Keynote Speakers

Global deterministic optimization: problems classification, approaches, and algorithms

Problems of finding global minimum of nonconvex functions over compact sets are considered. We start from the problem of deriving computationally checkable (tracktable) global optimization criteria. Then continuous optimization problems are discussed. Next class of problems is so called Lipschitz optimization problems. Here it is assumed that the objective function as well as constraint functions satisfy Lipschitz condition. Some rules of estimating the Lipschitz constants are presented. We also discuss efficiency of the existing methods of Lipschitz optimizartion. Essential part of the talk is devoted to very important case of d.c. optimization problems. D.c. optimization problems are formed by d.c. functions. A function is called a d.c. function if it can be represented as a difference of two continuous convex functions. We consider the most effective global optimization approaches and algorithms based on inner, outer approximation technique as well as on branch and bound schemes. Special attention is given to two key problems: concave programming and linear mixed integer programming. Finally, some global optimization solvers are discussed.

Tracing of Evolutionary Search Trajectories

Understanding the internal functioning of evolutionary algorithms is an essential requirement for improving their performance and reliability. Genetic algorithms emulate emergent systems in which complex patterns are formed from an initially simple and random pool of elementary structures. In GP, complexity emerges under the influence of stabilizing selection which preserves the useful genetic variation created by recombination and mutation. The mapping between the structures used for solution representation and those used for the evaluation of fitness has a major influence on algorithm behavior. Population-wide effects concerning building blocks, genetic diversity and bloat can be conceptually seen as results of the complex interaction between phenotypic operators (selection) and genotypic operators (mutation and recombination). We describe a framework for determining the exact patterns of building block and gene propagation through the generation and the way smaller elements are gradually assembled into more complex structures by the evolutionary algorithm. Within this framework, we can investigate the behavior of genetic operators and their influence on the evolutionary dynamics of the algorithm, and can develop mechanisms for steering the aforementioned dynamics towards improving GP solution quality. The talk will include a detailed overview of all the components of evolution tracking, such as the instrumentation of recombination and mutation operators, implementation of tree pattern matching and the concept of hyper-schema for tree individuals, as well as a prototype algorithm including these concepts as a way to dynamically steer mutation strength during the evolutionary run. Furthermore, we present more recent developments in the area of tree pattern matching which allow efficient computation of tree distances and the identification of repeated genotypic patterns inside the GP population. These new developments allow us to obtain improved performance in symbolic regression using a multi-objective evolutionary approach.