PERMUTATION-BASED GENETIC, TABU, AND VARIABLE NEIGHBORHOOD SEARCH HEURISTICS FOR MULTIPROCESSOR SCHEDULING WITH COMMUNICATION DELAYS

The multiprocessor scheduling problem with communication delays that we consider in this paper consists of finding a static schedule of an arbitrary task graph onto a homogeneous multiprocessor system, such that the total execution time (i.e. the time when all tasks are completed) is minimum. The task graph contains precedence relations as well as communication delays (or data transferring time) between tasks if they are executed on different processors. The multiprocessor architecture is assumed to contain identical processors connected in an arbitrary way, which is defined by a symmetric matrix containing minimum distances between every two processors. The solution is represented by a feasible permutation of tasks. In order to obtain the objective function value (i.e. schedule length, makespan), the feasible permutation has to be transformed into the actual schedule by the use of some heuristic method. For solving this NP-hard problem, we develop basic tabu search and variable neighborhood search heuristics, where various types of reduced Or-opt-like neighborhood structures are used for local search. A genetic search approach based on the same solution space is also developed. Comparative computational results on random graphs with up to 500 tasks and 8 processors are reported. On average, it appears that variable neighborhood search outperforms the other metaheuristics. In addition, a detailed performance analysis of both the proposed solution representation and heuristic methods is presented.Task scheduling, communication delays, metaheuristics, variable neighborhood search, tabu search, genetic algorithms

Variable Formulation and Neighborhood Search Methods for the Maximum Clique Problem in Graph

Doktorska disertacija se bavi temama rešavanja računarski teških problema kombinatorne optimizacije. Istaknut je problem maksimalne klike kao predstavnik određenih struktura u grafovima. Problem maksimalne klike i sa njim povezani problemi su formulisani kao nelinearne funkcije. Rešavani su sa ciljem otkrivanja novih metoda koje pronalaze dobre aproksimacije rešenja za neko razumno vreme. Predložene su varijante Metode promenljivih okolina na rešavanje maksimalne klike u grafu. Povezani problemi na grafovima se mogu primeniti na pretragu informacija, raspoređivanje, procesiranje signala, teoriju klasifikacije, teoriju kodiranja, itd. Svi algoritmi su implementirani i uspešno testirani na brojnim različitim primerima.This Ph.D. thesis addresses topics NP hard problem solving approaches in combinatorial optimization and according to that it is highlighted maximum clique problem as a representative of certain structures in graphs. Maximum clique problem and related problems with this have been formulated as non linear functions which have been solved to research for new methods and good solution approximations for some reasonable time. It has been proposed several different extensions of Variable Neighborhood Search method. Related problems on graphs could be applied on information retrieval, scheduling, signal processing, theory of classi_cation, theory of coding, etc. Algorithms are implemented and successfully tested on various different tasks