L. Darrell Whitley

Genetic algorithms and neural networks: optimizing connections and connectivity

Abstract Genetic algorithms are a robust adaptive optimization method based on biological principles. A population of strings representing possible problem solutions is maintained. Search proceeds by recombining strings in the population. The theoretical foundations of genetic algorithms are based on the notion that selective reproduction and recombination of binary strings changes the sampling rate of hyperplanes in the search space so as to reflect the average fitness of strings that reside in any particular hyperplane. Thus, genetic algorithms need not search along the contours of the function being optimized and tend not to become trapped in local minima. This paper is an overview of several different experiments applying genetic algorithms to neural network problems. These problems include 1. (1) optimizing the weighted connections in feed-forward neural networks using both binary and real-valued representations, and 2. (2) using a genetic algorithm to discover novel architectures in the form of connectivity patterns for neural networks that learn using error propagation. Future applications in neural network optimization in which genetic algorithm can perhaps play a significant role are also presented.

Evaluating evolutionary algorithms

Test functions are commonly used to evaluate the effectiveness of different search algorithms. However, the results of evaluation are as dependent on the test problems as they are on the algorithms that are the subject of comparison. Unfortunately, developing a test suite for evaluating competing search algorithms is difficult without clearly defined evaluation goals. In this paper we discuss some basic principles that can be used to develop test suites and we examine the role of test suites as they have been used to evaluate evolutionary search algorithms. Current test suites include functions that are easily solved by simple search methods such as greedy hill-climbers. Some test functions also have undesirable characteristics that are exaggerated as the dimensionality of the search space is increased. New methods are examined for constructing functions with different degrees of nonlinearity, where the interactions and the cost of evaluation scale with respect to the dimensionality of the search space.

An overview of evolutionary algorithms: practical issues and common pitfalls

Abstract An overview of evolutionary algorithms is presented covering genetic algorithms, evolution strategies, genetic programming and evolutionary programming. The schema theorem is reviewed and critiqued. Gray codes, bit representations and real-valued representations are discussed for parameter optimization problems. Parallel Island models are also reviewed, and the evaluation of evolutionary algorithms is discussed.

Lamarckian Evolution, The Baldwin Effect and Function Optimization

We compare two forms of hybrid genetic search. The first uses Lamarckian evolution, while the second uses a related method where local search is employed to change the fitness of strings, but the acquired improvements do not change the genetic encoding of the individual. The latter search method exploits the Baldwin effect. By modeling a simple genetic algorithm we show that functions exist where simple genetic algorithms without learning as well as Lamarckian evolution converge to the same local optimum, while genetic search utilizing the Baldwin effect converges to the global optimum. We also show that a simple genetic algorithm exploiting the Baldwin effect can sometimes outperform forms of Lamarckian evolution that employ the same local search strategy.

Adding learning to the cellular development of neural networks: Evolution and the baldwin effect

A grammar tree is used to encode a cellular developmental process that can generate whole families of Boolean neural networks for computing parity and symmetry. The development process resembles biological cell division. A genetic algorithm is used to find a grammar tree that yields both architecture and weights specifying a particular neural network for solving specific Boolean functions. The current study particularly focuses on the addition of learning to the development process and the evolution of grammar trees. Three ways of adding learning to the development process are explored. Two of these exploit the Baldwin effect by changing the fitness landscape without using Lamarckian evolution. The third strategy is Lamarckian in nature. Results for these three modes of combining learning with genetic search are compared against genetic search without learning. Our results suggest that merely using learning to change the fitness landscape can be as effective as Lamarckian strategies at improving search.

Cellular Genetic Algorithms

In this chapter, we introduce the applications of cellular automata in genetic algorithms. In the traditional sense, genetic algorithms (GA) originated from Darwin’s evolution theory. Borrowing from the natural law of “survival of the fittest”, through the genetic operations of selection, crossover and mutation, the individual’s adaptability gets improved. One important feature of genetic algorithms is that the optimization process is not dependent on gradient information, which makes it especially suitable for dealing with complex and nonlinear problems which are difficult to be solved by general searching methods.

Scheduling Space–Ground Communications for the Air Force Satellite Control Network

We present the first coupled formal and empirical analysis of the Satellite Range Scheduling application. We structure our study as a progression; we start by studying a simplified version of the problem in which only one resource is present. We show that the simplified version of the problem is equivalent to a well-known machine scheduling problem and use this result to prove that Satellite Range Scheduling is NP-complete. We also show that for the one-resource version of the problem, algorithms from the machine scheduling domain outperform a genetic algorithm previously identified as one of the best algorithms for Satellite Range Scheduling. Next, we investigate if these performance results generalize for the problem with multiple resources. We exploit two sources of data: actual request data from the U.S. Air Force Satellite Control Network (AFSCN) circa 1992 and data created by our problem generator, which is designed to produce problems similar to the ones currently solved by AFSCN. Three main results emerge from our empirical study of algorithm performance for multiple-resource problems. First, the performance results obtained for the single-resource version of the problem do not generalize: the algorithms from the machine scheduling domain perform poorly for the multiple-resource problems. Second, a simple heuristic is shown to perform well on the old problems from 1992; however it fails to scale to larger, more complex generated problems. Finally, a genetic algorithm is found to yield the best overall performance on the larger, more difficult problems produced by our generator.

Contrasting Structured and Random Permutation Flow-Shop Scheduling Problems: Search-Space Topology and Algorithm Performance

The use of random test problems to evaluate algorithm performance raises an important, and generally unanswered, question: Are the results generalizable to more realistic problems? Researchers generally assume that algorithms with superior performance on difficult, random test problems will also perform well on more realistic, structured problems. Our research explores this assumption for the permutation flow-shop scheduling problem. We introduce a method for generating structured flow-shop problems, which are modeled after features found in some real-world manufacturing environments. We perform experiments that indicate significant differences exist between the search-space topologies of random and structured flow-shop problems, and demonstrate that these differencescan affect the performance of certain algorithms. Yet despite these differences, and in contrast to difficult random problems, the majority of structured flow-shop problems were easily solved to optimality by most algorithms. For the problems not optimally solved, differences in performance were minor. We conclude that more realistic, structured permutation flow-shop problems are actually relatively easy to solve. Our results also raise doubts as to whether superior performance on difficult random scheduling problems translates into superior performance on more realistic kinds of scheduling problems.

Problem difficulty for tabu search in job-shop scheduling

Tabu search algorithms are among the most effective approaches for solving the job-shop scheduling problem (JSP). Yet, we have little understanding of why these algorithms work so well, and under what conditions. We develop a model of problem difficulty for tabu search in the JSP, borrowing from similar models developed for SAT and other NP-complete problems. We show that the mean distance between random local optima and the nearest optimal solution is highly correlated with the cost of locating optimal solutions to typical, random JSPs. Additionally, this model accounts for the cost of locating sub-optimal solutions, and provides an explanation for differences in the relative difficulty of square versus rectangular JSPs. We also identify two important limitations of our model. First, model accuracy is inversely correlated with problem difficulty, and is exceptionally poor for rare, very high-cost problem instances. Second, the model is significantly less accurate for structured, non-random JSPs. Our results are also likely to be useful in future research on difficulty models of local search in SAT, as local search cost in both SAT and the JSP is largely dictated by the same search space features. Similarly, our research represents the first attempt to quantitatively model the cost of tabu search for any NP-complete problem, and may possibly be leveraged in an effort to understand tabu search in problems other than job-shop scheduling.

The dispersion metric and the CMA evolution strategy

An algorithm independent metric is introduced that measures the dispersion of a uniform random sample drawn from the top ranked percentiles of the search space. A low dispersion function is one where the dispersion decreases as the sample is restricted to better regions of the search space. A high dispersion function is one where dispersion stay constant or increases as the sample is restricted to better regions of the search space. This distinction can be used to explain why the CMA Evolution Strategy is more efficient on some multimodal problems than on others.