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.

Sequential Optimization Method for the Design of Electromagnetic Device

Abstract: Three sequential optimization methods, sequential least square method, sequential Kriging method, and sequential linear Bayesian method, are presented for the optimization design of electromagnetic device. Sequential optimization method (SOM) is composed of coarse optimization process and fine optimization process. The main purpose of the former is to reduce the design space; while the target of the latter is to update the optimal design parameters. To illustrate the performance of the proposed methods, an analytic test function and the TEAM Workshop Problem 22 are investigated. Experimental results of test function demonstrate that SOM can obtain satisfactory solutions; and practical application illustrates that the number of finite element sample points is less than 1/10 compared with that by direct optimization method, while the optimal results are even better than that by direct optimization method.

Modeling transportation problems using concepts of swarm intelligence and soft computing

Abstract: Many real-world problems could be formulated in a way to fit the necessary form for discrete optimization. Discrete optimization problems could be solved by numerous different techniques that have appeared through years. Some of the techniques will provide optimal solution(s) to the problem and some of them will give “good enough” solution(s). Fundamental reason for developing techniques capable of producing solutions that are not necessarily optimal is the fact that many of discrete optimization problems are NP-complete. Metaheuristic algorithms are a common name for a set of general purpose techniques developed to provide solution to the problems belonging to discrete optimization. Mostly the techniques are based on natural metaphors. Countless problems in transportation engineering could be formulated as discrete optimization problems. Recently, researchers started studying the behavior of social insects (ants) in an attempt to use the swarm intelligence concept to develop artificial systems with the ability to search a problem's solution space in a way that is similar to the foraging search by a colony of social insects. The development of artificial systems does not entail the complete imitation of natural systems, but explores them in search of ideas for modeling. This research is partially devoted to the development of a new system based on foraging behavior of bee colonies - Bee System. The Bee System was tested through many instances of the Traveling Salesman Problem. Many transportation-engineering problems besides being of combinatorial nature are characterized by uncertainty. In order to treat these problems, the second part of the research is devoted to development of the algorithms combining existing results in the area of swarm intelligence (existing Ant System) and approximate reasoning. The proposed approach—Fuzzy Ant System is tested on the following two examples: Stochastic Vehicle Routing Problem and Schedule Synchronization in Public Transit.

Testing MVMO on learning-based real-parameter single objective benchmark optimization problems

Abstract: Mean-variance mapping optimization (MVMO) is an emerging evolutionary algorithm, which adopts a single-solution based approach and performs evolutionary operations within a normalized range of the search for all optimization variables. MVMO uses a special mapping function for mutation operation, which allows a controlled shift from exploration priority at early stages of the search process to exploitation at later stages. Recently, the MVMO has been extended to a population-based and hybrid variant denoted as MVMO-SH, which includes strategies for local search and multi-parent crossover. This paper provides an study on the performance of MVMO-SH on the IEEE-CEC 2015 competition test suite on learning-based real-parameter single objective optimization. Experimental results evidence the effectiveness of MVMO-SH for successfully solving different optimization problems with different mathematical properties and dimensionality.