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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.


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Journal ArticleDOI
TL;DR: A comparison of the numerical results obtained using the ADS with those of other metaheuristic techniques indicates that the proposed algorithm is capable of locating improved solutions using much lesser computational effort.

113 citations

Journal ArticleDOI
TL;DR: A modification of the Particle Swarm Optimization (PSO) algorithm is presented, which can adequately address system constraints while dealing with mixed-discrete variables, and is applied to a wide variety of standard test problems.
Abstract: Engineering design problems often involve non-linear criterion functions, including inequality and equality constraints, and a mixture of discrete and continuous design variables. Optimization approaches entail substantial challenges when solving such an all-inclusive design problem. In this paper, a modification of the Particle Swarm Optimization (PSO) algorithm is presented, which can adequately address system constraints while dealing with mixed-discrete variables. Continuous search (particle motion), as in conventional PSO, is implemented as the primary search strategy; subsequently, the discrete variables are updated using a deterministic nearest-feasible-vertex criterion. This approach is expected to alleviate the undesirable difference in the rates of evolution of discrete and continuous variables. The premature stagnation of candidate solutions (particles) due to loss of diversity is known to be one of the primary drawbacks of the basic PSO dynamics. To address this issue in high dimensional design problems, a new adaptive diversity-preservation technique is developed. This technique characterizes the population diversity at each iteration. The estimated diversity measure is then used to apply (i) a dynamic repulsion away from the best global solution in the case of continuous variables, and (ii) a stochastic update of the discrete variables. For performance validation, the Mixed-Discrete PSO algorithm is applied to a wide variety of standard test problems: (i) a set of 9 unconstrained problems, and (ii) a comprehensive set of 98 Mixed-Integer Nonlinear Programming (MINLP) problems. We also explore the applicability of this algorithm to a large scale engineering design problem---wind farm layout optimization.

113 citations

Proceedings ArticleDOI
06 Jul 1999
TL;DR: Experimental results show that the two-space genetic algorithm can find robust solutions for minimax optimization problems, and this paper uses the algorithm to solve a parallel machine scheduling problem with uncertain processing times.
Abstract: Robust discrete optimization is a technique for structuring uncertainty in the decision-making process. The objective is to find a robust solution that has the best worst-case performance over a set of possible scenarios. However, this is a difficult optimization problem. This paper proposes a two-space genetic algorithm as a general technique to solve minimax optimization problems. This algorithm maintains two populations. The first population represents solutions. The second population represents scenarios. An individual in one population is evaluated with respect to the individuals in the other population. The populations evolve simultaneously, and they converge to a robust solution and its worst-case scenario. Since minimax optimization problems occur in many areas, the algorithm will have a wide variety of applications. To illustrate its potential, we use the two-space genetic algorithm to solve a parallel machine scheduling problem with uncertain processing times. Experimental results show that the two-space genetic algorithm can find robust solutions.

113 citations

Journal ArticleDOI
TL;DR: The application of genetic algorithms to integrated discrete and configuration optimization of trusses is presented, mathematically formulated as a constrained nonlinear optimization problem with a mix of discrete sizing and continuous configuration variables.

113 citations


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