A framework is developed to explore the connection between effective optimization algorithms and the problems they are solving. A number of “no free lunch ” (NFL) theorems are presented which establish that for any algorithm, any elevated performance over one class of problems is offset by performance over another class. These theorems result in a geometric interpretation of what it means for an algorithm to be well suited to an optimization problem. Applications of the NFL theorems to information-theoretic aspects of optimization and benchmark measures of performance are also presented. Other issues addressed include time-varying optimization problems and a priori “head-to-head” minimax distinctions between optimization algorithms, distinctions that result despite the NFL theorems’ enforcing of a type of uniformity over all algorithms.

Evolutionary programming (EP) has been applied with success to many numerical and combinatorial optimization problems in recent years. EP has rather slow convergence rates, however, on some function optimization problems. In this paper, a "fast EP" (FEP) is proposed which uses a Cauchy instead of Gaussian mutation as the primary search operator. The relationship between FEP and classical EP (CEP) is similar to that between fast simulated annealing and the classical version. Both analytical and empirical studies have been carried out to evaluate the performance of FEP and CEP for different function optimization problems. This paper shows that FEP is very good at search in a large neighborhood while CEP is better at search in a small local neighborhood. For a suite of 23 benchmark problems, FEP performs much better than CEP for multimodal functions with many local minima while being comparable to CEP in performance for unimodal and multimodal functions with only a few local minima. This paper also shows the relationship between the search step size and the probability of finding a global optimum and thus explains why FEP performs better than CEP on some functions but not on others. In addition, the importance of the neighborhood size and its relationship to the probability of finding a near-optimum is investigated. Based on these analyses, an improved FEP (IFEP) is proposed and tested empirically. This technique mixes different search operators (mutations). The experimental results show that IFEP performs better than or as well as the better of FEP and CEP for most benchmark problems tested.

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This dissertation explores an immunological model of distributed detection, called negative detection, and studies its performance in the domain of intrusion detection on computer networks. The goal of the detection system is to distinguish between illegitimate behaviour (nonself ), and legitimate behaviour (self ). The detection system consists of sets of negative detectors that detect instances of nonself; these detectors are distributed across multiple locations. The negative detection model was developed previously; this research extends that previous work in several ways. Firstly, analyses are derived for the negative detection model. In particular, a framework for explicitly incorporating distribution is developed, and is used to demonstrate that negative detection is both scalable and robust. Furthermore, it is shown that any scalable distributed detection system that requires communication (memory sharing) is always less robust than a system that does not require communication...

Adaptive simulated annealing (ASA) is a global optimization algorithm based on an associated proof that the parameter space can be sampled much more efficiently than by using other previous simulated annealing algorithms. The author's ASA code has been publicly available for over two years. During this time the author has volunteered to help people via e-mail, and the feedback obtained has been used to further develop the code.

We present a novel, general, optimally fast, incremental way of searching for a universal algorithm that solves each task in a sequence of tasks. The Optimal Ordered Problem Solver (OOPS) continually organizes and exploits previously found solutions to earlier tasks, eciently searching not only the space of domain-specific algorithms, but also the space of search algorithms. Essentially we extend the principles of optimal nonincremental universal search to build an incremental universal learner that is able to improve itself through experience.

It is often claimed that Evolutionary Algorithms are superior to other optimization techniques, in particular, in situations where not much is known about the objective function to be optimized. In contrast to that Wolpert and Macready (1997) proved that all optimization techniques have the same behavior --- on average over all f : X ! Y where X and Y are finite sets. This result is called No Free Lunch Theorem. Here different scenarios of optimization are presented. It is argued why the scenario on which the No Free Lunch Theorem is based does not model real life optimization. For more realistic scenarios it is argued why optimization techniques differ in their efficiency. For a small example this claim is proved.

The No Free Lunch theorem is reviewed and cast within a simple framework for blackbox search. A duality result which relates functions being optimized to algorithms optimizing them is obtained and is used to sharpen the No Free Lunch theorem. Observations are made concerning problem description length within the context provided by the results of this paper. It is seen that No Free Lunch results are independent from whether or not the set of functions (over which a No Free Lunch result holds) is compressible.

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Evolutionary programming (EP) has been applied to many numerical and combinatorial optimisation problems successfully in recent years. One disadvantage of EP is its slow convergence to a good near optimum for some function optimisation problems. In this paper, we propose a fast EP (FEP) which uses a Cauchy instead of Gaussian mutation operator as the primary search operator. The relationship between FEP and classical EP (CEP) is similar to that between the fast simulated annealing and the classical version. Extensive empirical studies have been carried out to evaluate the performance of FEP for different function optimisation problems. Fifty runs have been conducted for each of the 23 test functions in our studies. Our experimental results show that FEP performs much better than CEP for multi-modal functions with many local minima while being comparable to CEP in performance for unimodal and multi-modal functions with only a few local minima. We emphasise in the paper that no single al...