Abstract: Most real-life problems can be represented as some kind of optimization problem. Easy optimization problems were solved long time ago so nowadays only hard problems are of research interest. Many discrete (combinatorial) as well as some continuous optimization problems are intractable, but of great practical interest. Traveling salesman problem (TSP) is a classic example that was researched for the longest period of time and because of that is often used as a benchmark.
The main problem with hard optimization problems is that there is enormous number of suboptimal solutions or local minima and there is no guidance how to search. Standard down-hill methods in this situation fail. Typical example of such function that is used as a benchmark is Rastrigin function that is a sphere modified by small cosine waves.
The oldest way to deal with such problems is Monte-Carlo method. It is equivalent of trying to find the deepest point in the oceans by measuring many times the depth at random locations and hoping that best measurement will be close to the global optimum. While Monte-Carlo method is usable for some applications, its blind search is not sufficient for many others. In this rather hopeless situation researchers turned from mathematically exact methods to belief. The nature is doing miraculous things. We know the results but we do not understand the mechanism. For hard optimization problems we try to mimic some nature processes. Older attempts included simulation of evolution (through genetic modifications and survival of the fittest) and simulated annealing. Recently, swarm intelligence become prominent using the fact that extremely simple individuals exhibit miraculous collective intelligence. Examples include ants colonies, honey bees colonies, flocks of birds, schools of fish etc.
These nature inspired metaheuristics simulate various natural phenomena. We talk about bee colony food finding or ant colony path finding, but in essence, in all these diverse mimicking we do two things. We exploit good found solutions, but also go to unknown places in order to avoid being trapped in local minima. The successfulness of any such algorithm is determined by proper balance between exploitation and exploration. This balance is maintained by adjusting certain parameters and also by applying some rules in certain situations. By doing such adjustments algorithm can become much better for some class of problems (off course, according to NFL theorem, it cannot become universally good for all problems). This plenary lecture will demonstrate few successful examples of such adjustments.

Brief Biography of the Speaker:
Milan Tuba received B. S. in Mathematics, M. S. in Mathematics, M. S. in Computer Science, M. Ph. in Computer Science, Ph. D. in Computer Science from University of Belgrade and New York University. From 1983 to 1994 he was in the U.S.A. first as a graduate student and teaching and research assistant at Vanderbilt University in Nashville and Courant Institute of Mathematical Sciences, New York University and later as an Assistant Professor of Electrical Engineering at Cooper Union Graduate School of Engineering, New York. During that time he was the founder and director of Microprocessor Lab and VLSI Lab, leader of scientific projects and supervisor of many theses. From 1994 he was Assistant professor of Computer Science and Director of Computer Center at University of Belgrade, from 2001 Associate Professor, Faculty of Mathematics, and from 2004 also a Professor of Computer Science and Dean of the College of Computer Science, Megatrend University Belgrade. He was teaching more than 20 graduate and undergraduate courses, from VLSI Design and Computer Architecture to Computer Networks, Operating Systems, Image Processing, Calculus and Queuing Theory. His research interest includes mathematical, queuing theory and heuristic optimizations applied to computer networks, image processing and combinatorial problems. He is the author of more than 130 scientific papers and a monograph. He is coeditor or member of the editorial board or scientific committee of number of scientific journals and conferences. Member of the ACM since 1983, IEEE 1984, New York Academy of Sciences 1987, AMS 1995, SIAM 2009. Participated in many WSEAS Conferences with plenary lectures and articles in Proceedings and Transactions.