Particle swarm optimization

Abstract

In this work is presented one newer method for optimization of continuous functions which belongs to the heuristic stochastic methods, i.e. to the methods of so called swarm intelligence. This method is mathematically and algorithmically very simple and might be applied successfully for solving a large number of nonlinear optimization problems with and without constraints. One proposal for treatment of constraints in this method is proposed in the paper and a computer program is written according to the described procedure. The method is illustrated by two examples, where one concerns to the optimization of a reinforced concrete beam with minimum costs as a objective function. Results obtained by this method are compared with the results obtained by the genetic algorithm and with the exact solution according to the Korush-Kuhn-Tucker theory. The differences between results obtained by this and exact method are negligible, so this method is very recomendable for solving big number of practical problems. .

U ovome radu je prikazana jedan noviji postupak za optimizaciju kontinualnih funkcija sa i bez ograničenja koji spada u stohastičke heurističke metode, odnosno u tzv. metode inteligencije rojeva. Postupak je matematički i algoritamski veoma jednostavan i može se uspešno primeniti za rešavanje velikog broja problema nelinearne optimizacije sa i bez ograničenja. U radu je predložen postupak za tretman ograničenja i napisan odgovarajući kompjuterski program. Postupak je ilustrovan sa dva primera, od kojih se jedan odnosi na optimizaciju armiranobetonskog nosača. Izvršeno je upoređenje rezultata dobijenih ovom metodom sa rezultatima dobijenim primenom gentskog algoritma i sa egzaktnim rešenjima na bazi teorije Koruša-Kuna-Takera. Razlike između rešenja dobijenog ovom metodom u odnosu na tačno rešenje su zanemarljive, zbog čega je ovaj metod veoma preporučljiv za rešavanje mnogih praktičnih problema. .