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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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Book ChapterDOI
01 Jan 2008
TL;DR: The future cannot be perfectly forcasted but instead should be considered random or uncertain, and this branch of optimization where there are uncertainties involved in the data or the model is popularly known as Stochastic Programming or stochastic optimization problems.
Abstract: In previous chapters, we looked at various optimization problems. Depending on the decision variables, objectives, and constraints, the problems were classified as LP, NLP, IP, MILP, or MINLP. However, as stated above, the future cannot be perfectly forcasted but instead should be considered random or uncertain. Optimization under uncertainty refers to this branch of optimization where there are uncertainties involved in the data or the model, and is popularly known as Stochastic Programming or stochastic optimization problems. In this terminology, stochastic refers to the randomness, and programming refers to the mathematical programming techniques like LP, NLP, IP, MILP, and MINLP. In the discrete optimization chapter, we came across probabilistic techniques like Simulated Annealing and Genetic Algorithms; these techniques are sometimes referred to as the stochastic optimization techniques because of the probabilistic nature of the method. In general, however, Stochastic Programming and stochastic optimization involves optimal decision making under uncertainty. For example, consider the LP example stated in Chapter 2 where, instead of having a fixed maximum supply of chemical X2, the supply can be uncertain, as shown in the following Stochastic Programming (optimization) problem.

65 citations

Journal ArticleDOI
TL;DR: The results illustrate that IIMOM is effective in capturing different kinds of preference structures of the designer, and it provides a complete and effective solution for medium- and small-scale multiobjective optimization problems.
Abstract: In most practical situations involving reliability optimization, there are several mutually conflicting goals such as maximizing the system reliability and minimizing the cost, weight and volume. This paper develops an effective multiobjective optimization method, the Intelligent Interactive Multiobjective Optimization Method (IIMOM). In IIMOM, the general concept of the model parameter vector is proposed. From a practical point of view, a designer's preference structure model is built using Artificial Neural Networks (ANNs) with the model parameter vector as the input and the preference information articulated by the designer over representative samples from the Pareto frontier as the desired output. Then with the ANN model of the designer's preference structure as the objective, an optimization problem is solved to search for improved solutions and guide the interactive optimization process intelligently. IIMOM is applied to the reliability optimization problem of a multi-stage mixed system with five di...

65 citations

Journal ArticleDOI
TL;DR: A novel solution encoding mechanism is introduced for handling discrete variables in the context of DE and its performance is evaluated over a plethora of public benchmarks problems for three well-known NP-hard scheduling problems.
Abstract: This paper presents a stochastic method based on the differential evolution (DE) algorithm to address a wide range of sequencing and scheduling optimization problems. DE is a simple yet effective adaptive scheme developed for global optimization over continuous spaces. In spite of its simplicity and effectiveness the application of DE on combinatorial optimization problems with discrete decision variables is still unusual. A novel solution encoding mechanism is introduced for handling discrete variables in the context of DE and its performance is evaluated over a plethora of public benchmarks problems for three well-known NP-hard scheduling problems. Extended comparisons with the well-known random-keys encoding scheme showed a substantially higher performance for the proposed. Furthermore, a simple slight modification in the acceptance rule of the original DE algorithm is introduced resulting to a more robust optimizer over discrete spaces than the original DE.

65 citations

Journal ArticleDOI
08 Mar 2018-PLOS ONE
TL;DR: More robust EV distribution paths with multiple distribution centers can be obtained using the robust optimization model based on Bertsimas’ theory of robust discrete optimization.
Abstract: To identify electrical vehicle (EV) distribution paths with high robustness, insensitivity to uncertainty factors, and detailed road-by-road schemes, optimization of the distribution path problem of EV with multiple distribution centers and considering the charging facilities is necessary. With the minimum transport time as the goal, a robust optimization model of EV distribution path with adjustable robustness is established based on Bertsimas' theory of robust discrete optimization. An enhanced three-segment genetic algorithm is also developed to solve the model, such that the optimal distribution scheme initially contains all road-by-road path data using the three-segment mixed coding and decoding method. During genetic manipulation, different interlacing and mutation operations are carried out on different chromosomes, while, during population evolution, the infeasible solution is naturally avoided. A part of the road network of Xifeng District in Qingyang City is taken as an example to test the model and the algorithm in this study, and the concrete transportation paths are utilized in the final distribution scheme. Therefore, more robust EV distribution paths with multiple distribution centers can be obtained using the robust optimization model.

64 citations


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