Convergence Of Evolutionary Algorithms Research Articles

An outward search to increase population diversity for optimization algorithms

Outward search (OS) is a new scheme proposed to provide diverse forms for improving convergence in evolutionary algorithms. Rather than using new functionalities, OS is performed using the differential-vector equations of an evolutionary algorithm. Three OS schemes are recommended in this study to obtain solutions that improve the performance of an evolutionary algorithm. The first one uses the original equations of the algorithm to generate either an OS solution or a candidate solution. The second utilizes the original equations to produce an OS solution and a candidate solution simultaneously for one individual. The last employs equations of another algorithm to create an OS solution for the studied algorithm. Three bio-inspired algorithms were examined using the CEC2015 benchmark suite to compare the respective performances of the proposed OS schemes. The results of the comparison indicate that searching regions outward from the current area outperformed examining oppositional locations obtained by opposition-based learning.

Evolutionary Algorithm Embedded With Bump-Hunting for Constrained Design Optimization

Abstract Real-world design optimization problems commonly entail constraints that must be satisfied for the design to be viable. Mathematically, the constraints divide the search space into feasible (where all constraints are satisfied) and infeasible (where at least one constraint is violated) regions. The presence of multiple constraints, constricted and/or disconnected feasible regions, non-linearity and multi-modality of the underlying functions could significantly slow down the convergence of evolutionary algorithms (EA). Since each design evaluation incurs some time/computational cost, it is of significant interest to improve the rate of convergence to obtain competitive solutions with relatively fewer design evaluations. In this study, we propose to accomplish this using two mechanisms: (a) more intensified search by identifying promising regions through “bump-hunting,” and (b) use of infeasibility-driven ranking to exploit the fact that optimal solutions are likely to be located on constraint boundaries. Numerical experiments are conducted on a range of mathematical benchmarks and empirically formulated engineering problems, as well as a simulation-based wind turbine design optimization problem. The proposed approach shows up to 53.48% improvement in median objective values and up to 69.23% reduction in cost of identifying a feasible solution compared with a baseline EA.

Complexity Analysis and Stochastic Convergence of Some Well-known Evolutionary Operators for Solving Graph Coloring Problem

The graph coloring problem is an NP-hard combinatorial optimization problem and can be applied to various engineering applications. The chromatic number of a graph G is defined as the minimum number of colors required to color the vertex set V(G) so that no two adjacent vertices are of the same color, and different approximations and evolutionary methods can find it. The present paper focused on the asymptotic analysis of some well-known and recent evolutionary operators for finding the chromatic number. The asymptotic analysis of different crossover and mutation operators helps in choosing the better evolutionary operator to minimize the problem search space and computational complexity. The choice of the right genetic operators facilitates an evolutionary algorithm to achieve faster convergence with lesser population size N through an adequate distribution of promising genes. The selection of an evolutionary operator plays an essential role in reducing the bounds for minimum color obtained so far for some of the benchmark graphs. This research also focuses on the necessary and sufficient conditions for the global convergence of evolutionary algorithms. The stochastic convergence of recent evolutionary operators for solving graph coloring is newly analyzed.

An exploration-enhanced elephant herding optimization

PurposeThe purpose of this paper is to propose an enhanced elephant herding optimization (EEHO) algorithm by improving the exploration phase to overcome the fast-unjustified convergence toward the origin of the native EHO. The exploration and exploitation of the proposed EEHO are achieved by updating both clan and separation operators.Design/methodology/approachThe original EHO shows fast unjustified convergence toward the origin specifically, a constant function is used as a benchmark for inspecting the biased convergence of evolutionary algorithms. Furthermore, the star discrepancy measure is adopted to quantify the quality of the exploration phase of evolutionary algorithms in general.FindingsIn experiments, EEHO has shown a better performance of convergence rate compared with the original EHO. Reasons behind this performance are: EEHO proposes a more exploitative search method than the one used in EHO and the balanced control of exploration and exploitation based on fixing clan updating operator and separating operator. Operatorγis added to EEHO assists to escape from local optima, which commonly exist in the search space. The proposed EEHO controls the convergence rate and the random walk independently. Eventually, the quantitative and qualitative results revealed that the proposed EEHO outperforms the original EHO.Research limitations/implicationsTherefore, the pros and cons are reported as follows: pros of EEHO compared to EHO – 1) unbiased exploration of the whole search space thanks to the proposed update operator that fixed the unjustified convergence of the EHO toward the origin and the proposed separating operator that fixed the tendency of EHO to introduce new elephants at the boundary of the search space; and 2) the ability to control exploration–exploitation trade-off by independently controverting the convergence rate and the random walk using different parameters – cons EEHO compared to EHO: 1) suitable values for three parameters (rather than two only) have to be found to use EEHO.Originality/valueAs the original EHO shows fast unjustified convergence toward the origin specifically, the search method adopted in EEHO is more exploitative than the one used in EHO because of the balanced control of exploration and exploitation based on fixing clan updating operator and separating operator. Further, the star discrepancy measure is adopted to quantify the quality of exploration phase of evolutionary algorithms in general. Operatorγthat added EEHO allows the successive local and global searching (exploration and exploitation) and helps escaping from local minima that commonly exist in the search space.

Wave models and dynamical analysis of evolutionary algorithms

By drawing an analogy between the population of an evolutionary algorithm and a gas system (which we call a particle system), we first build wave models of evolutionary algorithms based on aerodynamics theory. Then, we solve the models linear and quasi-linear hyperbolic equations analytically, yielding wave solutions. These describe the propagation of the particle density wave, which is composed of leftward and rightward waves. We demonstrate the convergence of evolutionary algorithms by analyzing the mechanism underlying the leftward wave, and investigate population diversity by analyzing the rightward wave. To confirm these theoretical results, we conduct experiments that apply three typical evolutionary algorithms to common benchmark problems, showing that the experimental and theoretical results agree. These theoretical and experimental analyses also provide several new clues and ideas that may assist in the design and improvement of evolutionary algorithms.

Accelerating evolutionary computation using a convergence point estimated by weighted moving vectors

We introduce weighted moving vectors to increase the accuracy of estimating a convergence point of population and evaluate its efficiency. Key point is to weight moving vectors according to their reliability when a convergence point is calculated instead of equal weighting of the original method. We propose two different methods to evaluate the reliability of moving vectors. The first approach uses the fitness gradient information between starting points and terminal points of moving vectors for their weights. When a fitness gradient is bigger, the direction of a moving vector may have more potential, and a higher weight is given to it. The second one uses the fitness of parents, i.e., starting points of moving vectors, to give weights for moving vectors. Because an individual with higher fitness may have a high probability of being close to the optimal area, it should be given a higher weight, vice versa. If the estimated point is better than the worst individual in current population, it is used as an elite individual and replace the worst one to accelerate the convergence of evolutionary algorithms. To evaluate the performance of our proposal, we employ differential evolution and particle swarm optimization as baseline algorithms in our evaluation experiments and run them on 28 benchmark functions from CEC 2013. The experimental results confirmed that introducing weights can further improve the accuracy of an estimated convergence point, which helps to make EC search faster. Finally, some open topics are given to discuss.

Enhanced Elephant Herding Optimization for Global Optimization

The elephant herding optimization (EHO) algorithm is a relatively novel population-based optimization technique, which mimics herding behavior and can be modeled into two operators: clan updating operators and separating operators. Also, in the literature, EHO has received a great deal of attention from researchers since it was proposed applied to many application fields for its advantages of excellent global optimization ability and ease of implementation. However, there is still an insufficiency in the EHO algorithm regarding its lack of exploitation, which leads to slow convergence. In this paper, we propose three enhanced versions of EHO based on the $\gamma $ value termed EEHO15, EEHO20, and EEHO25 to overcome the problems of fast unjustified convergence toward the origin of the basic EHO. The exploration/exploitation abilities of the EEHO algorithms are achieved by the updating of the two operators (clan and separation operator). To tackle this drawback, a constant function is used as a benchmark for inspecting the biased convergence of evolutionary algorithms in general. Moreover, we utilize CEC’17 test suite benchmark functions to test the performance of the proposed three versions of EEHO against EHO, particle swarm optimization (PSO), bird swarm algorithm (BSA), and ant lion optimizer (ALO) algorithms. Eventually, the experimental results revealed that the proposed EEHO algorithms extremely obtained better results compared with other competitive algorithms.

Research of practical convergence of evolutionary algorithms for optimal programmed control of a wheeled robot

Research of practical convergence of evolutionary algorithms for optimal programmed control of a wheeled robot

Study of the Practical Convergence of Evolutionary Algorithms for the Optimal Program Control of a Wheeled Robot

Evolutionary algorithms for solving the problem of the optimal program control are considered. The most popular evolutionary algorithms, the genetic algorithm (GA), the differential evolution (DE) algorithm, the particle swarm optimization (PSO), the bat-inspired algorithm (BIA), the bees algorithm (BA), and the grey wolf optimizer (GWO) algorithm are described. An experimental analysis of these algorithms and their comparison with gradient methods are given. An experiment was carried out to solve the problem of the optimal control of a mobile robot with phase constraints. Indicators of the best objective functional value, the average value for several startups, and the standard deviation were used to compare the algorithms.

Impact of Starting Position and Searching Mechanism on the Evolutionary Algorithm Convergence Rate

AbstractEvolutionary algorithms (EAs) have been used extensively to find globally optimal solutions for water distribution system (WDS) optimization problems. However, as these algorithms are being applied to increasingly complex systems, computational efficiency is becoming an issue, and hence approaches that enable near-optimal solutions to be identified within reasonable computational budgets have received increasing attention. One of these approaches is the initialization of EAs in a manner that accounts for domain knowledge of WDS design problems. Although the effectiveness of these initialization approaches has been studied previously, the impact of algorithm searching behavior on the speed with which near-optimal solutions can be found has not yet been examined. To this end, this study aims to investigate the relative impact of different algorithm initialization methods and searching mechanisms on the speed with which near-optimal solutions can be identified for large WDS optimization problems. Fit...

A Monte Carlo simulation based chaotic differential evolution algorithm for scheduling a stochastic parallel processor system

One of the main limitation of the application of evolutionary algorithms (EA) is the tendency to converge prematurely to a local optimum. The EAs suffer with the disadvantage of premature convergence and hence the study on convergence of EAs is always one of the most important research fields. Due to outstanding capability of chaos to avoid being trapped in local optimum, it can be considered as an efficient search tool. Therefore, in current paper, in order to taking properties of chaos, eight chaotic maps are employed within a differential evolution (DE) algorithm for solving a stochastic job scheduling problem. To speedup searching and avoid local optimum traps, the random sequences produced from chaotic maps are utilized instead of random variables in DE. Furthermore, to address the uncertainties arising in scheduling environments, Monte Carlo simulation is used. However, simulation is not an optimization approach. Therefore, we design the simulation-based optimization approach where a simulator is combined with chaotic DE. The simulation experiments are used to evaluate the quality of candidate solutions and the chaotic DE is utilized to find best-compromised solutions and then guide the search direction. The performance of simulation-based chaotic DE algorithm is investigated in a computational study, and the results show the outperformance of suggested method with respect to the traditional methods.

Structural and electronic properties of small silicon clusters

The atomic structure and electronic spectrum of silicon nanoclusters (Si-ncs) Si7, Si10,Si10H16 and Si10H20 are calculated using the evolutionary algorithm with total energy computed within density functional theory and generalized gradient approximation (DFT-GGA). When analysing the low-energy structures, we pay significant attention to their symmetry and interatomic bond geometry. The candidate structures arising in the process of evolutionary algorithm convergence are also considered and classified by their topology and grouping near local energy minima. Possible ways to improve the convergence of evolutionary computation are discussed. Addressing qualitative criteria for the ground-state atomic structure of Si-ncs, we consider correlations between the density of electronic states and the total energetics of clusters in the ground state and low-energy-isomer configurations.

Research on Chaos Theory Improved Evolutionary Algorithm

Because the basic evolutionary algorithm convergence speed is slow, prone to stagnation, the algorithm running time is too long, so according to chaos theory about the relationship between evolution and chaos, this paper design an improved evolutionary algorithm with chaotic mutation operator, the optimization of the contraction policy can improve the global search ability of effective, significantly improved the performance of the proposed algorithm.

Convergence of evolutionary algorithms on the n-dimensional continuous space

Evolutionary algorithms (EAs) are random optimization methods inspired by genetics and natural selection, resembling simulated annealing. We develop a method that can be used to find a meaningful tradeoff between the difficulty of the analysis and the algorithms' efficiency. Since the case of a discrete search space has been studied extensively, we develop a new stochastic model for the continuous n-dimensional case. Our model uses renewal processes to find global convergence conditions. A second goal of the paper is the analytical estimation of the computation time of EA with uniform mutation inside the (hyper)-sphere of volume 1, minimizing a quadratic function.

How can surrogates influence the convergence of evolutionary algorithms?

Surrogate-assisted evolutionary algorithms have been widely utilized in science and engineering fields, while rare theoretical results were reported on how surrogates influence the performances of evolutionary algorithms (EAs). This paper focuses on theoretical analysis of a (1+1) surrogate-assisted evolutionary algorithm ((1+1)SAEA), which consists of one individual and pre-evaluates a newly generated candidate using a first-order polynomial model (FOPM) before it is precisely evaluated at each generation. By performing comparisons between a unimodal problem and a multi-modal problem, we rigorously estimate the variation of exploitation ability and exploration ability introduced via the FOPM. Theoretical results show that the FOPM employed to pre-evaluate the candidates sometimes accelerate the convergence of evolutionary algorithms, while sometimes prevents the individuals from converging to the global optimal solution. Thus, appropriate adaptive strategies of candidate generation and surrogate control are needed to accelerate the convergence of the (1+1)EA. Then, the accelerating effect of FOPM decreases monotonically with p, the probability of performing precise function evaluation when a candidate is pre-evaluated worse than the present individual.

Multiple parents crossover operators: A new approach removes the overlapping solutions for sequencing problems

Maintaining population diversity throughout generations of Genetic Algorithms (GAs) is key to avoid premature convergence. Redundant solutions is one cause for the decreasing population diversity. To prevent the negative effect of redundant solutions, we propose a framework that is based on the multi-parents crossover (MPX) operator embedded in GAs. Because MPX generates diversified chromosomes with good solution quality, when a pair of redundant solutions is found, we would generate a new offspring by using the MPX to replace the redundant chromosome. Three schemes of MPX will be examined and will be compared against some algorithms in literature when we solve the permutation flowshop scheduling problems, which is a strong NP-Hard sequencing problem. The results indicate that our approach significantly improves the solution quality. This study is useful for researchers who are trying to avoid premature convergence of evolutionary algorithms by solving the sequencing problems.

Visual interactive evolutionary algorithm for high dimensional outlier detection and data clustering problems

Usual visualisation techniques for multidimensional datasets, such as parallel coordinates and scatterplot matrices, do not scale well to high numbers of dimensions. A common approach to solve this problem is dimensionality selection. Existing dimensionality selection techniques usually select pertinent dimension subsets that are significant to the user without loose of information. We present concrete cooperation between automatic algorithms, interactive algorithms and visualisation tools: the evolutionary algorithm is used to obtain optimal dimension subsets which represent the original dataset without loosing information for unsupervised mode (clustering or outlier detection). The last effective cooperation is a visualisation tool used to present the user interactive evolutionary algorithm results and let him actively participate in evolutionary algorithm searching with more efficiency resulting in a faster evolutionary algorithm convergence. We have implemented our approach and applied it to real dataset to confirm this approach is effective for supporting the user in the exploration of high dimensional datasets.

A Novel Algorithm for Path Planning of Mobile Robots in Dynamic Environment

Aimed to accuracy and convergence of Evolutionary Algorithms for path planning of robots in dynamic environment, this paper integrated cloud model into evolutionary algorithm to improved evolutionary operators. One-dimensional cloud operator was used evolution and mutation, at the same time the previous search results were used. Simulation results show that the method is effective in performance.

Clustered enhanced differential evolution for the blocking flow shop scheduling problem

A novel clustered population paradigm is presented in this paper which is based on Chaos principles of edges and attractors. Convergence in evolutionary algorithms is viewed as a manifestation through cyclic dynamics and thus a new population is developed which is clustered and separated through new segregation bias rules. This population is embedded on the Enhanced Differential Evolution and the flow shop scheduling problem with blocking is solved. The two flow shop benchmark problems of Rec/Car/Hel and Taillard are solved with this new approach and the results favorably compared with published results in literature. A total of 49 new upper bounds for the Taillard problems was obtained during experimentation.

Algorithme interactif pour la sélection de dimensions en détection d'outlier

Usual visualization methods for multidimensional data sets, do not scale well to high numbers of dimensions. We present concrete cooperation between automatic algorithms, interactive algorithms and visualization tools: the evolutionary algorithm is used to obtain optimal dimension subsets representing original data set without losing information for outlier detection using a new validity criterion. The last effective cooperation is a visualization tool used to present the user interactive evolutionary algorithm results and let him actively participate in evolutionary algorithm searching with more efficiency resulting in a faster evolutionary algorithm convergence.