exponential space requirement by using a last-in-first-out stack. The experimental results showed that, in average, IPPW reduced the number of variables by 33.3 % and the number of constraints by 64.3 % with respect to IPSAGE. This reduction of variables and constraints allowed IPPW to save approximately 14.9 % of the computing time of IPSAGE. The results also revealed that BBPW achieved a remarkable use of memory with respect to EASAGE. In average, BBPW required 2073 times less amount of memory than EASAGE for solving the same set of instances.

Comparative Study on Constructive Heuristics for the Vertex Separation Problem

The vertex separation problem (VSP) consists of finding a linear ordering of the vertices of an input graph that minimizes the maximum number of vertex separators at each cut-point induced by the ordering. VSP is an NP-hard problem whose efficient solution is relevant in fields such as very large scale integration design, computer language compiler design, graph drawing and bioinformatics. In the literature reviewed, we found several exact algorithms and two metaheuristics based on the variable neighborhood search approach. These metaheuristics are currently the best stochastic algorithms for solving VSP. One of the key points of their efficiency is the usage of heuristics to construct a high-quality initial solution that considerably improves the algorithm performance. In this chapter we augment the literature on VSP by proposing a new set of heuristics. The proposed constructive heuristics are compared with the best ones found in the state-of-the-art and with random solution generator (Rnd). Experimental results demonstrate the importance of constructive algorithms. The best constructive improves Rnd by 89.96 % in solution quality.

A Loading Procedure for the Containership Stowage Problem

This chapter deals with the containership stowage problem. It is an NP-hard combinatorial optimization whose goal is to find optimal plans for stowing containers into a containership with low operational costs, subject to a set of structural and operational constraints. In order to optimize a stowage planning, like in the literature, we have developed an approach that decomposes the problem hierarchically. This approach divides the problem into two phases: the first one consists of generating a relaxed initial solution, and the second phase is intended to make this solution feasible. In this chapter, we focus on the first phase of this approach, and a new loading procedure to generate an initial solution is proposed. This procedure produces solutions in short running time, so that, it could be applied to solve real instances.

A New Integer Linear Programming Model for the Cutwidth Minimization Problem of a Connected Undirected Graph

In this chapter we propose a new integer linear programming model based on precedences for the cutwidth minimization problem (CWP). A review of the literature indicates that this model is the only one reported for this problem. The results of the experiments with standard instances shows that the solution of the problem with the proposed model outperforms in quality and efficiency to the one reported in the state of the art. Our model increases the number of optimal solutions by 38.46 % and the gap reduction by 45.56 %. Moreover, this quality improvement is reached with a time solution reduction of 41.73 %. It is considered that the approach used in this work can be used in other linear ordering problems.