Convergence Properties Of Genetic Algorithms Research Articles

Hybrid Algorithm for Multiple Gravity-Assist and Impulsive Delta-V Maneuvers

A combination of multiple gravity-assist and impulsive Delta-V maneuvers is often required for interplanetary and interstellar space missions, such as NASA’s Voyager 1 and 2, Galileo, and Cassini missions. The design of such complex interplanetary missions is difficult with traditional mission analysis techniques because the mission must be prepruned to determine potential trajectories. Prepruning has been necessary because these mission often require the optimization of dozens of variables in a highly nonlinear and discontinuous design space. This process risks pruning nonintuitive solutions, which may potentially contain the optimal trajectory. In this paper, a hybrid optimization algorithm that is capable of determining optimal interplanetary trajectories, including the number of gravity assists and the planetary flyby order, is developed. The hybrid optimization algorithm uses a stochastic genetic algorithm to globally search the design space, as well as traditional nonlinear programming gradient-based optimization tools to determine locally optimal trajectories. By combining the global convergence properties of genetic algorithms with the accuracy of gradient-based solvers, a robust optimization algorithm capable of determining near-optimal solutions for a complex interplanetary space mission is developed.

Box-Complex Assisted Genetic Algorithm for Optimal Control of Batch Reactor

To enhance convergence property of Genetic Algorithm (GA), we in this work propose modification in GA by combining the global search property of GA with a convergence property of Box-Complex method. Using the current population of GA, new members are created using Box-Complex concept, which replaces equal number of worst population members. A comparative study of the proposed GA with the conventional GA and widely accepted Jumping Gene GA (JG GA) is presented in this work. We have considered two mathematical and a batch reactor optimal control applications for evaluating the efficacy of the proposed GA. There are two user defined parameters in the proposed algorithm, namely extent of Box-Complex Assistance(BCA), and expansion/contraction factor α. Effect of both these parameters on convergence is presented in this work for the proposed GA.

Applying Genetic Algorithms to the Data Traffic Scheduling and Performance Analysis of a Long-Term Evolution System

In this study it develops a superior transmission resource allocation method by using genetic algorithm. The convergence properties of genetic algorithm are employed to increase the transmission resource use efficiency of a base (station) to allow users to access wider bandwidth and to improve the system throughput and packet service rate. In this paper, it also studies the genetic algorithm convergent phenomena. The calculated system convergent time is significantly less than that of a long term evolution (LTE) frame duration. Finally, the system performances with and without implementing the genetic algorithm in resource allocations are simulated; their performances are compared to study the effectiveness of using the genetic algorithm in resource allocation.

Markov chain analysis of genetic algorithms applied to fitness functions perturbed concurrently by additive and multiplicative noise

We analyze the transition and convergence properties of genetic algorithms (GAs) applied to fitness functions perturbed concurrently by additive and multiplicative noise. Both additive noise and multiplicative noise are assumed to take on finitely many values. We explicitly construct a Markov chain that models the evolution of GAs in this noisy environment and analyze it to investigate the algorithms. Our analysis shows that this Markov chain is indecomposable; it has only one positive recurrent communication class. Using this property, we establish a condition that is both necessary and sufficient for GAs to eventually (i.e., as the number of iterations goes to infinity) find a globally optimal solution with probability 1. Similarly, we identify a condition that is both necessary and sufficient for the algorithms to eventually with probability 1 fail to find any globally optimal solution. Our analysis also shows that the chain has a stationary distribution that is also its steady-state distribution. Based on this property and the transition probabilities of the chain, we compute the exact probability that a GA is guaranteed to select a globally optimal solution upon completion of each iteration.

A Markov chain that models genetic algorithms in noisy environments

In this study, we construct a Markov chain that models genetic algorithms (GAs) in noisy environments. Fitness functions are assumed to be perturbed by additive or multiplicative random noise that takes on finitely many values. We first compute the transition probabilities of this Markov chain exactly. We then focus on the environment where fitness functions are additively disturbed and further analyze the chain in order to investigate the transition and convergence properties of GAs in this noisy environment. The Markov chain has only one positive recurrent communication class, and it follows immediately from this property that GAs eventually find at least one globally optimal solution with probability 1. Furthermore, our analysis shows that the chain has a stationary distribution that is also its steady-state distribution. Using this property and the transition probabilities of the chain, we derive an upper bound for the number of iterations sufficient to ensure with at least a specified probability that a GA selects a globally optimal solution upon termination.

On Stability and Classification Tools for Genetic Algorithms

Convergence of genetic algorithms in the form of asymptotic stability requirements is discussed. Some tools to measure convergence properties of genetic algorithms are introduced. A classification procedure is proposed that is based on the following conjecture: the entropy and the fractal dimension of trajectories of genetic algorithms produced by them are quantities that can characterize the algorithms. The role of these quantities as invariants of the algorithm classes is discussed together with the compression ratio of points of genetic algorithms.

On economic applications of the genetic algorithm: a model of the cobweb type

This paper explores the idea of using artificial adaptive agents in economic theory. In particular, we use Genetic Algorithms (GAs) to model the learning behavior of a population of adaptive and boundedly rational agents interacting in an economic system. We analyze the behavior of a GA in two versions of a model of the cobweb-type, one in which firms make only quantity choices, and the other one in which firms first decide to exit or to stay in the market, and subsequently decide how much to produce. We present simulations with different coding schemes and interpret the rather surprising differences between the results for different setups by employing the mathematical theory for GAs with state-dependent fitness functions. In particular, we explain the relationship between coding and convergence properties of GAs.

Genetic algorithms with noisy fitness

The convergence properties of genetic algorithms with noisy fitness information are studied here. In the proposed scheme, hypothesis testing methods are used to compare sample fitness values. The “best” individual of each generation is kept and a greater-than-zero mutation rate is used so that every individual will be generated with positive probability in each generation. The convergence criterion is different from the frequently-used uniform population criterion; instead, the sequence of the “best” individual in each generation is considered, and the algorithm is regarded as convergent if the sequence of the “best” individuals converges with probability one to a point with optimal average fitness.