Razvoj naprednih biološki inspirisanih algoritama za rešavanje optimizacionih problema primenjene mehanike

Abstract

U poslednjih petnaestak godina pojavljuju se metode koje sve bolje rešavaju komplikovane optimizacione probleme. Sve ove metode su nastale kao inspiracija sa odgovarajućim pojavama u prirodi, pa se i zovu biološki inspirisane metode. Najpoznatije su: genetski algoritmi (Genetic Algorithm - GA), diferencijalna evolucija (Differential Evolution DE), optimizacija rojem čestica (Particle Swarm Optmization PSO), optimizacija inspirisana kretanjem mrava (Ant Colony Optimization - ACO), kukavičja pretraga (Cuckoo Search – CS), algoritam svica (Firefly Algorithm – FA), algoritam slepog miša (Bat Algorithm – BA), optimizacija inspirisana kretanjem planktona (Krill Herd Algorithm – KHA) itd. Svi ovi algoritmi se mogu primeniti na veliki broj problema, daju mogućnost postavljanja širokog opsega za početne vrednosti projektnih promenljivih – tako da nije potrebno iskustvo pri određivanju bliskih početnih vrednosti, funkcija koja se optimizira ovim metodama ne mora biti diferencijabilna i neprekidna, nema ograničenja u odnosu na broj promenljivih koji se optimizira, primenljive su na veliki broj problema, zatim strukture njihovih algoritama nude velike mogućnosti nadogradnje – čime se može postići efikasnost algoritma jednostavnim modifikacijama. Metodologija istraživanja u ovom radu je fokusirana na četiri od gore pomenutih metoda: kukavičja pretraga (Cuckoo Search – CS), algoritam svica (Firefly Algorithm – FA), algoritam slepog miša (Bat Algorithm – BA), optimizacija inspirisana kretanjem planktona (Krill Herd Algorithm – KHA). Cilj istraživanja je da se naprave odgovarajuće modifikacije i hibridizacije pomenutih metoda, koje će postizati bolje rešenje u polju globalnih minimuma. Tako dobijeni algoritmi, testirani su na benčmark optimizacionim problemima primenjene mehanike koji postoje u literaturi. Takođe cilj istraživanja je i modeliranje nekih od navedenih problema više složenosti i testiranje ovako unapređenih algoritama na takve probleme. Ideja je da se uspostavi univerzalni algoritam kako bi se sa lakoćom primenio u rešavanju različitih optimizacionih problema u mašinstvu, odnosno primenjenoj mehanici u cilju dobijanja globalnog minimuma.

In the last fifteen years methods that better solve complex optimization problems appear. All these methods have emerged as an inspiration to the corresponding phenomena in nature, so they are called biologically inspired methods. The best known are: Genetic Algorithms (Genetic Algorithm - GA), differential evolution (DE Differential Evolution), Particle Swarm Optimization (PSO Particle Swarm optmization), optimization inspired by the movement of ants (Ant Colony Optimization - ACO), cuckoo searches (Cuckoo Search - CS) algorithm firefly (Firefly Algorithm - FA) algorithm bat (Bat Algorithm - BA), optimization inspired by the movement artick krill (Krill Herd Algorithm - KHA) etc. All of these algorithms can be applied to a large number of problems, give the possibility of setting up a wide range of initial values of the design variables - so you do not need experience in determining close initial value, a function that optimizes these methods may not be differentiable and continuous, no restrictions on the the number of variables that optimizes, are applicable to a large number of problems and structure of their algorithms offer great possibilities for upgrades - which can be achieved by simple modification of the efficiency of the algorithm. The research methodology, in this thesis, is focused on four of the above-mentioned methods: cuckoo searches (Cuckoo Search - CS) algorithm firefly (Firefly Algorithm - FA) algorithm bat (Bat Algorithm - BA), optimization inspired by the movement of plankton (Krill Herd Algorithm - KHA). The aim of the research is to make appropriate modifications and hybridization of these methods, which will achieve a better solution in the field of global minimum. The thus-obtained algorithms were tested on a benchmark problems by optimization in applied mechanics, that exist in the literature. Also the aim of the research is modeling some more complex problems and testing this advanced algorithms on such problems. The idea is to establish a universal algorithm which will be easily applied in solving various optimization problems in mechanical engineering or applied mechanics, in order to obtain the global minimum.