Methodologies for solving complex multi-objective combinatorial problems in engineering: An evolutionary approach

• Published in: ICA-ACCA : 2016 IEEE International Conference on Automatica : 19-21 October 2016 pp. 1 - 6
• Main Author: Donoso, Yezid
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.10.2016
• Subjects: Approximation algorithms; Complex Problems; Evolutionary Algorithms; Evolutionary computation; Heuristic algorithms; Linear programming; Measurement; Multi-Objective Evolutionary Algorithms; Multi-Objective Optimization Problems; Optimization; Sociology
• DOI: 10.1109/ICA-ACCA.2016.7778518

In real problems in Engineering, solving a problem is not enough; the solution of the problem must be the best solution possible. In other words, it is necessary to find the optimal solution. The solution is the best possible solution because in the real world this problem may have certain constraints by which the solutions found may be feasible, that is, they can be implemented in practice and, unfeasible or that they cannot be implemented. Some of these problems in engineering can be MOP (Multi-Objective Optimization Problem). A general MOP includes a set of η parameters (decision variables), a set of k objective functions and a set of m restrictions. The objective and restriction functions are functions of the decision variables where is possible to obtain a set of optimal values. Then the MOP can be expressed as: Optimize y = f(x) = (f1(x), f2(x),..., fk(x)) Subject to e(x) = (e1(x), e2(x),..., em(x)) 0 Where χ = (x1, x2,..., xn) X y = (y1,y2,...,yk) Y. The method evolutionary algorithm (EA) refers to searching and optimization techniques based on the evolution model proposed by Charles Darwin. Genetic algorithms are used in several areas especially for searching and optimizations. In the real case the algorithm is implemented by choosing a coding for the possible solutions to the problem. The coding is done through chains of bits, numbers or characters that represent the chromosomes. The crossing and mutation operations are applied in a very simple way through functions of vector value manipulation. The EAs are interesting given the fact that at first glance they seem especially apt to deal with the difficulties presented by MOPs. The reason for this is that they can return an entire set of solutions after a simple run and they do not have any other of the limitations of traditional techniques. In addition, some researchers have suggested that the EAs would behave better than other blind searching techniques.