Nonlinear Programming Based on Particle Swarm Optimization
Actual optimization problems to find a solution optimizing a certain objective function under given constraints are often formulated as nonlinear programming problems. If both the objective function and the constrained region are convex, the problem is called a convex programming problem. For convex programming problems, efficient optimization methods such as the sequential quadratic programming method, the generalized reduced gradient method, and so forth, have been proposed. On the other hand, there has been established no efficient optimization method for nonconvex nonlinear programming problems.
In recent years, metaheuristics such as simulated annealing and genetic algorithm have drawn considerable attention. For example, RGENOCOP V that is the floating point type genetic algorithm introducing updating of a basepoint solution of homomorphism to generate initial population is propsed and its effectiveness is shown in . However, since optimization problems in the real world become larger and more complicated, a high speed and accurate optimization method is expected.
In this research, to deal with these drawbacks of the original PSO methods, we incorporate the bisection method and a homomorphous mapping to carry out the search considering constraints. In addition, we propose the multiple stretching technique and modified move schemes of particles to restrain the stopping around local optimal solutions.
KeywordsSearch Point Nonlinear Programming Problem Local Optimal Solution Move Scheme Bisection Method
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