Elena Popovici

Understanding cooperative co-evolutionary dynamics via simple fitness landscapes

Cooperative co-evolution is often used to solve difficult optimization problems by means of problem decomposition. Its performance for such tasks can vary widely from good to disappointing. One of the reasons for this is that attempts to improve co-evolutionary performance using traditional EC analysis techniques often fail to provide the necessary insights into the dynamics of co-evolutionary systems, a key factor affecting performance. In this paper we use two simple fitness landscapes to illustrate the importance of taking a dynamical systems approach to analyzing co-evolutionary algorithms in order to understand them better and to improve their problem solving performance.

The effects of interaction frequency on the optimization performance of cooperative coevolution

Cooperative coevolution is often used to solve difficult optimization problems by means of problem decomposition. Its performance on this task is influenced by many design decisions. It would be useful to have some knowledge of the performance effects of these decisions, in order to make the more beneficial ones. In this paper we study the effects on performance of the frequency of interaction between populations. We show them to be problem-dependent and use dynamics analysis to explain this dependency.

Sequential versus Parallel Cooperative Coevolutionary Algorithms for Optimization

There continues to be a growing interest in the use of coevolutionary algorithms (CoEAs) to solve difficult computational problems. In particular, cooperative CoEAs are often used for optimization by means of problem decomposition. In addition to the parameters of traditional evolutionary algorithms (EAs), CoEAs have a set of coevolution specific parameters whose values can greatly influence performance. In this paper we study the effects on optimization performance of a parameter called update timing, which controls whether the CoEA runs its subcomponents sequentially or in parallel. This has been studied in [T. Jansen and R. P. Wiegand. Sequential versus parallel cooperative coevolutionary (1+1) EAs. In Proceedings of the IEEE International Congress on Evolutionary Computation. IEEE Press, 2003.] for pseudo-boolean functions. By contrast, we perform the analysis for functions defined on continuous real-number domains. We show the performance effects to be dependent on a problem property called best-response curves and use dynamics analysis to explain this dependency.

The dynamics of the best individuals in co-evolution

There continues to be a growing interest in the use of co-evolutionary algorithms to solve difficult computational problems. However, their performance has varied widely from good to disappointing. The main reason for this is that co-evolutionary systems can display quite complex dynamics. Therefore, in order to efficiently use co-evolutionary algorithms for problem solving, one must have a good understanding of their dynamical behavior. To build such understanding, we have constructed a methodology for analyzing co-evolutionary dynamics based on trajectories of best-of-generation individuals. We applied this methodology to gain insights into how to tune certain algorithm parameters in order to improve performance.

Relationships between internal and external metrics in co-evolution

Co-evolutionary algorithms (CEAs) have been applied to optimization and machine learning problems with often mediocre results. One of the causes for the unfulfilled expectations is the discrepancy between the external problem solving goal and the internal mechanisms of the algorithm. In this paper, we investigate in a principled way the relationships between the internal subjective metric used as fitness by a co-evolutionary algorithm and the external objective metric measuring the algorithms progress towards the envisioned goal. We point out the complexity of these relationships and explain their causes.

Understanding EA dynamics via population fitness distributions

This paper introduces a new tool to be used in conjunction with existing ones for a more comprehensive understanding of the behavior of evolutionary algorithms. Several research groups including [1],[3],[4] have shown how deeper insights into EA behavior can be obtained by focusing on the changes to the entire population fitness distribution rather than just ”best-so-far” curves. But characterizing how repeated applications of selection and reproduction modify this distribution over time proved to be very difficult to achieve analytically and was done successfully for only a few very specialized EAs and/or very simple fitness landscapes.

Analysis of coevolution for worst-case optimization

The problem of finding entities with the best worst-case performance across multiple scenarios arises in domains ranging from job shop scheduling to designing physical artifacts. In spite of previous successful applications of evolutionary computation techniques, particularly coevolution, to such domains, little work has examined utilizing coevolution for optimizing worst-case behavior. Previous work assesses certain algorithm mechanisms using aggregate performance on test problems. We examine fitness and population trajectories of individual algorithm runs, making two observations: first, that aggregate plots wash out important effects that call into question what these algorithms can produce; and second, that none of the mechanisms is generally better than the rest. More importantly, our dynamics analysis explains how the interplay of algorithm properties and problem properties influences performance. These contributions argue in favor of a reassessment of what makes for a good worst-case coevolutionary algorithm and suggest how to design one.

On the practicality of optimal output mechanisms for co-optimization algorithms

Co-optimization problems involve one or more search spaces and a means of assessing interactions between entities in these spaces. Assessing a potential solution requires aggregating in some way the outcomes of a very large or infinite number of such interactions. This layer of complexity presents difficulties for algorithm design that are not encountered in ordinary optimization. For example, what a co-optimization algorithm should output is not at all obvious. Theoretical research has shown that some output selection mechanisms yield better overall performance than others and described an optimal mechanism. This mechanism was shown to be strictly better than a greedy method in common use, but appeared prohibitive from a practical standpoint. In this paper we exhibit the optimal output mechanism for a particular class of co-optimization problems and a certain definition of better overall performance, and provide quantitative characterizations of domains for which this optimal mechanism becomes straightforward to implement. We conclude with a discussion of potential extensions of this work to other problem classes and other views on performance.