Nonstationary Function Optimization Using Genetic Algorithms with Dominance and Diploidy

Specifically, we apply genetic algorithms that include diploid genotypes and dominance operators to a simple nonstationary problem in function optimization: an oscillating, blind knapsack problem. In doing this, we find that diploidy and dominance induce a form of long term distributed memory that stores and occasionally remembers good partial solutions that were once desirable. This memory permits faster adaptation to drastic environmental shifts than is possible without the added structures and operators. This paper investigates the use of diploid representations and dominance operators in genetic algorithms (GAs) to improve performance in environments that vary with time. The mechanics of diploidy and dominance in natural genetics are briefly discussed, and the usage of these structures and operators in other GA investigations is reviewed. An extension of the schema theorem is developed which illustrates the ability of diploid GAs with dominance to hold alternative alleles in abeyance. Both haploid and diploid GAs are applied to a simple time varying problem: an oscillating, blind knapsack problem. Simulation results show that a diploid GA with an evolving dominance map adapts more quickly to the sudden changes in this problem environment than either a haploid GA or a diploid GA with a fixed dominance map. These proof-of-principle results indicate that diploidy and dominance can be used to induce a form of long term distributed memory within a population of structures. In the remainder of this paper, we explore the mechanism, theory, and implementation of dominance and diploidy in artificial genetic search. We start by examining the role of diploidy and dominance in natural genetics, and we briefly review examples of their usage in genetic algorithm circles. We extend the schema theorem to analyze the effect of these structures and mechanisms. We present results from computational experiments on a 17-object, oscillating, blind 0-1 knapsack problem. Simulations with adaptive dominance maps and diploidy are able to adapt more quickly to sudden environmental shifts than either a haploid genetic algorithm or a diploid genetic algorithm with fixed dominance map. These results are encouraging and suggest the investigation of dominance and diploidy in other GA applications in search and machine learning.  Real world problems are seldom independent of time. If you don't like the weather, wait five minutes and it will change. If this week gasoline costs $1.30 a gallon, next week it may cost $0.89 a gallon or perhaps $2.53 a gallon. In these and many more complex ways, real world environments are both nonstationary and noisy. Searching for good solutions or good behavior under such conditions is a difficult task; yet, despite the perpetual change and uncertainty, all is not lost. History does repeat itself, and what goes around does come around. The horrors of Malthusian extrapolation rarely come to pass, and solutions that worked well yesterday are at least somewhat likely to be useful when circumstances are somewhat similar tomorrow or the day after. The temporal regularity implied in these observations places a premium on search augmented by selective memory. In other words, a system which does not learn the lessons of its history is doomed to repeat its mistakes. THE MECHANICS OF NATURAL DOMINANCE AND DIPLOIDY It is surprising to some genetic algorithm newcomers that tpe most commonly used GA is modeled after the mechanics of haploid genetics. After all, don't most elementary genetics textbooks start off with a discussion of Mendel's pea plants and some mention of diploidy and dominance? The reason for this disparity between genetic algorithm practice and genetics textbook coverage is due to the success achieved by early GA investigators (Hollstien, 1971; De Jong, 1975) using haploid chromosome models on stationary problems. It was found that surprising efficacy and efficiency could be obtained using single stranded (haploid) chromosomes under the action of reproduction and crossover. As a result, later investigators of artificial genetic search have tended to ignore diploidy and dominance. In this section we examine the mechanics of diploidy and dominance to understand their roles in shielding alternate In this paper, we investigate the behavior of a genetic algorithm augmented by structures and operators capable of exploiting the regularity and repeatability of many nonstationary environments.