Runtime analysis of non-elitist populations: from classical optimisation to partial information

Although widely applied in optimisation, relatively little has been proven rigorously about the role and behaviour of populations in randomised search processes. This paper presents a new method to prove upper bounds on the expected optimisation time of population-based randomised search heuristics that use non-elitist selection mechanisms and unary variation operators. Our results follow from a detailed drift analysis of the population dynamics in these heuristics. This analysis shows that the optimisation time depends on the relationship between the strength of the selective pressure and the degree of variation introduced by the variation operator. Given limited variation, a surprisingly weak selective pressure suffices to optimise many functions in expected polynomial time. We derive upper bounds on the expected optimisation time of non-elitist Evolutionary Algorithms (EA) using various selection mechanisms, including fitness proportionate selection. We show that EAs using fitness proportionate selection can optimise standard benchmark functions in expected polynomial time given a sufficiently low mutation rate. As a second contribution, we consider an optimisation scenario with partial information, where fitness values of solutions are only partially available. We prove that non-elitist EAs under a set of specific conditions can optimise benchmark functions in expected polynomial time, even when vanishingly little information about the fitness values of individual solutions or populations is available. To our knowledge, this is the first runtime analysis of randomised search heuristics under partial information

Optimal selection of weighting functions by genetic algorithms to design H∞ Anti-roll bar controllers for heavy vehicles

International audienceMulti-criterion optimization is so far popular for many complex engineering problems. The objective of active anti-roll bar of heavy vehicles is to maximize roll stability to prevent rollover in dangerous cases. However, such a performance objective must be balanced with the energy consumption of the anti-roll bar system, which is not a trivial task. In a previous work, the authors proposed an H∞ active anti-roll bar controller for which the weighting functions were chosen by trials and errors during the design step. In this paper, Genetic Algorithms (GAs) are proposed to find optimal weighting functions for the H∞ control synthesis. Such a general procedure is applied to the case of active anti-roll bar control in heavy vehicles. Thanks to GAs, the conflicting objectives between roll stability and torques generated are handled using one high level parameter only. The multi-criterion optimization solution is illustrated via the Pareto frontier. Simulations, performed in the frequency and time domains, emphasize the efficiency of the proposed method

Genetic Evolution of Neural Networks

Evolutionary computation has been around ever since the late 50s. This thesis aims at elaborate on genetic algorithms, a subset of evolutionary computation, with particular regard to the field of neuroevolution, which is the application of GAs to the generation of functioning neural networks. The most widely adopted techniques are thereby explained and contrasted. The experimentation chapter finally shows an implementation of a genetic algorithm, inspired by existing algorithms, with the objective of optimizing a novel kind of artificial neural network

Enhancing the diversity of genetic algorithm for improved feature selection

Genetic algorithm (GA) is one of the most widely used population-based evolutionary search algorithms. One of the challenging optimization problems in which GA has been extensively applied is feature selection. It aims at finding an optimal small size subset of features from the original large feature set. It has been found that the main limitation of the traditional GA-based feature selection is that it tends to get trapped in local minima, a problem known as premature convergence. A number of implementations are presented in the literature to overcome this problem based on fitness scaling, genetic operator modification, boosting genetic population diversity, etc. This paper presents a new modified genetic algorithm based on enhanced population diversity, parents' selection and improved genetic operators. Practical results indicate the significance of the proposed GA variant in comparison to many other algorithms from the literature on different datasets. ©2010 IEEE

Analysis of Linkage-Friendly Genetic Algorithms

Evolutionary algorithms (EAs) are stochastic population-based algorithms inspired by the natural processes of selection, mutation, and recombination. EAs are often employed as optimum seeking techniques. A formal framework for EAs is proposed, in which evolutionary operators are viewed as mappings from parameter spaces to spaces of random functions. Formal definitions within this framework capture the distinguishing characteristics of the classes of recombination, mutation, and selection operators. EAs which use strictly invariant selection operators and order invariant representation schemes comprise the class of linkage-friendly genetic algorithms (lfGAs). Fast messy genetic algorithms (fmGAs) are lfGAs which use binary tournament selection (BTS) with thresholding, periodic filtering of a fixed number of randomly selected genes from each individual, and generalized single-point crossover. Probabilistic variants of thresholding and filtering are proposed. EAs using the probabilistic operators are generalized fmGAs (gfmGAs). A dynamical systems model of lfGAs is developed which permits prediction of expected effectiveness. BTS with probabilistic thresholding is modeled at various levels of abstraction as a Markov chain. Transitions at the most detailed level involve decisions between classes of individuals. The probability of correct decision making is related to appropriate maximal order statistics, the distributions of which are obtained. Existing filtering models are extended to include probabilistic individual lengths. Sensitivity of lfGA effectiveness to exogenous parameters limits practical applications. The lfGA parameter selection problem is formally posed as a constrained optimization problem in which the cost functional is related to expected effectiveness. Kuhn-Tucker conditions for the optimality of gfmGA parameters are derived

Genetic optimization of fuzzy membership functions for cloud resource provisioning

The successful usage of fuzzy systems can be seen in many application domains owing to their capabilities to model complex systems by exploiting knowledge of domain experts. Their accuracy and performance are, however, primarily dependent on the design of its membership functions and control rules. The commonly employed technique to design membership functions is to exploit the knowledge of domain experts. However, in certain application domains, the knowledge of domain experts are limited and therefore, cannot be relied upon. Alternatively, optimization techniques such as genetic algorithms are utilized to optimize the various design parameters of fuzzy systems. In this paper, we report a case study of optimizing the membership functions of a fuzzy system using genetic algorithm, which is an important part of our recently developed cloud elasticity framework. This work aims to improve the overall performance of the framework. Results obtained from this research work demonstrate performance improvement in comparison with our previous experimental settings

Using a Genetic Algorithm to Optimize an Electric Field Ionization Pulse

Experimentally, we would like to demonstrate the process of selective field ionization of electrons as evidence of quantum control in a system of ultracold rubidium-85 Rydberg atoms. In order to accomplish this, an electric field pulse which is optimized to take an initial Rydberg electron state and produce the desired ionization spectra is necessary. We utilize techniques from artificial intelligence to develop a genetic algorithm for the optimization process. Our algorithm is computationally tested on an artificially constructed quantum system consisting of four energy states. In evaluating the viability of any given field pulse, we calculate the probability of an electron being found in a given state at a certain maximum field value by numerically evolving the electron’s wave function over time

Genetic Algorithm Parameter Optimization: Applied to Sensor Coverage

Genetic Algorithms are powerful tools, which when set upon a solution space will search for the optimal answer. These algorithms though have some associated problems, which are inherent to the method such as pre-mature convergence and lack of population diversity. These problems can be controlled with changes to certain parameters such as crossover, selection, and mutation. This paper attempts to tackle these problems in GA by having another GA controlling these parameters. The values for crossover parameter are: one point, two point, and uniform. The values for selection parameters are: best, worst, roulette wheel, inside 50%, outside 50%. The values for the mutation parameter are: random and swap. The system will include a control GA whose population will consist of different parameters settings. While this GA is attempting to find the best parameters it will be advancing into the search space of the problem and refining the population. As the population changes due to the search so will the optimal parameters. For every control GA generation each of the individuals in the population will be tested for fitness by being run through the problem GA with the assigned parameters. During these runs the population used in the next control generation is compiled. Thus, both the issue of finding the best parameters and the solution to the problem are attacked at the same time. The goal is to optimize the sensor coverage in a square field. The test case used was a 30 by 30 unit field with 100 sensor nodes. Each sensor node had a coverage area of 3 by 3 units. The algorithm attempts to optimize the sensor coverage in the field by moving the nodes. The results show that the control GA will provide better results when compared to a system with no parameter changes