Multimodal Search Research Articles

Evolutionary optimization in multimodal search space

Optimization by a simple evolution strategy based on a mutation and selection scheme without recombination was tested for its efficiency in multimodal search space. A modified Rastrigin function served as an objective function providing fitness landscapes with many local optima. It turned out that the evolutionary algorithm including adaptive stepsize control is wellsuited for optimization. The process is able to efficiently surmount local energy barriers and converge to the global optimum. The relation between the optimization time available and the optimal number of offspring was investigated and a simple rule proposed. Several numbers of offspring are nearly equally suited in a smooth search space, whereas in rough fitness landscapes an optimum is observed. In either case both very large and very small numbers of offspring turned out to be unfavourable for optimization.

Evolutionary optimization in multimodal search space

Evolutionary optimization in multimodal search space

Attraction Toward Feeding Conspecifics when Food Patches are Exhaustible

Animals that forage in groups commonly share patches of food discovered by one or a few individuals.

Artificial neural networks and simulated molecular evolution are potential tools for sequence-oriented protein design.

The potential of artificial neural filter systems for feature extraction from amino acid sequences is discussed. Analysis of signal peptidase I cleavage-sites in protein precursor sequences serves as an example application. Trained neural networks can be used as the fitness function in an evolutionary protein design cycle termed 'simulated molecular evolution' which is an entirely computer-based method for the rational design of locally encoded amino acid sequence features. The design procedure itself is regarded as an optimization process which can follow several schemes. Gradient search, diffusive search, and evolution strategy have been compared with regard to their usefulness for optimization. It turns out that gradient search is well suited for optimization in smooth fitness landscapes without local minima, whereas evolution strategy seems to be a method of choice for optimization in a high-dimensional multimodal search space. This is concluded from optimization experiments using a multimodal example function.

Global optimization methods for multimodal inverse problems

Global optimization methods such as simulated annealing and genetic algorithms are potentially useful in attacking the multimodal search calculations which arise in a number of geophysical inverse problems. In the one-dimensional waveform inversion problem considered here, the optimization method must find a one-dimensional earth structure which produces a seismogram that agrees with an observed seismogram. Both simulated annealing and genetic algorithms provide satisfactory performance when the earth structure has only 15 free parameters. As this number is increased to 22, and then 30 parameters both techniques become more costly. Genetic algorithms, however, still yielded accurate solutions for problems with 30 free parameters, a point at which simulated annealing was only marginally useful. The superior performance of genetic algorithms may reflect the nonproximate search methods used by them or, possibly, the more complex and capacious memory available to a genetic algorithm for storing its accumulated experience.

Optimum design of composite laminates using genetic algorithms

The use of genetic algorithms (GAs) for the design of composite laminates is presented. Unlike the traditional hill-climbing techniques, GAs are global search procedures based on the mechanics of natural selection with the result that they are robust over a wide range of environments, particularly the multimodal search spaces encountered in composite design. The GA requires coding of the design variables as a finite-length string over a finite alphabet. Here, the design variables are the lamina orientations and stacking sequence required for maximum laminate strength and/or stiffness with minimum weight. Numerical results are presented to demonstrate that the genetic algorithm can be a viable alternative to traditional search procedures in the design of composite laminates. Finally, based on the results of this study several suggestions are mentioned for improvement in the performance of the genetic algorithm.

An heuristic strategy for multimodal search†

A heuristic search is described which has the aim of finding practically all extrema of a given non-linear functional. A standard unimodal descent algorithm is employed for finding individual extrema. This basic algorithm is applied repeatedly using various computed initial points and starting directions. Through an additional vise of several learning cycles most available extrema can be found. Numerical experiments indicate that the method is certainly very efficient for functionals of dimensions 15– 20 with 20–25 extrema.

Stochastic Automata Models with Applications to Learning Systems

The performance of variable-structure stochastic automata in stationary random environments has been extensively studied for the case when the environment's response is 0 or 1 (P model). A method is suggested for extending the updating schemes known for the P model to the S model, where the environment's output can lie in the interval [0,1], and a class of optimal nonlinear schemes for the S model is derived. Computer simulations reveal the superior performance of the S model in multimodal search even when the bounds on the performance function are unknown.

Special Multimodality and Adaptivity in Renju Game

Some aspects of a special multimodality and adaptivity in a two-person game, renju (a Japanese alignment game on a board) are presented. It is argued that such a renju multimodality will surely be a new basis of ideas and understanding of adaptive processes in artificial inttelligence requiring multimodal optimum search. The necessary concepts are developed, such as distance between any two points, four directions, string, jumstring, costring, dead (jum)string, and criterion function of a placed stone (piece or chip) on a renju board. The essential aspects of renju multimodality and adaptivity studied here are as follows: possible values of the criterion function, realized number of the highest peak (lowest valley) formed by the criterion function within a game, height of maximum peak versus the issue of the game, possible number of the highest peak (lowest valley), illustration of the criterion function, developing processes of peak and valley, adaptive mobility of the optimum point, and practical appearance of the multimodality of renju problems.