Evolutionary algorithms and swarm intelligence techniques have been shown to successfully solve optimization problems where the goal is to find a single optimal solution. In multimodal domains where the goal is the locate multiple solutions in a single search space, these techniques fail. Niching algorithms extend existing global optimization algorithms to locate and maintain multiple solutions concurrently. In this thesis, strategies are developed that utilize the unique characteristics of the particle swarm optimization algorithm to perform niching. Shrinking topological neighborhoods and optimization with multiple subswarms are used to identify and stably maintain niches. Solving systems of equations and multimodal functions are used to demonstrate the effectiveness of the new algorithms. / Dissertation (MS)--University of Pretoria, 2005. / Computer Science / unrestricted

Optimization forms an intrinsic part of the design and implementation of modern systems, such as industrial systems, communication networks, and the configuration of electric or electronic components. Population-based single-solution optimization algorithms such as Particle Swarm Optimization (PSO) have been shown to perform well when a number of optimal or suboptimal solutions exist. However, some problems require algorithms that locate all or most of these optimal and suboptimal solutions. Such algorithms are known as niching or speciation algorithms. Several techniques have been proposed to extend the PSO paradigm so that multiple optima can be located and maintained within a convoluted search space. A significant number of these implementations are subswarm-based, that is, portions of the swarm are optimized separately. Niches are formed to contain these subswarms, a process that often requires user-specified parameters, as the sizes and placing of the niches are unknown. This thesis presents a new niching technique that uses the vector dot product of the social and cognitive direction vectors to determine niche boundaries. Thus, a separate niche radius is calculated for each niche, a process that requires minimal knowledge of the search space. This strategy differs from other techniques using niche radii where a niche radius is either required to be set in advance, or calculated from the distances between particles. The development of the algorithm is traced and tested extensively using synthetic benchmark functions. Empirical results are reported using a variety of settings. An analysis of the algorithm is presented as well as a scalability study. The performance of the algorithm is also compared to that of two other well-known PSO niching algorithms. To conclude, the vector-based PSO is extended to locate and track multiple optima in dynamic environments. / Thesis (PhD)--University of Pretoria, 2010. / Computer Science / unrestricted

No / This paper introduces a new technique called species conservation for evolving paral-lel subpopulations. The technique is based on the concept of dividing the population into several species according to their similarity. Each of these species is built around a dominating individual called the species seed. Species seeds found in the current gen-eration are saved (conserved) by moving them into the next generation. Our technique has proved to be very effective in finding multiple solutions of multimodal optimiza-tion problems. We demonstrate this by applying it to a set of test problems, including some problems known to be deceptive to genetic algorithms.

Dealing with optimization problems with more than one objective has been an important research area in evolutionary computation. The class of multi-objective problems (MOPs) is an important one because multi-objectivity exists in almost all aspects of human life; whereby there usually exist several compromises in each problem. Multi-objective evolutionary algorithms (MOEAs) have been applied widely in many real-world problems. This is because (1) they work with a population during the course of action, which hence offer more flexible control to find a set of efficient solutions, and (2) real-world problems are usually black-box where an explicit mathematical representation is unknown. However, MOEAs usually require a large amount of computational effort. This is a sub- stantial challenge in bringing MOEAs to practice. This thesis primarily aims to address this challenge through an investigation into issues of scalability and the balance between exploration and exploitation. These have been outstanding research challenges, not only for MOEAs, but also for evolutionary algorithms in general. A distributed framework of local models using explicit niching is introduced as an overarching umbrella to solve multi-objective optimization problems. This framework is used to address the two-part question about first, the role of communication messages and second, the role of explicit niching in distributed evolutionary multi-objective optimization. The concept behind the framework of local models is for the search to be conducted locally in different areas of the decision search space, which allows the local models to be distributed on different processing nodes. During the optimization process, local models interact (exchange messages) with each other using rules inspired from Particle Swarm Optimization (PSO). Hence, the hypothesis of this work is that running simultaneously several search engines in different local areas is better for exploiting local information, while exchanging messages among those diverse engines can provide a better exploration strategy. For this framework, as the models work locally, they gain access to some global knowledge of each other. In order to validate the proposed framework, a series of experiments on a wide range of test problems was conducted. These experiments were motivated by the following studies which in their totality contribute to the verification of our hypothesis: (1) studying the performance of the framework under different aspects such as initialization, convergence, diversity, scalability, and sensitivity to the framework's parameters, (2) investigating interleaving guidance in both the decision and objective spaces, (3) applying local models using estimation of distributions, (4) evaluating local models in noisy environments and (5) the role of communication messages and explicit niching in distributed computing. The experimental results showed that: (1) the use of local models increases the chance of MOEAs to improve their performance in finding the Pareto optimal front, (2) interaction strategies using PSO rules are suitable for controlling local models, and that they also can be coupled with specialization in order to refine the obtained non-dominated set, (3) estimation of distribution improves when coupled with local models, (4) local models work well in noisy environments, and (5) the communication cost in distributed systems with local models can be reduced significantly by using summary information (such as the direction information naturally determined by local models) as the communication messages, in comparison with conventional approaches using descriptive information of individuals. In summary, the proposed framework is a successful step towards efficient distributed MOEAs.

Evolutionary algorithms belongs among the youngest and the most progressive methods of solving difficult optimization tasks. They received huge popularity mainly due to good experimental results in optimization, a simplicity of the implementation and a high modularity, which is an ability to be modified for different problems. Among the most frequently used Evolutionary algorithms belongs Genetic Algorithm, Differential Evolution and Evolutionary Strategy. It is able to apply these algorithms and theirs variants to both continuous, discrete and mixed optimization tasks. A subject of this theses is to compare three main types of algorithms on the catalyst optimization task with mixed variables, linear constraints and experimentally evaluated fitness function.