José Crispín Zavala-Díaz

Search Algorithm for the Constraint Satisfaction Problem of VRPTW

This paper presents an algorithm called CSP-IRPTW for the vehicles routing problem with time windows (VRPTW), which applies the PCP method (precedence constraint posting) used for models of scheduling as a CSP (constraint satisfaction problem). PCP involves the calculation of the shortest path in partial and global form, between pairs of nodes and among all the nodes respectively, in the graph that represents the VRPTW model. In order to apply PCP to VRPTW, the problem is treated as a CSP. The results show that the proposed search algorithm is efficient in the search for the global optimum for some problems.

Selection of an Investment Portfolio by Means of a Mathematical Model of Optimization Applied to Mexican Stock-Market in Period of Debacle

In this paper appears a behavior analysis of the Mexican stock-market between a previous period to the economic debacle of the 2008 and during the period of the first month of the debacle. We propose to use a mathematical model of linear programming for the selection of an investment portfolio in Mexican stock-market. The mathematical model is based on the modification of Markowitz Model and Capital Assets Pricing Model. The model proposed contains two functions objective: 1) to maximize the return and 2) to minimize the risk. The Application of the proposed model to select an investment portfolio was realized with the public data of Mexican stock-market taking a sample from the stock-exchange, than they are part of the calculation of the Index of Prices and Quotations. The results show that our model is able to determine an investment portfolio with very different scenes and in period of debacle. Also it does determine that when comparing two investment portfolios are better to select the portfolio with the greater return instead of the portfolio with the smaller risk.

Mathematical Model for Optimizing the Composition of an Investment Portfolio for the Mexican Stock Market

A linear programming mathematical model is presented, which permits to compose an investment portfolio that achieves the maximal return at minimal risk from public information published on the web page of the Mexican stock exchange (BMV). Each of the linear programming problems (return maximization and risk minimization) is solved individually, and their optimal values are compared against those of a portfolio obtained using a statistical method. The results show that it is possible to compose a portfolio at minimal risk at time zero, and that the portfolio obtained by the statistical method is different from the one obtained by solving the optimization mathematical model.

Scheduling Algorithm for the Job Shop Scheduling Problem

This paper presents an algorithm that applies a new mechanism in order to generate scheduling which allows for evaluation of the quality of solutions that are obtained in the job shop scheduling problem (JSSP). In this research, the quality of the solution is evaluated by using the makespan as an objective function. It is demonstrated experimentally that the proposed algorithm has better efficiency and efficacy when compared to the classic form of scheduling generation used to evaluate the quality of the solution in the JSSP. The efficiency and efficacy obtained by the proposed algorithm make it possible to generate and evaluate a greater number of better quality solutions in less time, so a greater exploration of the solution space for the JSSP can be conducted.

A Solution to the Strongly Correlated 0-1 Knapsack Problem by a Binary Branch and Bound Algorithm

In this paper is presented the Binary Branch-and-Bound Algorithm (BBBA) and its application to determine the solution of the 0-1 Knapsack Problem. The algorithm solves different instances (uncorrelated, weakly and strongly correlated) in time (Kn). The proposed algorithm was experimentally compared with the Pisinger Model, based on the obtained results it is demonstrated the ability of the proposed algorithm to solve problems that the Pisinger algorithm cannot solve.

Branch and Bound Hybrid Algorithm to Determine the Exact or Approximate Solution of the 0/1 Knapsack Problem with One Parameter

In this paper, the Zavala-Cruz algorithm is presented to solve the knapsack problem with one parameter. The foundation of the algorithm is shown; it is based largely on the algorithm of Horowitz-Sahni, with the lower and upper bounds taken from Dantzig, and the artifices of simulated annealing used to in order to escape of the local optimums. The Zavala-Cruz algorithm defines the search space and the rules to branch and prune, with which avoids the backtracking and this accelerates quicker the convergence to an exact or approximate solution. The Zavala-Cruz algorithm determines the exact solution for all the uncorrelated instances and for some of the weakly correlated instances. It also determines the approximate solution for the strongly correlated instances. These solutions were obtained along the whole parameter, including the transition phase, where the most complex instances are found, and where in some cases the instances are not computable. For each instance and for each value of the parameter, a multiple of n2 was used in order to branch and prune, obtaining convergence with kn2 iterations in all cases.

MISMA: An Approach to Mexican Information Security Methodology and Architecture for PYMES

In Mexico the computer science security is growing, but not therefore the initiatives of law nor the standards in the matter of computer science security, although they exist international standard of computer science security the recommendations are not adopted due to infrastructure differences and that contain there, and that cannot be adopted by the Mexican companies. The main idea to propose a methodology and architecture for the small and medium companies is with the purpose of providing a tool that allows the companies to count on basic a computer science security system that allows diminishing the security problems.