Oswaldo Aguirre

Applications and performance of the non-numerical ranking preferences method for post-Pareto optimality

Abstract Most real-world engineering optimization problems are implicitly or explicitly multi-objective, and approaches to find the best feasible solution to be implemented can be quite challenging for the decision-maker. In this kind of problem, either the analyst determines a single solution or identifies a set of nondominated solutions, often referred to as Pareto-optimal set. Although, several methods for solving multi-objective optimization problems have been developed and studied, little prior work has been done on the evaluation of results obtained in multi-objective optimization. This selection stage is often referred as post-Pareto optimality. This paper presents a method based on preferences rankings provided from the decision-maker. The method is clearly advantageous because there is no need to provide specific weight values; the only requirement is to provide a non-nominal ranking. Several examples are used to show the performance of the algorithm.

An Evolutionary Game Theory Approach for Intelligent Patrolling

Abstract In order to achieve a secure country, many security policies and strategies have been implemented and numerous security force s have been enlisted such as regular police forces, Army, and Navy, among others. Each security force has different roles and responsibilities. One important area of concern related to national security is border security. Border protection is a chall enging problem due to the different types of illegal activity that must to be controlled such as drug smuggling, terrorist attacks, illegal immigration, etc. One common approach to achieve border security is patrolling. Patrolling can be defined as the act of traveling an area in regular intervals in order to secure it against different threats. This paper presents a hybrid method that combines an evolutionary approach and game theory concepts in order to define the multi-agent patrolling strategy that simultaneously optimizes maximum idleness, infiltration ratio, and total patrolling cost.

Multiple objective system reliability post-Pareto optimality using self organizing trees

Multiple objective system reliability optimization problems have been become more popular in engineering and have been deeply covered in literature. There are different approaches to address multiple objective optimization problems depending of the area and special characteristics of the problem. Most of the methods developed to solve these types of problems consist in a Pareto set of optimal solutions. At this point the decision-maker has to select one solution among the Pareto set. This task is not trivial due to the large size of the set to choose for. This work presents a new method based on self-organizing trees for reducing the size of Pareto-optimal sets. The method is tested in several Pareto sets from different multiple objective system reliability optimization problems including a network reliability design problem.

A Clustering Method Based on Dynamic Self Organizing Trees for Post-Pareto Optimality Analysis

Multiple objective optimization involves the simultaneous optimization of several objective functions. Solving this type of problem involves two stages; the optimization stage and the post-Pareto analysis stage. The first stage focuses in obtaining a set of nondominated solutions while the second one involves the selection of one solution from the Pareto set. Most of the work found in the literature focuses in the first stage. However, the decision making stage is as important as obtaining the set of nondominated solutions. Selecting one solution over others, or reducing the number of alternatives to choose from is not a simple task since the Pareto-optimal set can potentially contain a very large number of solutions. This paper introduces the dynamic self organizing tree algorithm as a method to perform post-Pareto analysis. This algorithm offers two main advantages: there is no need to provide an initial number of clusters, and at each hierarchical level, the algorithm optimizes the number of clusters, and can reassign data from previous hierarchical levels in order to rearrange misclustered data. The proposed method is tested in a well-known multiple objective optimization problem in order to show the performance of the algorithm.