Volume 19, Issue 1 (2008), pp. 45–62
The aim is to investigate two emerging information technologies in graduate studies and scientific cooperation. Internet is the first technology. The open source is the second. They help each other in many ways. The joint influence of both is regarded in this paper.
Results of complexity theory show the limitations of exact analysis. That explains popularity of heuristic algorithms. It is well known that efficiency of heuristics depends on the parameters. Therefore automatic procedures for tuning the heuristics help to compare results of different heuristics and enhance their efficiency.
The theory and some applications of Bayesian Approach were discussed in (Mockus, 2006a). In this paper examples of Bayesian Approach to automated tuning of heuristics are investigated. This is the Bayesian Heuristic Approach, in short. The examples of traditional methods of optimization, including applications of linear and dynamic programming, will be investigated in the next paper. These three papers represents three parts of the same work. However each part can be read independently.
All the algorithms are implemented as platform independent Java applets or servlets. Readers can easily verify and apply the results for studies and for real life optimization problems.
The theoretical result is application of unified Bayesian Heuristic Approach for different discrete optimization models. The practical result is adaptation of these models for graduate distance studies and scientific collaboration by a common java global optimization framework.
The software is regularly updated and corrected responding to new programming tools and users reports. However the general structure of web sites remains. The information is on the web site: http://pilis.if.ktu.lt/~mockus and four mirror sites.
Volume 13, Issue 3 (2002), pp. 311–332
Real life scheduling problems are solved by heuristics with parameters defined by experts, as usual. In this paper a new approach is proposed where the parameters of various heuristics and their random mixtures are optimized to reduce the average deviations from the global optimum.
In many cases the average deviation is a stochastic and multi-modal function of heuristic parameters. Thus a stochastic global optimization is needed. The Bayesian heuristic approach is developed and applied for this optimization. That is main distinctive feature of this work. The approach is illustrated by flow-shop and school scheduling examples. Two versions of school scheduling models are developed for both traditional and profiled schools. The models are tested while designing schedules for some Lithuanian schools. Quality of traditional schedules is defined by the number of teacher “windows”. Schedules of profiled schools are evaluated by user defined penalty functions. That separates clearly subjective and objective data. This is the second specific feature of the proposed approach.
The software is developed for the Internet environment and is used as a tool for research collaboration and distance graduate studies. The software is available at web-sites and can be ran by standard net browsers supporting Java language. The care is taken that interested persons could easily test the results and apply the algorithms and software for their own problems.
Volume 3, Issue 2 (1992), pp. 198–224
A random walk dan be used to model various types of discrete random processes. It may be of interest at some point to find the peak of this function. A direct method of doing so involves evaluating the function at every point and recording the highest value. However, it may be desirable to find the peak without having, to evaluate the function at every point. A search technique was developed to find the peak of a random walk with a minimal number of function evaluations using probabilistic means to guess at where the peak will most likely occur given the parameters of a specific function. A computer program was written to implement the search strategy and a series-of random walk functions of varying lengths were generated to test its performance. Data was compiled and the results show that the search is capable of finding the peak with a significant reduction in the number of function evaluations needed for a point by point search, especially for functions of greater walk length.
Volume 2, Issue 2 (1991), pp. 248–254
In well-known statistical models of global optimization only values of objective functions are taken into consideration. However, efficient algorithms of local optimization are also based on the use of gradients of objective functions. Thus, we are interested in a possibility of the use of gradients in statistical models of multimodal functions, aiming to create productive algorithms of global optimization.
Volume 1, Issue 1 (1990), pp. 71–88
In the paper the global optimization is described from the point of an interactive software design. The interactive software that implements numeric methods and other techniques to solve global optimization problems is presented. Some problems of such a software design are formulated and discussed.