Convergence enhanced genetic algorithm with successive zooming method for solving continuous optimization problems

This paper presents results from the application of the genetic algorithm (GA) technique to the design optimization of hydrofoil and marine propeller incorporating potential based boundary element method (BEM). Although, larger population size as implemented by simple genetic algorithm (SGA) could find the optimal individual after a fewer number of generations than smaller population size, it is penalized by a longer amount of time to evaluate fitness in every generation. An investigation is, therefore, conducted in this research to implement micro genetic algorithm (μGA) with a very small population, and with simple genetic parameters, in order to achieve faster convergence to better solution from generation to generation. The technique is applied here to optimize hydrofoils of different plan forms, e.g., rectangular, elliptical, trapezoidal etc. Firstly, the hydrofoil design parameters, such as, angle of incidence, maximum thickness and camber ratios, aspect ratio, taper ratio, angle of sweep etc. are initialized randomly and the generated hydrofoil is analyzed by potential based boundary element method. GA then updates the design parameters over generation after generation and finally, finds an improved hydrofoil of maximum lift-drag ratio or minimum drag coefficient satisfying some design constraints. An improved blade or hydrofoil section is also designed by GA satisfying some design constraints. Finally, the technique is applied to the optimum design of marine propeller. In this study, μGA is found useful and prospective tool for the design optimization of hydrofoil and marine propeller due to its faster convergence. Keywords: Genetic algorithm, boundary element method, hydrofoil, propeller, design optimization  doi: 10.3329/jname.v1i1.2038 Journal of Naval Architecture and Marine Engineering 1(2004) 47-61

A good exploration ability can ensure that the method jumps out of local optimum in multimodal problems and a good exploitation can ensure an algorithm converge faster to global optimum values. So, this paper proposes a new hybrid sperm swarm optimization and genetic algorithm to obtain global optimal solutions termed HSSOGA which is developed based on the concept of balancing the exploration and exploitation capability by merging Sperm Swarm Optimization (SSO), which has a fast convergence rate, and a Genetic Algorithm (GA) that can explore a search domain efficiently. To ensure that the proposed method delivers good performance, it is evaluated with 11 standard test function problems consisting of 5 unimodal and 6 multimodal functions. The proposed HSSOGA set is compared with conventional GA and SSO methods, as well as with several hybrid methods such as Hybrid Firefly and Particle Swarm Optimization (HFPSO), hybrid Simulated Annealing and Genetic Algorithm (SAGA), Hybrid Particle Swarm Optimization and Genetic Algorithm (HFPSO), hybrid Particle Swarm Optimization and Grey Wolf Optimization (PSOGWO), and closely related Hybrid Sperm Swarm Optimization and Gravitational Search Algorithm (HSSOGSA). The results are evaluated in terms of each method’s best fitness, mean, standard deviation, and convergence rates. The numerical experiment results show that HSSOGA has better convergence towards the true global optimum values as compared to the conventional and existing hybrid methods in most unimodal and multimodal test function problems.

When using genetic and evolutionary algorithms for network design, choosing a good representation scheme for the construction of the genotype is important for algorithm performance. One of the most common representation schemes for networks is the characteristic vector representation. However, with encoding trees, and using crossover and mutation, invalid individuals occur that are either under- or over-specified. When constructing the offspring or repairing the invalid individuals that do not represent a tree, it is impossible to distinguish between the importance of the links that should be used. These problems can be overcome by transferring the concept of random keys from scheduling and ordering problems to the encoding of trees. This paper investigates the performance of a simple genetic algorithm (SGA) using network random keys (NetKeys) for the one-max tree and a real-world problem. The comparison between the network random keys and the characteristic vector encoding shows that despite the effects of stealth mutation, which favors the characteristic vector representation, selectorecombinative SGAs with NetKeys have some advantages for small and easy optimization problems. With more complex problems, SGAs with network random keys significantly outperform SGAs using characteristic vectors. This paper shows that random keys can be used for the encoding of trees, and that genetic algorithms using network random keys are able to solve complex tree problems much faster than when using the characteristic vector. Users should therefore be encouraged to use network random keys for the representation of trees.

BackgroundProtein structure prediction (PSP) has important applications in different fields, such as drug design, disease prediction, and so on. In protein structure prediction, there are two important issues. The first one is the design of the structure model and the second one is the design of the optimization technology. Because of the complexity of the realistic protein structure, the structure model adopted in this paper is a simplified model, which is called off-lattice AB model. After the structure model is assumed, optimization technology is needed for searching the best conformation of a protein sequence based on the assumed structure model. However, PSP is an NP-hard problem even if the simplest model is assumed. Thus, many algorithms have been developed to solve the global optimization problem. In this paper, a hybrid algorithm, which combines genetic algorithm (GA) and tabu search (TS) algorithm, is developed to complete this task.ResultsIn order to develop an efficient optimization algorithm, several improved strategies are developed for the proposed genetic tabu search algorithm. The combined use of these strategies can improve the efficiency of the algorithm. In these strategies, tabu search introduced into the crossover and mutation operators can improve the local search capability, the adoption of variable population size strategy can maintain the diversity of the population, and the ranking selection strategy can improve the possibility of an individual with low energy value entering into next generation. Experiments are performed with Fibonacci sequences and real protein sequences. Experimental results show that the lowest energy obtained by the proposed GATS algorithm is lower than that obtained by previous methods.ConclusionsThe hybrid algorithm has the advantages from both genetic algorithm and tabu search algorithm. It makes use of the advantage of multiple search points in genetic algorithm, and can overcome poor hill-climbing capability in the conventional genetic algorithm by using the flexible memory functions of TS. Compared with some previous algorithms, GATS algorithm has better performance in global optimization and can predict 3D protein structure more effectively.

In order to overcome the drawbacks of Simple Genetic Algorithm such as cannot get the most optimal result, low convergence speed et al. Cellular Simple Genetic Algorithm-a new genetic algorithm based on Cellular Automata-is presented in this paper. Compared with the Simple Genetic Algorithm, the experiment results show the Cellular Simple Genetic Algorithm has remarkable advantages in following aspects: reducing the search-time and improving the precise of target function.

The application of genetic algorithms (GAs) to many optimization problems in organizations often results in good performance and high quality solutions. For successful and efficient use of GAs, it is not enough to simply apply simple GAs (SGAs). In addition, it is necessary to find a proper representation for the problem and to develop appropriate search operators that fit well to the properties of the genotype encoding. The representation must at least be able to encode all possible solutions of an optimization problem, and genetic operators such as crossover and mutation should be applicable to it. In this paper, serial alternation strategies between two codings are formulated in the framework of dynamic change of genotype encoding in GAs for function optimization. Likewise, a new variant of GAs for difficult optimization problems denoted {\it Split-and-Merge} GA (SM-GA) is developed using a parallel implementation of an SGA and evolving a dynamic exchange of individual representation in the context of Dual Coding concept. Numerical experiments show that the evolved SM-GA significantly outperforms an SGA with static single coding.

The Graph Partitioning Problem (GPP) is one of the fundamental multimodal combinatorial problems that has many applications in computer science. Many algorithms have been devised to obtain a reasonable approximate solution for the GP problem. This paper applies different Genetic Algorithms in solving GP problem. In addition to using the Simple Genetic Algorithm (SGA), it introduces a new genetic algorithm named the Adaptive Population Genetic Algorithm (APGA) that overcomes the premature convergence of SGA. The paper also presents a new approach using niching methods for solving GPP as a multimodal optimization problem. The paper also presents a comparison between the four genetic algorithms; Simple Genetic Algorithm (SGA), Adaptive Population Genetic Algorithm (APGA) and the two niching methods; Sharing and Deterministic Crowding. when applied to the graph partitioning problem. Results proved the superiority of APGA over SGA and the ability of niching methods in obtaining a set of multiple good solutions.KeywordsGenetic AlgorithmPremature ConvergenceTournament SelectionSimple Genetic AlgorithmSimilar IndividualThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This paper presents a crowding niche cellular genetic algorithm (referred to NCGA) aiming at solving the problems of local convergence and non-uniform population distribution in traditional genetic algorithm. The selecting operation in traditional genetic algorithm is improved by bringing in the concept of neighbors of cellular genetic algorithm, and the population distribution is greatly enhanced by introducing crowding niche mechanism, which betters the ability of global searching and helps to avoid the population local convergence. Meanwhile, the paper describes the crowding niche cellular genetic algorithm in details and compares it with simple genetic algorithm （SGA） and simple niche genetic algorithm （NGA）; the comparison results reveal that, NCGA outperforms the other two algorithms in terms of convergence rate and population diversity.

The genetic algorithm(GA) is efficient method for topological optimization problem of truss structures because it is possible to obtain global optimum on non-convex design space. The bottleneck of this method is that a large number of function evaluations and structural analyses are necessarily. Performance of the GA depends on first arrangement of string positions and the crossover operator strongly when the simple GA apply to the topological optimization problems. If inadequate correspondence between design variables and the string positions is used, good solution is hardly obtained in spite of numerous calculations. The objective of this study is development a new genetic algorithm specialized to the topological optimization problem of the truss structure improving the calculation efficiency and reliability to obtain optimum solution. To overcome disadvantage of the simple GA, biased crossover operation with string position rearrangement is proposed. Highly fitted gene is crated and inherited by using this procedure. Minimum weight design of the truss structure consists of nine nodes are carried out by using simple G A and proposed GA, and calculation performance is compared. From the result, it is confirmed that the proposed GA is more effective and reliable in comparison with the simple GA.

University examination timetabling problem is a complicated, multi-constraint combinatorial optimization problem. The current grouping genetic algorithm could get a better optimistic solution. Although the block encoding technique was applied in, the probabilities of crossover and mutation operation were still based on simple genetic algorithm. So the universality of this algorithm is not very well because the same probabilities of crossover and mutation operation could obtain different effects in different cases of examination arrangements. To find a more general algorithm, an Improved Adaptive Genetic Algorithm (IAGA) for practical applications was presented in this paper. IAGA can reconstruct the probabilities of crossover and mutation operation according to different cases of examination arrangements. To make further improvement of its convergence speed and overcome premature problem, IAGA appropriately adjusts mutation operation by Population's Maturity in addition. Moreover, the Memory Operator was added into the Algorithm to ensure getting the global optimization solution. Finally, IAGA was tested in function optimization and Examination Timetabling problems, and the experiments show that the results are promoted very well.

This paper presents new algorithm AVSS-HSGA for optimization problems. The proposed method is a technique such that the search space of genetic algorithm (GA) can change as the need arises. It is possible to obtain the higher-fitness answer more easily than the conventional genetic algorithm introduced by the technique. It is applied to optimum design of the multi-input PSS in power system, which contains low-frequency oscillations, and the validity of the proposed method is compared with the conventional GA.

An intelligent crossover methodology within the genetic algorithm (GA) is explored within both mathematical and finite element arenas improving both design and solution convergence time. This improved intelligent crossover outperforms the traditional genetic algorithm combined with a rule-based approach utilizing domain specific knowledge developed by Webb, et al. [1]. The encoding of the improved crossover consists of two chromosome strings within the genetic algorithm where the first string represents the design or solution string, and the second string represents chromosome crossover string intelligence. This improved crossover methodology saves the best population members or designs evaluated from each generation and applies crossover chromosome intelligence to the best saved population members paired with globally selected parents. Enhanced features of this crossover methodology employ the random selection of the best designs from the prior generation as a potential parent coupled with alternating intelligence pairing methods. In addition to this approach, two globally selected parents possess the ability to mate utilizing crossover chromosome string intelligence maintaining the integrity of a global GA search. Overall, the final population following crossover employs both global and best generation design chromosome strings to maximize creativity while enhancing the solution search. This is a modification to a conventional GA that can be translated into GA encoding. This technique is explored initially through a Base 10 mathematical application followed by the examination of plate structural optimization considering stress and displacement constraints. Results from crossover intelligence are compared with the conventional genetic algorithm and from Webb, et al. [1] which illustrates the outcome of a two phase genetic optimization algorithm.

Genetic algorithm (GA) is an effective method to tackle combinatorial optimization problems. Since the limitation of encoding method, the search space of GA should be regular. Unfortunately, for constraint optimizations, this precondition is unsatisfied. To obtain a regular search space, a commonly used method is penalty functions. But the setting of a good penalty function is difficult. In this paper, a novel algorithm, called search space filling and shrinking algorithm (SSFSA), is proposed. SSFSA first seeks a smaller search space which covers all the feasible domains, then fills the unfeasible search space to acquire a regular search space. Search space shrinking diminishes the search space, so shortens the searching time. Search space filling repairs the irregular search space, and makes GA execute effectively. Experimental results show that SSFSA outperforms penalty methods'.

In recent years, extensive works on genetic algorithms have been reported covering various applications. Genetic algorithms (GAs) have received significant interest from researchers and have been applied to various optimization problems. They offer many advantages such as global search characteristics, and this has led to the idea of using this programming method in modelling dynamic non-linear systems. In this paper, a methodology for model structure selection based on a genetic algorithm was developed and applied to non-linear discrete-time dynamic systems. First the effect of different combinations of GA operators on the performance of the model developed is studied. A proposed algorithm called modified GA, or MGA, is presented and a comparison between a simple GA and a modified GA is carried out. The performance of the proposed algorithm is also compared to the model developed using the orthogonal least squares (OLS) algorithm. The adequacy of the developed models is tested using one-step-ahead prediction and correlation-based model validation tests. The results show that the proposed algorithm can be employed as an algorithm to select the structure of the proposed model.

Genetic algorithms (GAs) have become a popular optimization tool for many areas of research and topology optimization an effective design tool for obtaining efficient and lighter structures. In this paper, a versatile, robust and enhanced GA is proposed for structural topology optimization by using problem-specific knowledge. The original discrete black-and-white (0–1) problem is directly solved by using a bit-array representation method. To address the related pronounced connectivity issue effectively, the four-neighbourhood connectivity is used to suppress the occurrence of checkerboard patterns. A simpler version of the perimeter control approach is developed to obtain a well-posed problem and the total number of hinges of each individual is explicitly penalized to achieve a hinge-free design. To handle the problem of representation degeneracy effectively, a recessive gene technique is applied to viable topologies while unusable topologies are penalized in a hierarchical manner. An efficient FEM-based function evaluation method is developed to reduce the computational cost. A dynamic penalty method is presented for the GA to convert the constrained optimization problem into an unconstrained problem without the possible degeneracy. With all these enhancements and appropriate choice of the GA operators, the present GA can achieve significant improvements in evolving into near-optimum solutions and viable topologies with checkerboard free, mesh independent and hinge-free characteristics. Numerical results show that the present GA can be more efficient and robust than the conventional GAs in solving the structural topology optimization problems of minimum compliance design, minimum weight design and optimal compliant mechanisms design. It is suggested that the present enhanced GA using problem-specific knowledge can be a powerful global search tool for structural topology optimization. Copyright © 2005 John Wiley & Sons, Ltd.