Alina Martinez-Oropeza

Neighborhood Hybrid Structure for Discrete Optimization Problems

In this paper a comparative analysis of a neighborhood structures group are presented, including a hybrid structure, which arises of a combination of this set of structures. The efficiency and effectiveness of each structure was tested using the Classical Symmetric Travelling Salesman Problem. This study identifies the neighborhood structure that allows performing a better exploration and exploitation of the space solutions to discrete optimization problems. A neighborhood hybrid structure proposed has better performance comparing with other techniques, this is experimentally proved, in addition a competitive efficiency is shown.

Feasible Initial Population with Genetic Diversity for a Population-Based Algorithm Applied to the Vehicle Routing Problem with Time Windows

A stochastic algorithm for obtaining feasible initial populations to the Vehicle Routing Problem with Time Windows is presented. The theoretical formulation for the Vehicle Routing Problem with Time Windows is explained. The proposed method is primarily divided into a clustering algorithm and a two-phase algorithm. The first step is the application of a modified -means clustering algorithm which is proposed in this paper. The two-phase algorithm evaluates a partial solution to transform it into a feasible individual. The two-phase algorithm consists of a hybridization of four kinds of insertions which interact randomly to obtain feasible individuals. It has been proven that different kinds of insertions impact the diversity among individuals in initial populations, which is crucial for population-based algorithm behavior. A modification to the Hamming distance method is applied to the populations generated for the Vehicle Routing Problem with Time Windows to evaluate their diversity. Experimental tests were performed based on the Solomon benchmarking. Experimental results show that the proposed method facilitates generation of highly diverse populations, which vary according to the type and distribution of the instances.

Simulated Annealing Algorithm for the Weighted Unrelated Parallel Machines Problem

In this paper, a solution is presented to the unrelated parallel machines problem that minimizes the total weighted completion time. Simulated annealing is applied to the problem, which is modeled as a Weighted Bipartite Matching Problem. Experimental results with benchmarks are presented, evaluating the efficiency and efficacy of the algorithm. It is then compared with an exact algorithm that solves the pondered model of Integer Linear Programming. The results demonstrate that Simulated Annealing Algorithm has high performance because for all the evaluated instances, it finds the optimum global solution.

Simulated Annealing Algorithm for 2D Image Compression

In this paper a new sign coding approximation method for the wavelet coefficients in a 2D image codec based on a simulated annealing metaheuristic is presented. The efficiency of the proposed algorithm versus a genetic algorithm using benchmarks of Kodak is compared and showing that the proposed sign prediction algorithm is efficient and provides a significant reduction of wavelet coefficients sign information in the final bit-stream. The results show that, by including sign coding capabilities to a nonembedded encoder, the sign compression gain is up to 17.35%, being the rate-distortion (R/D) performance improvement up to 0.25 dB.

Relaxation of Job Shop Scheduling Problem Using a Bipartite Graph

This paper addresses the Job Shop Scheduling Problem (JSSP). Basic constraints are established and it is modeled by a disjunctive graph. The model was mapped to Unrelated Parallel Machines Problem through a bipartite graph. An analysis of constraints is made in both problems to perform a relaxation of the manufacturing problem. Conducting the relaxation of JSSP, it is that any operation can be assigned to any machine, in addition, the precedence constraint between two operations longer applies. The application of approximated bipartite graph model is shown as a new alternative model to represent the JSSP problem, it may be an option to work with this type of problems instead of the disjunctive graph model.

Solving a Real Constraint Satisfaction Model for the University Course Timetabling Problem: A Case Study

This paper proposes a real mathematical constraint satisfaction model which defines the timetabling problem in the Faculty of Chemical Sciences and Engineering (FCSE) at the Autonomous University of Morelos State, Mexico. A Constructive Approach Algorithm (CAA) is used to obtain solutions in the proposed model. A comparison is made between the CAA’s results and the schedule generated by the FCSE administration. Using the constraint satisfaction model, it is possible to improve the allocation of class hours in the FCSE so that classroom use is more efficient.

Variable Neighborhood Search for Non-deterministic Problems

A comparative analysis of several neighborhood structures is presented, including a variable neighborhood structure, which corresponds to a combination of the neighborhood structures evaluated in this paper. The performance of each neighborhood structure was tested using large random instances generated in this research and well-known benchmarks such as the Classical Symmetric Traveling Salesman Problem and the Unrelated Parallel Machines Problem. Experimental results show differences in the performance of the variable neighborhood search when it is applied to problems with differing complexity. Contrary to reports in literature about variable neighborhood searches, its performance varies according to the complexity of the problem.

Tuning an Iterated Local Search Algorithm for Wavelet Sign Coding for 2D Image Compression

Wavelet transforms have proved to be very powerful tools for image compression. Previous studies have verified that there is a strong correlation between the sign of a wavelet coefficient and the signs of their neighbors. This correlation opens the possibility of using a sign predictor in order to improve the image compression process. In this paper a new sign coding approximation method for the wavelet coefficients in a 2D image codec based on an iterated local search algorithm (ILS) is presented. The efficiency of the proposed algorithm versus simulated annealing algorithm (SA) and genetic algorithm (GA) using standard images and benchmarks of Kodak is compared. The proposed sign prediction algorithm is as efficient as other methods and it provides a significant reduction of wavelet coefficients sign information in the final bit-stream.

Percolationby links appliedto the minimum spanning tree problem

This work shows the procedure to optimize the problem of minimum spanning tree applied to percolation by links problem. The aim is improving the structural quality in a complex network by means of a non-directed graph in a square lattice. Moreover, it defines the size of initial population, the number of edges and the running time for each instance of the proposed problem. Experimental results show that proposed algorithm find good quality solutions efficiently for instances of 10, 100, 200,300,400 and 500 vertices. Tackling an instance of 500 vertices for percolation links problem is an important contribution of this research. This work shows the procedure to optimize the problem of minimum spanning tree applied to percolation by links problem. The aim is improving the structural quality in a complex network by means of a non-directed graph in a square lattice. Moreover, it defines the size of initial population, the number of edges and the running time for each instance of the proposed problem. Experimental results show that proposed algorithm find good quality solutions efficiently for instances of 10, 100, 200,300,400 and 500 vertices. Tackling an instance of 500 vertices for percolation links problem is an important contribution of this research.

Unsupervised Clustering Method for the Capacited Vehicle Routing Problem

In this paper an unsupervised clustering method for the Capacited Vehicle Routing Problem is proposed. Advantages and disadvantages of the proposed algorithm are weighed, and comparisons are made to some clustering algorithms commonly used in the literature to tackle routing problems. Experimental tests were performed using Solomon and Hering/Homberger benchmarks applied to different distributions. The proposed algorithm is demonstrated as effective for the attempted problem, with the ability to improve upon weaknesses in some of the clustering algorithms in the literature.