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

A dynamic parameter encoding method was previously presented by Schraudolph and Belew [J Mach Learn 9 (1992) 9] for solving optimizing problems using discrete zooming factors. In contrast, the current paper proposes a successive zooming genetic algorithm (SZGA) for identifying global solutions using continuous zooming factors. To improve the local fine-tuning capability of a genetic algorithm (GA), a new method is introduced whereby the search space is zoomed around the design point with the best fitness per 100 generations. Furthermore, the reliability of the optimized solution is determined based on a theory of probability. To demonstrate the superiority of the proposed algorithm, a simple genetic algorithm, micro-genetic algorithm, and the proposed algorithm were compared as regards their ability to minimize multi-modal continuous functions and simple continuous functions. The results confirmed that the proposed SZGA significantly improved the ability of a GA to identify a precise global minimum. As an example of structural optimization, SZGA was applied to the optimal location of support points for weight minimization in the radial gate of a dam structure. The proposed algorithm identified a more exact optimum value than the conventional GAs.     

Solution searching for multivariable optimization problems by a momentum genetic algorithm

Genetic algorithms (GAs) have emerged as powerful solution searching mechanisms, especially for nonlinear and multivariable optimization problems. Generally, it is time-consuming for GAs to find the solutions, and sometimes they cannot find the global optima. In order to improve their search performance, we propose a fast GA algorithm called momentum GA, which employs momentum offspring (MOS) and constant range mutation (CRM). MOS, which generates offspring based on the best individuals of current and past generations, is considered to have the effect of fast searching for the optimum solutions. CRM is considered to have the ability to avoid the production of ineffective individuals and maintain the diversity of the population. In order to verify the performance of our proposed method, a comparison between momentum GA and the conventional mean will be implemented by utilizing optimization problems of two multivariable functions and neural network training problems with different activation functions. Simulations show that the proposed method has good performance regardless of the small values of the population size and generation number in the GA. This work was presented in part at the 12th International Symposium on Artificial Life and Robotics, Oita, Japan, January 25–27, 2007     

Multi-objective topology optimization through GA-based hybridization of partial solutions

In a recent project the authors have developed an approach to assist the identification of the optimal topology of a technical system, capable of overcoming geometrical contradictions that arise from conflicting design requirements. The method is based on the hybridization of partial solutions obtained from mono-objective topology optimization tasks. In order to investigate efficiency, effectiveness and potentialities of the developed hybridization algorithm, a comparison among the proposed approach and traditional topology optimization techniques such as Genetic Algorithms (GAs) and gradient-based methods is presented here. The benchmark has been performed by applying the hybridization algorithm to several case studies of multi-objective optimization problems available in literature. The obtained results demonstrate that the proposed approach is definitely less expensive in terms of computational requirements, than the conventional application of GAs to topology optimization tasks, still keeping the same effectiveness in terms of searching the global optimum solution. Moreover, the comparison among the hybridized solutions and the solutions obtained through GAs and gradient-based optimization methods, shows that the proposed algorithm often leads to very different topologies having better performances.     

Evolving structural design solutions using an implicit redundant Genetic Algorithm

Performing synthesis during conceptual design provides substantial cost savings by selecting an efficient design topology and geometry, in addition to selecting the structural member properties. A new evolutionary-based representation, which combines redundancy and implicit fitness constraints, is introduced to represent and search for design solutions in an unstructured, multi-objective structural frame problem. The implicit redundant representation genetic algorithm, in tandem with the unstructured problem domain definition, allows the evaluation of diverse frame topologies and geometries. The IRR GA allows the representation of a variable number of location independent parameters, which overcomes the fixed parameter limitations of standard GAs. The novel frame designs evolved by the IRR GA synthesis design method compare favourably with traditional frame design solutions calculated by trial and error. Received May 27, 1999     

MCEDA: A novel many-objective optimization approach based on model and clustering

To solve many-objective optimization problems (MaOPs) by evolutionary algorithms (EAs), the maintenance of convergence and diversity is essential and difficult. Improved multi-objective optimization evolutionary algorithms (MOEAs), usually based on the genetic algorithm (GA), have been applied to MaOPs, which use the crossover and mutation operators of GAs to generate new solutions. In this paper, a new approach, based on decomposition and the MOEA/D framework, is proposed: model and clustering based estimation of distribution algorithm (MCEDA). MOEA/D means the multi-objective evolutionary algorithm based on decomposition. The proposed MCEDA is a new estimation of distribution algorithm (EDA) framework, which is intended to extend the application of estimation of distribution algorithm to MaOPs. MCEDA was implemented by two similar algorithm, MCEDA/B (based on bits model) and MCEDA/RM (based on regular model) to deal with MaOPs. In MCEDA, the problem is decomposed into several subproblems. For each subproblem, clustering algorithm is applied to divide the population into several subgroups. On each subgroup, an estimation model is created to generate the new population. In this work, two kinds of models are adopted, the new proposed bits model and the regular model used in RM-MEDA (a regularity model based multi-objective estimation of distribution algorithm). The non-dominated selection operator is applied to improve convergence. The proposed algorithms have been tested on the benchmark test suite for evolutionary algorithms (DTLZ). The comparison with several state-of-the-art algorithms indicates that the proposed MCEDA is a competitive and promising approach.     

Self-adaptive Bat Algorithm With Genetic Operations

Swarm intelligence in a bat algorithm (BA) provides social learning. Genetic operations for reproducing individuals in a genetic algorithm (GA) offer global search ability in solving complex optimization problems. Their integration provides an opportunity for improved search performance. However, existing studies adopt only one genetic operation of GA, or design hybrid algorithms that divide the overall population into multiple subpopulations that evolve in parallel with limited interactions only. Differing from them, this work proposes an improved self-adaptive bat algorithm with genetic operations (SBAGO) where GA and BA are combined in a highly integrated way. Specifically, SBAGO performs their genetic operations of GA on previous search information of BA solutions to produce new exemplars that are of high-diversity and high-quality. Guided by these exemplars, SBAGO improves both BA’s efficiency and global search capability. We evaluate this approach by using 29 widely-adopted problems from four test suites. SBAGO is also evaluated by a real-life optimization problem in mobile edge computing systems. Experimental results show that SBAGO outperforms its widely-used and recently proposed peers in terms of effectiveness, search accuracy, local optima avoidance, and robustness.      

A modified distance method for multicriteria optimization, using genetic algorithms

The common application areas of Genetic Algorithms (GAs) have been to single criterion difficult optimization problems. The GA selection mechanism is often dependent upon a single valued scalar objective funtion. In this paper, we present results of a modified distance method. The distance method was proposed earlier by us, for solving multiple criteria problems with GAs. The Pareto set estimation method, which is fundamental to multicriteria analysis, is used to perform the multicriteria optimization using GAs. First, the Pareto set is found out from the population of the initial generation of the GA. The fitness of a new solution, is calculated by a distance measure with reference to the Pareto set of the previous runs. We calculate the distances of a solution from all the Pareto solutions found since the previous run, but the minimum of these distances is taken under consideration while evaluating the fitness of the solution. Thus the GA tries to maximize the distance of future Pareto solutions from present Pareto solutions in the positive Pareto space of the given problem. Here we modify distance method, by using an improved algorithm to assign and make use of the latent potential of the Pareto solutions which are found during the runs. Two detailed numerical examples and computer generated results are also presented.     

A novel optimization approach for minimum cost design of trusses

This paper describes new optimization strategies that offer significant improvements in performance over existing methods for bridge-truss design. In this study, a real-world cost function that consists of costs on the weight of the truss and the number of products in the design is considered. We propose a new sizing approach that involves two algorithms applied in sequence – (1) a novel approach to generate a “good” initial solution and (2) a local search that attempts to generate the optimal solution by starting with the final solution from the previous algorithm. A clustering technique, which identifies members that are likely to have the same product type, is used with cost functions that consider a cost on the number of products. The proposed approach gives solutions that are much lower in cost compared to those generated in a comprehensive study of the same problem using genetic algorithms (GA). Also, the number of evaluations needed to arrive at the optimal solution is an order of magnitude lower than that needed in GAs. Since existing optimization techniques use cost functions like those of minimum-weight truss problems to illustrate their performance, the proposed approach is also applied to the same examples in order to compare its relative performance. The proposed approach is shown to generate solutions of not only better quality but also much more efficiently. To highlight the use of this sizing approach in a broader optimization framework, a simple geometry optimization algorithm that uses the sizing approach is presented. This algorithm is also shown to provide solutions better than the existing results in literature.     

A double-multiplicative dynamic penalty approach for constrained evolutionary optimization

The present paper proposes a double-multiplicative penalty strategy for constrained optimization by means of genetic algorithms (GAs). The aim of this research is to provide a simple and efficient way of handling constrained optimization problems in the GA framework without the need for tuning the values of penalty factors for any given optimization problem. After a short review on the most popular and effective exterior penalty formulations, the proposed penalty strategy is presented and tested on five different benchmark problems. The obtained results are compared with the best solutions provided in the literature, showing the effectiveness of the proposed approach.     

Improved genetic algorithm with two-level approximation for truss topology optimization

Truss topology optimization using Genetic Algorithms (GAs) usually requires large computational cost, especially for large-scale problems. To decrease the structural analyses, a GA with a Two-level Approximation (GATA) was proposed in a previous work, and showed good computational efficiency with less structural analyses. However, this optimization method easily converges to sub-optimum points, resulting in a poor ability to search for a global optimum. Therefore, to address this problem, we propose an Improved GA with a Two-level Approximation (IGATA) which includes several modifications to the approximation function and simple GA developed previously. A Branched Multi-point Approximation (BMA) function, which is efficient and without singularity, is introduced to construct a first-level approximation problem. A modified Lemonge penalty function is adopted for the fitness calculation, while an Elite Selection Strategy (ESS) is proposed to improve the quality of the initial points. The results of numerical examples confirm the lower computational cost of the algorithm incorporating these modifications. Numerous numerical experiments show good reliability of the IGATA given appropriate values for the considered parameters.     

Countering the negative search bias of ant colony optimization in subset selection problems

In their quest to find a good solution to a given optimization problem, metaheuristic search algorithms intend to explore the search space in a useful and efficient manner. Starting from an initial state or solution(s), they are supposed to evolve towards high-quality solutions. For some types of genetic algorithms (GAs), it has been shown that the population of chromosomes can converge to very bad solutions, even for trivial problems. These so-called deceptive effects have been studied intensively in the field of GAs and several solutions to these problems have been proposed. Recently, similar problems have been noticed for ant colony optimization (ACO) as well. As for GAs, ACO's search can get biased towards low-quality regions in the search space, probably resulting in bad solutions. Some methods have been proposed to investigate the presence and strength of this negative bias in ACO. We present a framework that is capable of eliminating the negative bias in subset selection problems. The basic Ant System algorithm is modified to make it more robust to the presence of negative bias. A profound simulation study indicates that the modified Ant System outperforms the original version in problems that are susceptible to bias. Additionally, the proposed methodology is incorporated in the Max–Min AS and applied to a real-life subset selection problem.     

A hybrid biogeography-based optimization algorithm for job shop scheduling problem

In this paper, a hybrid biogeography-based optimization (HBBO) algorithm has been proposed for the job-shop scheduling problem (JSP). Biogeography-based optimization (BBO) is a new bio-inpired computation method that is based on the science of biogeography. The BBO algorithm searches for the global optimum mainly through two main steps: migration and mutation. As JSP is one of the most difficult combinational optimization problems, the original BBO algorithm cannot handle it very well, especially for instances with larger size. The proposed HBBO algorithm combines the chaos theory and “searching around the optimum” strategy with the basic BBO, which makes it converge to global optimum solution faster and more stably. Series of comparative experiments with particle swarm optimization (PSO), basic BBO, the CPLEX and 14 other competitive algorithms are conducted, and the results show that our proposed HBBO algorithm outperforms the other state-of-the-art algorithms, such as genetic algorithm (GA), simulated annealing (SA), the PSO and the basic BBO.     

IMMIGRANTS-ENHANCED MULTI-POPULATION GENETIC ALGORITHMS FOR DYNAMIC SHORTEST PATH ROUTING PROBLEMS IN MOBILE AD HOC NETWORKS

One of the most important characteristics in mobile wireless networks is the topology dynamics, that is, the network topology changes over time as a result of energy conservation or node mobility. Therefore, the shortest path (SP) routing problem turns out to be a dynamic optimization problem in mobile wireless networks. In this article, we propose to use multi-population genetic algorithms (GAs) with an immigrants scheme to solve the dynamic SP routing problem in mobile ad hoc networks, which are the representative of new generation wireless networks. Two types of multi-population GAs are investigated. One is the forking GA in which a parent population continuously searches for a new optimum and a number of child populations try to exploit previously detected promising areas. The other is the shifting-balance GA in which a core population is used to exploit the best solution found and a number of colony populations are responsible for exploring different areas in the solution space. Both multi-population GAs are enhanced by an immigrants scheme to handle the dynamic environments. In the construction of the dynamic network environments, two models are proposed and investigated. One is called the general dynamics model, in which the topologies are changed because the nodes are scheduled to sleep or wake up. The other is called the worst dynamics model, in which the topologies are altered because some links on the current best shortest path are removed. Extensive experiments are conducted based on these two models. The experimental results show that the proposed multi-population GAs with immigrants enhancement can quickly adapt to the environmental changes (i.e., the network topology changes) and produce high-quality solutions after each change.     

A new evolutionary approach to cutting stock problems with and without contiguity

Evolutionary algorithms (EAs) have been applied to many optimization problems successfully in recent years. The genetic algorithm (GAs) and evolutionary programming (EP) are two different types of EAs. GAs use crossover as the primary search operator and mutation as a background operator, while EP uses mutation as the primary search operator and does not employ any crossover. This paper proposes a novel EP algorithm for cutting stock problems with and without contiguity. Two new mutation operators are proposed. Experimental studies have been carried out to examine the effectiveness of the EP algorithm. They show that EP can provide a simple yet more effective alternative to GAs in solving cutting stock problems with and without contiguity. The solutions found by EP are significantly better (in most cases) than or comparable to those found by GAs.Scope and purposeThe one-dimensional cutting stock problem (CSP) is one of the classical combinatorial optimization problems. While most previous work only considered minimizing trim loss, this paper considers CSPs with two objectives. One is the minimization of trim loss (i.e., wastage). The other is the minimization of the number of stocks with wastage, or the number of partially finished items (pattern sequencing or contiguity problem). Although some traditional OR techniques (e.g., programming based approaches) can find the global optimum for small CSPs, they are impractical to find the exact global optimum for large problems due to combinatorial explosion. Heuristic techniques (such as various hill-climbing algorithms) need to be used for large CSPs. One of the heuristic algorithms which have been applied to CSPs recently with success is the genetic algorithm (GA). This paper proposes a much simpler evolutionary algorithm than the GA, based on evolutionary programming (EP). The EP algorithm has been shown to perform significantly better than the GA for most benchmark problems we used and to be comparable to the GA for other problems.     

Multi-objective genetic local search algorithm using Kohonen’s neural map

Genetic Algorithms (GAs) are population based global search methods that can escape from local optima traps and find the global optima regions. However, near the optimum set their intensification process is often inaccurate. This is because the search strategy of GAs is completely probabilistic. With a random search near the optimum sets, there is a small probability to improve current solution. Another drawback of the GAs is genetic drift. The GAs search process is a black box process and no one knows that which region is being searched by the algorithm and it is possible that GAs search only a small region in the feasible space. On the other hand, GAs usually do not use the existing information about the optimality regions in past iterations.In this paper, a new method called SOM-Based Multi-Objective GA (SBMOGA) is proposed to improve the genetic diversity. In SBMOGA, a grid of neurons use the concept of learning rule of Self-Organizing Map (SOM) supporting by Variable Neighborhood Search (VNS) learn from genetic algorithm improving both local and global search. SOM is a neural network which is capable of learning and can improve the efficiency of data processing algorithms. The VNS algorithm is developed to enhance the local search efficiency in the Evolutionary Algorithms (EAs). The SOM uses a multi-objective learning rule based-on Pareto dominance to train its neurons. The neurons gradually move toward better fitness areas in some trajectories in feasible space. The knowledge of optimum front in past generations is saved in form of trajectories. The final state of the neurons determines a set of new solutions that can be regarded as the probability density distribution function of the high fitness areas in the multi-objective space. The new set of solutions potentially can improve the GAs overall efficiency. In the last section of this paper, the applicability of the proposed algorithm is examined in developing optimal policies for a real world multi-objective multi-reservoir system which is a non-linear, non-convex, multi-objective optimization problem.     

A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm

Genetic algorithms (GAs), which are directed stochastic hill climbing algorithms, are a commonly used optimization technique and are generally applied to single criterion optimization problems with fairly complex solution landscapes. There has been some attempts to apply GA to multicriteria optimization problems. The GA selection mechanism is typically dependent on a single-valued objective function and so no general methods to solve multicriteria optimization problems have been developed so far. In this paper, a new method of transformation of the multiple criteria problem into a single-criterion problem is presented. The problem of transformation brings about the need for the introduction of thePareto set estimation method to perform the multicriteria optimization using GAs. From a given solution set, which is the population of a certain generation of the GA, the Pareto set is found. The fitness of population members in the next GA generation is calculated by a distance metric with a reference to the Pareto set of the previous generation. As we are unable to combine the objectives in some way, we resort to this distance metric in the positive Pareto space of the previous solutions, as the fitness of the current solutions. This new GA-based multicriteria optimization method is proposed here, and it is capable of handling any generally formulated multicriteria optimization problem. The main idea of the method is described in detail in this paper along with a detailed numerical example. Preliminary computer generated results show that our approach produces better, and far more Pareto solutions, than plain stochastic optimization methods.     

基于可调变异算子求解遗传算法的欺骗问题*

针对遗传算法GA(genetic algorithm)欺骗问题的某些特点,从理论上对变异算子进行分析,提出了解决GA欺骗问题的一种新的方法.该算法能够在遗传搜索过程中改变变异算子的方向和概率,使变异算子可调,这样可以有效地消除遗传算法中的欺骗性条件,保持群体的多样性,使GA能顺利地收敛到全局最优解.     

Structural topology optimization using ant colony optimization algorithm

The ant colony optimization (ACO) algorithm, a relatively recent bio-inspired approach to solve combinatorial optimization problems mimicking the behavior of real ant colonies, is applied to problems of continuum structural topology design. An overview of the ACO algorithm is first described. A discretized topology design representation and the method for mapping ant's trail into this representation are then detailed. Subsequently, a modified ACO algorithm with elitist ants, niche strategy and memory of multiple colonies is illustrated. Several well-studied examples from structural topology optimization problems of minimum weight and minimum compliance are used to demonstrate its efficiency and versatility. The results indicate the effectiveness of the proposed algorithm and its ability to find families of multi-modal optimal design.     

Domain-specific initial population strategy for compliant mechanisms using customized genetic algorithm

Genetic algorithms (GAs) can precisely handle the discrete structural topology optimization of single-piece elastic structures called compliant mechanisms. The initial population of these elastic structures is mostly generated by assigning the material at random. This causes disconnected or unfeasible designs and further rule-based repairing can result in representation degeneracy. However, the problem-specific initial population can affect the performance of GAs like other operators. In this paper, a domain-specific initial population strategy is developed that generates geometrically feasible structures for path generating compliant mechanisms (PGCMs). It is coupled with the elitist non-dominated sorting genetic algorithm (NSGA-II) which has been customized for structural topology optimization. The performance of initial population strategy over random initialization using customized NSGA-II is checked on single and bi-objective optimization problems. Based on the results, it is observed that the custom initialization outperforms the random initialization by dominating all the solutions and exploring larger area of posed objectives. The elastic structures obtained by solving two examples of PGCMs using domain specific initial population strategy are also presented.     

Constraint handling in genetic algorithms using a gradient-based repair method

Constraint handling is one of the major concerns when applying genetic algorithms (GAs) to solve constrained optimization problems. This paper proposes to use the gradient information derived from the constraint set to systematically repair infeasible solutions. The proposed repair procedure is embedded into a simple GA as a special operator. Experiments using 11 benchmark problems are presented and compared with the best known solutions reported in the literature. Our results are competitive, if not better, compared to the results reported using the homomorphous mapping method, the stochastic ranking method, and the self-adaptive fitness formulation method.