R. Paul Wiegand

Bridging the Gap Between Theory and Practice

While the gap between theory and practice is slowly closing, the evolutionary computation community needs to concentrate more heavily on the middle ground. This paper defends the position that contemporary analytical tools facilitate such a concentration. Empirical research can be improved by considering modern analytical techniques in experimental design. In addition, formal analytical extensions of empirical works are possible. We justify our position by way of a constructive example: we consider a recent empirically-based research paper and extend it using modern techniques of asymptotic analysis of run time performance of the algorithms and problems investigated in that paper. The result is a more general understanding of the performance of these algorithms for any size of input, as well as a better understanding of the underlying reasons for some of the previous results. Moreover, our example points out how important it is that empirical researchers motivate their parameter choices more clearly. We believe that providing theorists with empirical studies that are well-suited for formal analysis will help bridge the gap between theory and practice, benefitting the empiricist, the theorist, and the community at large.

The Cooperative Coevolutionary (1+1) EA

Coevolutionary algorithms are variants of traditional evolutionary algorithms and are often considered more suitable for certain kinds of complex tasks than noncoevolutionary methods. One example is a general cooperative coevolutionary framework for function optimization. This paper presents a thorough and rigorous introductory analysis of the optimization potential of cooperative coevolution. Using the cooperative coevolutionary framework as a starting point, the CC (11) EA is defined and investigated from the perspective of the expected optimization time. The research concentrates on separability, a key property of objective functions. We show that separability alone is not sufficient to yield any advantage of the CC (11) EA over its traditional, non-coevolutionary counterpart. Such an advantage is demonstrated to have its basis in the increased explorative possibilities of the cooperative coevolutionary algorithm. For inseparable functions, the cooperative coevolutionary set-up can be harmful. We prove that for some objective functions the CC (11) EA fails to locate a global optimum with overwhelming probability, even in infinite time; however, inseparability alone is not sufficient for an objective function to cause difficulties. It is demonstrated that the CC (11) EA may perform equal to its traditional counterpart, and may even outperform it on certain inseparable functions.

Black-box search by elimination of fitness functions

In black-box optimization an algorithm must solve one of many possible functions, though the precise instance is unknown. In practice, it is reasonable to assume that an algorithm designer has some basic knowledge of the problem class in order to choose appropriate methods. In traditional approaches, one focuses on how to select samples and direct search to minimize the number of function evaluations to find an optima. As an alternative view, we consider search processes as determining which function in the problem class is the unknown target function by using samples to eliminate candidate functions from the set. We focus on the efficiency of this elimination process and construct an idealized method for optimal elimination of fitness functions. From this, we place our technique in context by relating performances of our idealized method to common search heuristics (e.g., (1+1) EA), and showing how our ideas relate to No Free Lunch theory. In our discussion, we address some of the practicalities of our method. Though in its early stages, we believe that there is utility in search methods based on ideas from our elimination of functions method, and that our viewpoint provides promise and new insight about black-box optimization.

A Sensitivity Analysis of a Cooperative Coevolutionary Algorithm Biased for Optimization

Recent theoretical work helped explain certain optimization- related pathologies in cooperative coevolutionary algorithms (CCEAs). Such explanations have led to adopting specific and constructive strate- gies for improving CCEA optimization performance by biasing the algo- rithm toward ideal collaboration. This paper investigates how sensitivity to the degree of bias (set in advance) is affected by certain algorithmic and problem properties. We discover that the previous static biasing approach is quite sensitive to a number of problem properties, and we propose a stochastic alternative which alleviates this problem. We be- lieve that finding appropriate biasing rates is more feasible with this new biasing technique.

Spatial Embedding and Loss of Gradient in Cooperative Coevolutionary Algorithms

Coevolutionary algorithms offer great promise as adaptive problem solvers but suffer from several known pathologies. Historically, spatially embedded coevolutionary algorithms seem to have succeeded where other coevolutionary approaches fail; however, explanations for this have been largely unexplored. We examine this idea more closely by looking at spatial models in the context of a particular coevolutionary pathology: loss of gradient. We believe that loss of gradient in cooperative coevolution is caused by asymmetries in the problem or initial conditions between populations, driving one population to convergence before another. Spatial models seem to lock populations together in terms of evolutionary change, helping establish a type of dynamic balance to thwart loss of gradient. We construct a tunably asymmetric function optimization problem domain and conduct an empirical study to justify this assertion. We find that spatial restrictions for collaboration and selection can help keep population changes balanced when presented with severe asymmetries in the problem.

The Effects of Representational Bias on Collaboration Methods in Cooperative Coevolution

Cooperative coevolutionary algorithms (CCEAs) have been applied to many optimization problems with varied success. Recent empirical studies have shown that choices surrounding methods of collaboration may have a strong impact on the success of the algorithm. Moreover, certain properties of the problem landscape, such as variable interaction, greatly influence how these choices should be made. A more general view of variable interaction is one that considers epistatic linkages which span population boundaries. Such linkages can be caused by the decomposition of the actual problem, as well as by CCEA representation decisions regarding population structure. We posit that it is the way in which represented problem components interact, and not necessarily the existence of cross-population epistatic linkages that impacts these decisions. In order to explore this issue, we identify two different kinds of representational bias with respect to the population structure of the algorithm, decompositional bias and linkage bias. We provide analysis and constructive examples which help illustrate that even when the algorithms representation is poorly suited for the problem, the choice of how best to select collaborators can be unaffected.

A Visual Demonstration of Convergence Properties of Cooperative Coevolution

We introduce a model for cooperative coevolutionary algorithms (CCEAs) using partial mixing, which allows us to compute the expected long-run convergence of such algorithms when individuals’ fitness is based on the maximum payoff of some N evaluations with partners chosen at random from the other population. Using this model, we devise novel visualization mechanisms to attempt to qualitatively explain a difficult-to-conceptualize pathology in CCEAs: the tendency for them to converge to suboptimal Nash equilibria. We further demonstrate visually how increasing the size of N, or biasing the fitness to include an ideal-collaboration factor, both improve the likelihood of optimal convergence, and under which initial population configurations they are not much help.

Introductory tutorial on coevolution

This tutorial is designed to introduce coevolution to those with a working familiarity with evolutionary computation. The tutorial begins by providing some basic background into what coevolution is and how it has been historically employed. The fundamental mechanics of varying types of coevolutionary algorithms are covered next, focusing heavily on issues that distinguish coevolution from traditional EC. Common pathologies are categorized and discussed, then remedies for those challenges and progress monitoring methods are introduced to the audience. The tutorial concludes with a summary and a look forward to the topics discussed in the advanced tutorial on coevolution.

Evolving a Non-playable Character team with Layered Learning

Layered Learning is an iterative machine learning technique used to train agents how to perform tasks. The technique decomposes a task into simpler components and trains the agent to learn how to perform progressively more complex sub-tasks to solve the overall task. Layered Learning has been successfully used to instruct computer programs to solve Boolean-logic problems, teach robots how to walk, and train RoboCup soccer playing agents. The proposed work answers the question of how well does Layered Learning apply to the evolved development of a heterogeneous team of Non-playable Characters (NPCs) in a video game. The work compares the use of Layered Learning against evolving NPCs with monolithic based approaches. Experiment data show that Layered Learning can result in the successful development of NPCs and demonstrates that the approach performs well against monolithic evaluation.

On the performance effects of unbiased module encapsulation

A recent theoretical investigation of modular representations shows that certain modularizations can introduce a distance bias into a landscape. This was a static analysis, and empirical investigations were used to connect formal results to performance. Here we replace this experimentation with an introductory runtime analysis of performance. We study a base-line, unbiased modularization that makes use of a complete module set (CMS), with special focus on strings that grow logarithmically with the problem size. We learn that even unbiased modularizations can have profound effects on problem performance. Our (1+1) CMS-EA optimizes a generalized OneMax problem in Ω(n2) time, provably worse than a (1+1) EA. More generally, our (1+1) CMS-EA optimizes a particular class of concatenated functions in O(2lm k n) time, where lm is the length of module strings and k is the number of module positions, when the modularization is aligned with the problem separability. We compare our results to known results for traditional EAs, and develop new intuition about modular encapsulation. We observe that search in the CMS-EA is essentially conducted at two levels (intra- and extra-module) and use this observation to construct a module trap, requiring super-polynomial time for our CMS-EA and O(n ln n) for the analogous EA.