In this paper a scalability test over eleven scalable benchmark functions, provided by the current workshop (Evolutionary Algorithms and other Metaheuristics for Continuous Optimization Problems-A Scalability Test), are conducted for accelerated DE using generalized opposition-based learning (GODE). The average error of the best individual in the population has been reported for dimensions 50, 100, 200, and 500 in order to compare with the results of other algorithms which are participating in this workshop. Current work is based on opposition-based differential evolution (ODE) and our previous work, accelerated PSO by generalized OBL.

Genetic programming (GP) is an illogical method for automatic programming. It shows creativity in discovering a desired program to solve problem, but in essence bases its searching principle on software testing. This paper is dedicated to establishing a novel GP which combines classical GP and formal approaches like Hoare’s logic, model checking, and automaton, etc. The result indicates these methods can collaborate in the framework pretty well. As has been demonstrated by the experiment, they work in a way that preserves their advantages while each compensates for the deficiencies of the other. So, once an approximate program is obtained, we can say with certainty it is correct with respect to its corresponding pre- and post-conditions.

There exist many difficulties when investment portfolio problems based on Markowitz model are solved by using some traditional methods, such as Newton method, conjugate gradient method, etc. One of the difficulties is that Markowitz model has rigorous constraint conditions. Evolutionary computation is a parallel global optimization algorithm with high efficiency and it has been widely used in portfolio investment field. A heuristic subspace searching algorithm is put forward in this paper for solving investment portfolio optimization problems based on Markowitz model. The experimental results indicate that this algorithm has an improved efficiency compared with traditional evolutionary computation.

Reuse (or reusability) plays an important role in the software engineering. The software reuse technique, considered as an effective approach to improve the productivity, can reduce the cost in software design and development. This paper introduces the concept of reuse in the software into the chromosome and presents an evolutionary modeling algorithm based on the overlapped reuse. Furthermore, a new gene reading & computing machine is constructed for calculating the fitness of chromosome which has the characteristic of reusability. As a new kind of modeling algorithm, this is a new research way for evolutionary modeling.

In the paper, for many-objective optimization problems, the authors pointed out that the Pareto Optimality is unfair, unreasonable and imperfect for Many-objective Optimization Problems (MOPs) underlying the hypothesis that all objectives have equal importance and propose a new evolutionary decision theory. The key contribution is the discovery of the new definition of optimality called E-optimality for MOP that is based on a new conception, so called E-dominance, which not only considers the difference of the number of superior and inferior objectives between two feasible solutions, but also considers the values of improved objective functions underlying the hypothesis that all objectives in the problem have equal importance. Two new evolutionary algorithms for E-optimal solutions are proposed. Because the new relation-≺Eof E-dominance is not transitive, so a new way must be found for consideration of convergence properties of algorithms. A Boolean function better used as a select strategy is defined The convergence theorems of the new evolutionary algorithms are proved. Some numerical experiments show that the new evolutionary decision theory is better than Pareto decision theory for many-objective function optimization problems.

Optimum multiuser detection (OMD) in direct-sequence code-division multiple access (DS-CDMA) communication systems is a combinatorial optimization problem and has been proven NP-complete. Many heuristics have been presented to solve this problem, but few of them consider the fitness landscape of OMD carefully. In this paper, we analyze the fitness landscape of OMD, including the neighborhood structure and the distribution of local optima. Numerical results give hints on how to design efficient heuristic algorithms for the problem. A meta-heuristic algorithm considering the analysis results is proposed With a proper local search and a well-chosen perturbation strategy, the proposed algorithm can find the (near) optimal solution rapidly with lower computational complexity. Simulation results show it outperforms other heuristic multiuser detection algorithms when the number of users is large. In the condition of small number of users, it can achieve the bit error rate (BER) bound of OMD.

Particle swarm optimization (PSO) has shown its fast search speed in many complicated optimization and search problems. However, PSO could often easily fall into local optima. This paper presents an improved PSO with adaptive jump. The proposed method combines a novel jump strategy and an adaptive Cauchy mutation operator to help escape from local optima. The new algorithm was tested on a suite of well-known benchmark functions with many local optima. Experimental results were compared with some similar PSO algorithms based on Gaussian distribution and Cauchy distribution, and showed better performance on those test functions.

Dynamic Multi-Objective TSP (DMOTSP), a new research filed of evolutionary computation, is an NP-hard problem which comes from the applications of mobile computing and mobile communications. Because the characters of DMOTSP change with time, the method of designing a single algorithm can not effectively solve this extremely complicated and diverse optimization problem according to NFLTs for optimization. In this paper, a new approach to designing algorithm, mufti-algorithm co-evolution strategy (MACS), for DMOTSP is proposed Through multi-algorithm co-evolution, MACS can accelerate algorithm’s convergence, make Pareto set maintain diversity and make Pareto front distribute evenly with a complementary performance of these algorithms and avoiding the limitations of a single algorithm. In experiment, taking the three-dimensional benchmark problem CHN144+5 with two-objective for example, the results show that MACS can solve DMOTSP effectively with faster convergence, better diversity of Pareto set and more even distribution of Pareto front than single algorithm.

The quality of an approximation set usually includes two aspects-- approaching distance and spreading diversity. This paper introduces a new technique for assessing the diversity of an approximation to an exact Pareto-optimal front. This diversity is assessed by using an ldquoexposure degreerdquo of the exact Pareto-optimal front against the approximation set. This new technique has three advantages: Firstly, The ldquoexposure degreerdquo combines the uniformity and the width of the spread into a direct physical sense. Secondly, it makes the approaching distance independent from the spreading diversity at the most. Thirdly, the new technique works well for problems with any number of objectives, while the widely used diversity metric proposed by Deb would work poor in problems with 3 objectives or over. Experimental computational results show that the new technique assesses the diversity well.

This paper proposes a new evolutionary algorithm with lower dimensional crossover and gradient-based mutation for real-valued optimization problems with constraints. The crossover operator of the new algorithm searches a lower dimensional neighbor of the parent points where the neighbor center is the barycenter of the parents, and therefore the new algorithm converges fast. The gradient-based mutation is used to converge fast for the problems with equality constraints and active inequality constraints. And the new algorithm is simple and easy to be implemented. We have used 24 constrained benchmark problems to test the new algorithm. The experimental results show it works better than or competitive to a known effective algorithm.

The lognormal self-adaptation has been used extensively in evolutionary programming (EP) and evolution strategies (ES) to adjust the search step size for each objective variable. The Particle Swarm Optimization (PSO) relies on two kinds of factors: velocity and position of particles to generate better particles. In this paper, we propose Self-Adaptive Velocity PSO (SAVPSO) in which we firstly introduce lognormal self-adaptation strategies to efficiently control the velocity of PSO. Extensive empirical studies have been carried out to evaluate the performance of SAVPSO, standard PSO and some other improved versions of PSO. From the experimental results on 7 widely used test functions, we can show that SAVPSO outperforms standard PSO.

In this paper, we focus on the study of evolutionary algorithms for solving multiobjective optimization problems with a large number of objectives. First, a comparative study of a newly developed dynamical multiobjective evolutionary algorithm (DMOEA) and some modern algorithms, such as the indicator-based evolutionary algorithm, multiple single objective Pareto sampling, and nondominated sorting genetic algorithm II, is presented by employing the convergence metric and relative hypervolume metric. For three scalable test problems (namely, DTLZ1, DTLZ2, and DTLZ6), which represent some of the most difficult problems studied in the literature, the DMOEA shows good performance in both converging to the true Pareto-optimal front and maintaining a widely distributed set of solutions. Second, a new definition of optimality (namely, L-optimality) is proposed in this paper, which not only takes into account the number of improved objective values but also considers the values of improved objective functions if all objectives have the same importance. We prove that L-optimal solutions are subsets of Pareto-optimal solutions. Finally, the new algorithm based on L-optimality (namely, MDMOEA) is developed, and simulation and comparative results indicate that well-distributed L-optimal solutions can be obtained by utilizing the MDMOEA but cannot be achieved by applying L-optimality to make a posteriori selection within the huge Pareto nondominated solutions. We can conclude that our new algorithm is suitable to tackle many-objective problems.

This paper proposes a new evolutionary algorithm, called lower-dimensional-search evolutionary algorithm (LDSEA). The crossover operator of the new algorithm searches a lower-dimensional neighbor of the parent points where the neighbor center is the barycenter of the parents therefore the new algorithm converges fast, especially for high-dimensional constrained optimization problems. The niche-impaction operator and the mutation operator preserve the diversity of the population to make the LDSEA algorithm not to be trapped in local optima as much as possible. What's more is that the LDSEA algorithm is simple and easy to be implemented. We have used the 24 constrained benchmark problems [18] to test the LDSEA algorithm. The experimental results show it works better than or competitive to a known effective algorithm [7] for higher-dimensional constrained optimization problems.

This paper proposes a method for the classification of land cover in remote sensing imagery using evolutionary artificial neural networks (EANN) compared against multilayer perceptrons (MLP) with backpropagation algorithm. Evolutionary neural networks have combined the features of artificial neural networks (ANN) and evolutionary algorithms (EA) in the way that simultaneously evolving ANN architecture and weights. The parsimony of evolved ANN is encouraged by preferring node mutation and connection mutation. This enables consistent reductions of mean square errors of spectral classification with respect to sample pixels. Land-cover classification experiments were carried out by EANN-based classifiers and MLP-based classifiers in a 300times300 pixels Landsat-7 Enhanced Thematic Mapper plus (ETM+) high-resolution image of Zhaoyuan in Shandong province in eastern China. We found that the use of evolutionary algorithms for finding the optimal ANN results mainly in improvements in overall accuracy of an ANN with backpropagation algorithm and produce more compact ANN with good generalization ability in comparison with MLP. It is observed that classification accuracy of up to 90% is achievable for Landsat data produced by EANN.

There are rather few articles in the literature so far that deal with dynamic multi-objective optimization problems. This article introduces a dynamic orthogonal multi-objective evolutionary algorithm called "DOMOEA", that generalizes an earlier paper of ours (on an orthogonal multi-objective evolutionary algorithm (OMOEA-II) (Zeng et al., 2005)) to dynamic environments. DOMOEA solves a particular class of dynamic multi-objective optimization problems, namely those that have continuous decision variables. This new algorithm uses the evolutionary results, before any environmental change, as the initial population after the environmental change. It applies an "orthogonal design method" to enhance the fitness of the population during the static stages between two successive changes of environment. We obtained satisfactory results when testing this algorithm against the benchmark problems proposed in the literature. Our new algorithm is based on an ordinary evolutionary algorithm that does not have the capacity to detect environmental changes. Hence it has a comparatively simple structure, making comparisons with other dynamic multi-objective evolutionary algorithms relatively easy.

An orthogonal hill-climbing algorithm for dynamic optimization problems with continuous variables (labeled ODHC ) is proposed in present paper. The local peak climber is not a solution x, but rather a "niche", a small hyperrectangle. An orthogonal design method is employed on the niches for the niche to climb a potentially peak fast. An archive is used to store the latest found higher peaks for the ODHC algorithm learning from the past search. The randomly creating niches implement the global search. Numerical experiments show that the ODHC algorithm performs a lot better than the SOS (self organizing scouts) algorithm [J. Branke, T. Kaufler, C. Schmidt, and H. Schmeck. A multipopulation approach to dynamic optimization problems. Adaptive Computing in Design and Manufacturing. Springer, 2000.].

In this paper, a new multi-objective evolutionary algorithm for solving high complex multi-objective problems is presented based on the rule of energy minimizing and the law of entropy increasing of particle systems in phase space, Through the experiments it proves that this algorithm can quickly obtains the Pareto solutions with high precision and uniform distribution. And the results of the experiments show that this algorithm can avoid the premature phenomenon of problems better than the traditional evolutionary algorithm because it can drive all the individuals to participate in the evolving operation in each generation.

A robust dynamic evolutionary algorithm (labeled RODEA), where both the robust calculation and mutation operator are based on an orthogonal design, is proposed in this paper. Previous techniques calculate the mean effective objective (for robust) by using samples without much evenly distributing over the neighborhood. The samples by using orthogonal array distribute evenly. Therefore the calculation of mean effective objective more robust. The new technique is generalized from the ODEA algorithm [1]. An orthogonal design method is employed on the niches for the mutation operator to find a potentially good solution that may become the representative in the niche. The fitness of the offspring is therefore likely to be higher than that of its parent. We propose a complex benchmark, consisting of moving function peaks, to test our new approach. Numerical experiments show that the moving solutions of the algorithm are a little worse in objective value but robust.

This paper introduces an orthogonal evolutionary algorithm for dynamic optimization problems with continuous variables (called ODEA). Its population does not consist of individuals, but rather of "niches". Each niche selects the best solution found so far as its representative. An orthogonal design method is employed to find a potentially good solution that may become the representative of the niche in the mutation operator. We employ a complex benchmark to test the new approach. Numerical experiments show that the ODEA algorithm performs a lot better than the SOS (self organizing scouts) algorithm in Branke, Kaufler, Schmidt and Schmeck, (2000).

Dynamic optimisation problems are becoming increasingly important; meanwhile, progress in optimisation techniques and in computational resources are permitting the development of effective systems for dynamic optimisation, resulting in a need for objective methods to evaluate and compare different techniques. The search for effective techniques may be seen as a multi-objective problem, trading off time complexity against effectiveness; hence benchmarks must be able to compare techniques across the Pareto front, not merely at a single point. We propose benchmarks for the dynamic travelling salesman problem, adapted from the CHN-144 benchmark of 144 Chinese cities for the static travelling salesman problem. We provide an example of the use of the benchmark, and illustrate the information that can be gleaned from analysis of the algorithm performance on the benchmarks.

In this paper, we construct an evolutionary algorithm. It yields good performance on a collection of elliptic parameter identification problems. The evolutionary algorithm has a good tolerability for the noise in the observed data. Even when the noise level is up to 10%, we can also get such a good result. The result of numerical experiments shows explicitly that the algorithm is very fit for solving this kind of inverse problem but not very sensitive to the noise.

In this paper, an orthogonal multi-objective evolutionary algorithm (OMOEA) is proposed for multi-objective optimization problems (MOPs) with constraints. Firstly, these constraints are taken into account when determining Pareto dominance. As a result, a strict partial-ordered relation is obtained, and feasibility is not considered later in the selection process. Then, the orthogonal design and the statistical optimal method are generalized to MOPs, and a new type of multi-objective evolutionary algorithm (MOEA) is constructed. In this framework, an original niche evolves first, and splits into a group of sub-niches. Then every sub-niche repeats the above process. Due to the uniformity of the search, the optimality of the statistics, and the exponential increase of the splitting frequency of the niches, OMOEA uses a deterministic search without blindness or stochasticity. It can soon yield a large set of solutions which converges to the Pareto-optimal set with high precision and uniform distribution. We take six test problems designed by Deb, Zitzler et al., and an engineering problem (W) with constraints provided by Ray et al. to test the new technique. The numerical experiments show that our algorithm is superior to other MOGAS and MOEAs, such as FFGA, NSGAII, SPEA2, and so on, in terms of the precision, quantity and distribution of solutions. Notably, for the engineering problem W, it finds the Pareto-optimal set, which was previously unknown.

This paper proposes an evolutionary approach to build the equivalent circuit model for electrochemical impedance spectroscopy. It works by using a hybrid evolutionary modeling algorithm (HEMA) whose main idea is to embed a genetic algorithm (GA) in gene expression programming (GEP) where GEP is employed to discover and optimize the structure of a circuit, while the GA is employed to optimize the parameters of all the electric components contained in the circuit. By running the HEMA, the computer can automatically find suitable circuit structures as well as optimize the component parameters simultaneously. Compared with most available methods, it has the advantages of automation of modeling process, great diversity of model structures, high stability and efficiency of parameter optimization.

A fast algorithm is proposed to find the nondominated set for multiobjective optimization problems in this paper. Two accelerated techniques are adopted in the algorithm. One is that the algorithm can yield an integer rank set after it indexes the search space. Based on this, the goal is changed into determination of the nondominated set of the integer rank set. The other is that the nondominated check sequence follows that the likely nondominated members are first checked, and that the check process is stopped when the remaining members in the nondominated check sequence are dominated. The computational complexity of the new algorithm is analyzed theoretically. Experimental results show that the new method performs much better than KLP (a famous effective algorithm) when the search space contains a large nondominated set. Moreover, the two new techniques introduced in this paper are very useful for multiobjective evolutionary algorithms (MOEAs) to improve the computational speed.

Traditional genetic operators are often semi-blind due to their randomness and lack of knowledge about problem and lessons from past generations. In this paper, an immunology-guided genetic algorithm, which aims to guide the search direction of genetic operators, is developed to conquer these disadvantages. By simulating memory mechanism and vaccination in immunology, a gene library is established and a vaccination process is integrated into genetic operators. We apply this clever genetic operators to solving TSP, a representative combinatorial optimization problem, and detail the construction of gene library and inver-over operator with vaccination mechanism. Experiment results show that the performance of the original inver-over operator has been significantly improved both in convergent speed and the ability of finding optimum for TSPs.

In this paper, we propose the adaptive neighborhood-based multi-parent cross-over operator (ANMX), a novel search operator for real-coded genetic algorithms, which generates offspring by the linear non-convex combination of several relative-parents, each of which is uniformly sampled in the respective neighborhoods of randomly selected parents in the population. ANMX is a general variation operator in essence, for it not only takes on the form of a multi-parent crossover operator but also implicitly has some of the characteristics of a mutation operator. To enhance the efficiency, we introduce a mechanism for adapting the range of neighborhoods according to the evolutionary progress. Numerical experiments using a suite of test functions, which are widely studied in the field of evolutionary computation, show good search ability of the proposed operator for functions with multimodality and/or epistasis.

Multi-objective optimal evolutionary algorithms (MOEA) are effective algorithms to solve multi-objective optimal problem (MOP). Because ranking which used by most MOEAs has some disadvantages, We propose a new method that uses better function to compare candidate solutions and tree structure to express the relationship of solutions. Experiments show that the new algorithm can converge to the Pareto front, and maintains the diversity of population. When the algorithm is extended to a MOP with constraints, it can also get a good result. Most important of all, the algorithm is simple but highly efficient.

We present a parallel elite-subspace evolutionary algorithm for solving systems of nonlinear equations. On the basis of numerical experiments, we find that our algorithm has an outstanding universal characteristics and superior convergence as well. All of the solutions can be obtained within a short period of time.

Magic square construction is a complex and hard permutation problem of recreational combinatorics with a long history. Not only does the complexity consist in that the number of magic squares increases rapidly with the order of magic square, but also in that the percentage of magic squares in the possible permutation of the first n/sup 2/ natural numbers decreases with the order. Based on the two-phase construction conjecture, we propose an improved evolutionary algorithm for magic square construction. Mutation operators are specially designed so that the mutation domain can be located and the mutation probabilities adjusted adaptively, which include the number pair permutations, the row permutations and column permutations. In addition, some heuristics-based local permutations, like the row/column local rectification and the local diagonal rectification, are used to complement the stochastic mechanism. Computational results show that, the two-phase construction conjecture is computationally effective, and the improved evolutionary algorithm is highly efficient for magic square construction.

A new algorithm is proposed to solve constrained multiobjective problems. The constraints of the MOPs are taken account of in determining Pareto dominance. As a result, the feasibility of solutions is not an issue. At the same time, it takes advantage of both the orthogonal design method to search evenly, and the statistical optimal method to speed up the computation. The output of the technique is a large set of solutions with high precision and even distribution. Notably, for an engineering problem WATER, it finds the Pareto-optimal set, which was previously unknown.

Many real world optimization problems are time-dependent and some of them can be modeled by the dynamic TSPs (DTSPs). A DTSP is harder than a general TSP, which is a NP-hard problem, because the city number and the cost matrix of a DTSP are time varying. Although DTSP is a very common and important model in real world systems, few literatures have discussed this related issues. There are many open questions about DTSP urgently needed to be answered. We first give a mathematical model and the optimization objective for DTSP. Then we discuss why evolutionary algorithms (EAs) are effective for solving DTSPs and give some key points for designing efficient DTSP EAs. By defining three dynamic operators, we proposed an evolutionary algorithm for DTSPs. The experiments show the new algorithm is suitable for solving DTSPs. At the end, we also give some preliminary ideas for reinforcing the efficiency of EAs for DTSPs.

This paper presents a new approach to handle constrained optimization using evolutionary algorithms. The new technique converts constrained optimization to a two-objective optimization: one is the original objective function, the other is the degree function violating the constraints. By using Pareto-dominance in the multi-objective optimization, individual's Pareto strength is defined. Based on Pareto strength and minimal generation gap (MGG) model, a new real-coded genetic algorithm is designed. The new approach is compared with some other evolutionary optimization techniques on several benchmark functions. The results show that the new approach outperforms those existing techniques in feasibility, effectiveness and generality. Especially for some complicated optimization problems with inequality and equality constraints, the proposed method provides better numerical accuracy.

In this article, we discuss a theory of the optimal trajectory for evolutionary algorithms from the optimal control theory of dynamical system. Control strategies are derived using theoretical results, such as the selection mechanism and the stopping condition for the design, analysis and application of evolutionary algorithms.

In this paper, we present an effective dynamical evolutionary algorithm (DEA) to handle constrained optimization problems. The novelty of DEA is that we design a new select mechanism based on the principle of energy minimization of statistical mechanics. The algorithm has been evaluated numerically using several benchmark problems. The numerical results show our approach is superior to any other published results known by the authors.

Recently Tao Guo (1999) proposed a stochastic search algorithm in his PhD thesis for solving function optimization problems. He combined the subspace search method (a general multi-parent recombination strategy) with the population hill-climbing method. The former keeps a global search for the overall situation, and the latter maintains the convergence of the algorithm. Guo's algorithm has many advantages, such as the simplicity of its structure, the high accuracy of its results, the wide range of its applications, and the robustness of its use. In this paper a preliminary theoretical analysis of the algorithm is given and some numerical experiments are performed using Guo's algorithm to demonstrate the theoretical results. Three asynchronous parallel algorithms with different granularities for MIMD machines are designed by parallelizing Guo's algorithm.

This paper presents a new algorithm for modeling one-dimensional (1-D) dynamic systems by higher-order ordinary differential equation (HODE) models instead of the ARMA models as used in traditional time series analysis. A two-level hybrid evolutionary modeling algorithm (THEMA) is used to approach the modeling problem of HODE's for dynamic systems. The main idea of this modeling algorithm is to embed a genetic algorithm (GA) into genetic programming (GP), where GP is employed to optimize the structure of a model (the upper level), while a GA is employed to optimize the parameters of the model (the lower level). In the GA, we use a novel crossover operator based on a nonconvex linear combination of multiple parents which works efficiently and quickly in parameter optimization tasks. Two practical examples of time series are used to demonstrate the THEMA's effectiveness and advantages.

The paper presents a new idea for modeling and predicting one dimensional time series using higher order ordinary differential equations (HODEs) models instead of the models as used in traditional time series analysis. Accordingly, based on the idea of two-level evolutionary modeling in the HEMA algorithm (H.Q. Cao et al., 1998), a dynamic hybrid evolutionary modeling algorithm called DHEMA is proposed to approach this task. By running the DHEMA, the modeling process and the predicting process can be carried on concurrently and dynamically with the renewing of observed data. Two practical examples are used to examine the effectiveness of the algorithm in performing the real time modeling and predicting tasks of time series.