Multi-point Crossover Research Articles

Ab initio protein fold prediction using evolutionary algorithms: Influence of design and control parameters on performance

True ab initio prediction of protein 3D structure requires only the protein primary structure, a physicochemical free energy model, and a search method for identifying the free energy global minimum. Various characteristics of evolutionary algorithms (EAs) mean they are in principle well suited to the latter. Studies to date have been less than encouraging, however. This is because of the limited consideration given to EA design and control parameter issues. A comprehensive study of these issues was, therefore, undertaken for ab initio protein fold prediction using a full atomistic protein model. The performance and optimal control parameter settings of twelve EA designs where first established using a 15-residue polyalanine molecule-design aspects varied include the encoding alphabet, crossover operator, and replacement strategy. It can be concluded that real encoding and multipoint crossover are superior, while both generational and steady-state replacement strategies have merits. The scaling between the optimal control parameter settings and polyalanine size was also identified for both generational and steady-state designs based on real encoding and multipoint crossover. Application of the steady-state design to met-enkephalin indicated that these scalings are potentially transferable to real proteins. Comparison of the performance of the steady state design for met-enkephalin with other ab initio methods indicates that EAs can be competitive provided the correct design and control parameter values are used.

Nonlinear inversion of potential-field data using a hybrid-encoding genetic algorithm

Using a genetic algorithm to solve an inverse problem of complex nonlinear geophysical equations is advantageous because it does not require computer gradients of models or “good” initial models. The multi-point search of a genetic algorithm makes it easier to find the globally optimal solution while avoiding falling into a local extremum. As is the case in other optimization approaches, the search efficiency for a genetic algorithm is vital in finding desired solutions successfully in a multi-dimensional model space. A binary-encoding genetic algorithm is hardly ever used to resolve an optimization problem such as a simple geophysical inversion with only three unknowns. The encoding mechanism, genetic operators, and population size of the genetic algorithm greatly affect search processes in the evolution. It is clear that improved operators and proper population size promote the convergence. Nevertheless, not all genetic operations perform perfectly while searching under either a uniform binary or a decimal encoding system. With the binary encoding mechanism, the crossover scheme may produce more new individuals than with the decimal encoding. On the other hand, the mutation scheme in a decimal encoding system will create new genes larger in scope than those in the binary encoding. This paper discusses approaches of exploiting the search potential of genetic operations in the two encoding systems and presents an approach with a hybrid-encoding mechanism, multi-point crossover, and dynamic population size for geophysical inversion. We present a method that is based on the routine in which the mutation operation is conducted in the decimal code and multi-point crossover operation in the binary code. The mix-encoding algorithm is called the hybrid-encoding genetic algorithm (HEGA). HEGA provides better genes with a higher probability by a mutation operator and improves genetic algorithms in resolving complicated geophysical inverse problems. Another significant result is that final solution is determined by the average model derived from multiple trials instead of one computation due to the randomness in a genetic algorithm procedure. These advantages were demonstrated by synthetic and real-world examples of inversion of potential-field data.

A genetic algorithm for scheduling staff of mixed skills under multi-criteria

We consider the problem of scheduling staff with mixed skills. We formulate the problem as a multi-criteria optimization model, where the primary objective is to minimize the total cost for assigning staff to meet the manpower demands over time, the secondary objective is to seek a solution with the maximum surplus of staff among the solutions with almost same level of assigning cost, and the tertiary objective is to reduce the variation of staff surplus over different scheduling periods. This is a new model to handle the staff scheduling problem, which is motivated by the operational requirements in some local service organizations. We propose a new genetic algorithm (GA) to solve the problem. The proposed GA differs from traditional GAs in the following components: (1) it performs its parent selection by using a ranking scheme that considers successively the three criteria; (2) it uses a multi-point crossover operator based on the hamming distance between schedules; and (3) it adopts a heuristic to resolve the problem of infeasibility created by crossover operations. Computational results are reported, which show the effectiveness of the proposed approach in finding desirable solutions.

IMPROVEMENTS OF SIMPLE GENETIC ALGORITHM IN STRUCTURAL DESIGN

The efficiency of Simple Genetic Algorithm (SGA) can be improved by some strategies. They are elitest strategy, multi-point crossover, identification of passive design variables, gradual increase of penalty parameter, and bit-wise local search. Topology optimization using GA is also discussed in this paper and examples are given. Five numerical examples show the efficiency and the optimum solutions of GA are greatly improved by these strategies. © 1997 John Wiley & sons, Ltd.

Discrete Optimization of Ship Structures from the Viewpoint of Practical Design

In practical design of ship structures, it is obvious that some structural elements, for instance, longitudinals, must be chosen from a given set of standard discrete values being available commercially. Furthermore, some integer parameters such as the number of transverse web frames in the midship segment should be considered as the design variables to be optimized. In view of those facts, we investigate especially how to deal with the above kinds of discrete design variables in this paper. A cargo ship with large hatch opening is taken as the numerical example. The structural construction cost of hold length between two transverse bulkheads is chosen as the objective function to be minimized by genetic algorithms. Besides the conventional variable design parameters, some particular parameters such as the serial number of standard shaped steel for longitudinals and for transverse frames, the number of longitudinals in a given length, the number of transverse web frames in the midship segment, etc., are also selected as the design variables from the viewpoint of practical design. For each design variable, we describe it by a specific length binary string with a corresponding relationship to its available discrete values. Through the numerical analyses, it shows that the present method is a simple yet efficient method to deal with the discrete optimization of ship structures. The search efficiency of some genetic strategies such as the elitist preserving selection, the multi-point crossover and the uniform crossover is also investigated in this paper.

On modeling genetic algorithms for functions of unitation

We discuss a novel model for analyzing the working of Genetic Algorithms (GAs), when the objective function is a function of unitation. The model is exact (not approximate), and is valid for infinite populations. Functions of unitation depend only on the number of 1's in any string. Hence, we only need to model the variations in the distribution of strings with respect to the number of 1's in the strings. We introduce the notion of a Binomial Distributed Population (BDP) as the building block of our model, and we show that the effect of uniform crossover on BDPs is to generate two other BDPs. We demonstrate that a population with any general distribution may be decomposed into several BDPs. We also show that a general multipoint crossover may be considered as a composition of several uniform crossovers. Based on these results, the effects of mutation and crossover on the distribution of strings have been characterized, and the model has been defined. GASIM-a Genetic Algorithm Simulator for functions of unitation-has been implemented based on the model, and the exactness of the results obtained from GASIM has been verified using actual Genetic Algorithm runs. The time complexity of the GA simulator derived from the model is O(l(3)) (where l is the string length), a significant improvement over previous models with exponential time complexities.

A formal analysis of the role of multi-point crossover in genetic algorithms

On the basis of early theoretical and empirical studies, genetic algorithms have typically used 1 and 2-point crossover operators as the standard mechanisms for implementing recombination. However, there have been a number of recent studies, primarily empirical in nature, which have shown the benefits of crossover operators involving a higher number of crossover points. From a traditional theoretical point of view, the most surprising of these new results relate to uniform crossover, which involves on the averageL/2 crossover points for strings of lengthL. In this paper we extend the existing theoretical results in an attempt to provide a broader explanatory and predictive theory of the role of multi-point crossover in genetic algorithms. In particular, we extend the traditional disruption analysis to include two general forms of multi-point crossover:n-point crossover and uniform crossover. We also analyze two other aspects of multi-point crossover operators, namely, their recombination potential and exploratory power. The results of this analysis provide a much clearer view of the role of multi-point crossover in genetic algorithms. The implications of these results on implementation issues and performance are discussed, and several directions for further research are suggested.