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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.


Papers
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01 Nov 1999
TL;DR: This paper investigates the structure of polyhedral M-convex and L- Convex functions from the dual viewpoint of analysis and combinatorics and provides some properties and characterizations.
Abstract: The concepts of M-convex and L-convex functions were proposed by Murota in 1996 as two mutually conjugate classes of discrete functions over integer lattice points. M/L-convex functions are deeply connected with the well-solvability in nonlinear combinatorial optimization with integer variables. In this paper, we extend the concept of M-convexity and L-convexity to polyhedral convex functions, aiming at clarifying the well-behaved structure in well-solved nonlinear combinatorial optimization problems in real variables. The extended M/L-convexity often appears in nonlinear combinatorial optimization problems with piecewise-linear convex cost. We investigate the structure of polyhedral M-convex and L-convex functions from the dual viewpoint of analysis and combinatorics and provide some properties and characterizations. It is also shown that polyhedral M/L-convex functions have nice conjugacy relationships.

51 citations

Journal ArticleDOI
TL;DR: Through mathematical and structural optimization problems, the validity of PSO for the mixed decision variables is examined and the penalty parameter for the penalty function is determined.
Abstract: Particle Swarm Optimization (PSO) for mixed integer programming problems is proposed. PSO is mainly a method to find a global or quasi-minimum for a nonlinear and nonconvex optimization problem, and there have been few studies into optimization problems with discrete decision variables. In this paper, we present the treatment of discrete variables. To treat discrete decision variables as a penalty function, it is possible to treat all decision variables as a continuous decision variable. As a result, the penalty parameter for the penalty function is needed. In this paper, we also present how to determine the penalty parameter for the penalty function. Through mathematical and structural optimization problems, we examine the validity of PSO for the mixed decision variables. © 2006 Wiley Periodicals, Inc. Electr Eng Jpn, 157(2): 40–49, 2006; Published onlinein Wiley InterScience www.interscience.wiley.com). DOI 10.1002/eej.20337

51 citations

Journal ArticleDOI
TL;DR: A novel particle swarm optimization based meta-heuristic algorithm is presented to solve multi-objective combinatorial optimization problems and is compared with other evolutionary strategy like SPEA and NSGA-II on pseudo-Boolean discrete problems and multi- objective 0/1 knapsack problem.
Abstract: The Combinatorial problems are real world decision making problem with discrete and disjunctive choices. When these decision making problems involve more than one conflicting objective and constraint, it turns the polynomial time problem into NP-hard. Thus, the straight forward approaches to solve multi-objective problems would not give an optimal solution. In such case evolutionary based meta-heuristic approaches are found suitable. In this paper, a novel particle swarm optimization based meta-heuristic algorithm is presented to solve multi-objective combinatorial optimization problems. Here a mapping method is considered to convert the binary and discrete values (solution encoded as particles) to a continuous domain and update it using the velocity and position update equation of particle swarm optimization to find new set of solutions in continuous domain and demap it to discrete values. The performance of the algorithm is compared with other evolutionary strategy like SPEA and NSGA-II on pseudo-Boolean discrete problems and multi-objective 0/1 knapsack problem. The experimental results confirmed the better performance of combinatorial particle swarm optimization algorithm.

50 citations

Proceedings ArticleDOI
14 Dec 1994
TL;DR: This paper proposes a tracking algorithm for estimating the track of a maneuvering target in a cluttered environment using the Viterbi algorithm for discrete optimization.
Abstract: It is well recognized that for target tracking in a cluttered environment, obtaining a correct measurement to track association is an important step because it has a great influence on the final tracking results. Recent research efforts have been focusing on the application of discrete optimization techniques to the data association problem. In this paper, we propose a tracking algorithm for estimating the track of a maneuvering target in a cluttered environment using the Viterbi algorithm for discrete optimization. >

50 citations

Journal ArticleDOI
TL;DR: The purpose of this paper is to provide the details of how such a problem can be cast in the form of a conic quadratic optimization problem, making use of Melan’s static theorem.

50 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202313
202236
2021104
2020128
2019113
2018140