Discrete optimization

About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.

Playing with Duality: An overview of recent primal?dual approaches for solving large-scale optimization problems

Abstract: Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. However, deriving efficient strategies that jointly bring into play the primal and dual problems is a more recent idea that has generated many important new contributions in recent years. These novel developments are grounded in the recent advances in convex analysis, discrete optimization, parallel processing, and nonsmooth optimization with an emphasis on sparsity issues. In this article, we aim to present the principles of primal?dual approaches while providing an overview of the numerical methods that have been proposed in different contexts. Last but not least, primal?dual methods lead to algorithms that are easily parallelizable. Today, such parallel algorithms are becoming increasingly important for efficiently handling high-dimensional problems.

Application of 0-1 integer programming to multitarget tracking problems

Abstract: This paper presents a new approach to the solution of multi-target tracking problems. 0-1 integer programming methods are used to alleviate the combinatorial computing difficulties that accompany any but the smallest of such problems. Multitarget tracking is approached as an unsupervised pattern recognition problem. A multiple-hypothesis test is performed to determine which particular combination of the many feasible tracks is most likely to represent actual targets. This multiple hypothesis test is shown to have the computational structure of the set packing and set partitioning problems of 0-1 integer programming. Multitarget tracking problems that are translated into this form can be rapidly solved, using well-known discrete optimization techniques such as implicit enumeration.

A new hybrid method based on Particle Swarm Optimization, Ant Colony Optimization and 3-Opt algorithms for Traveling Salesman Problem

Abstract: The Traveling Salesman Problem (TSP) is one of the standard test problems used in performance analysis of discrete optimization algorithms. The Ant Colony Optimization (ACO) algorithm appears among heuristic algorithms used for solving discrete optimization problems. In this study, a new hybrid method is proposed to optimize parameters that affect performance of the ACO algorithm using Particle Swarm Optimization (PSO). In addition, 3-Opt heuristic method is added to proposed method in order to improve local solutions. The PSO algorithm is used for detecting optimum values of parameters α and β which are used for city selection operations in the ACO algorithm and determines significance of inter-city pheromone and distances. The 3-Opt algorithm is used for the purpose of improving city selection operations, which could not be improved due to falling in local minimums by the ACO algorithm. The performance of proposed hybrid method is investigated on ten different benchmark problems taken from literature and it is compared to the performance of some well-known algorithms. Experimental results show that the performance of proposed method by using fewer ants than the number of cities for the TSPs is better than the performance of compared methods in most cases in terms of solution quality and robustness.