A New Evolutionary Algorithm Based on Simplex Crossover and PSO Mutation for Constrained Optimization Problems

For constrained optimization problems, evolutionary algorithms often utilize a penalty function to deal with constraints, even if it is difficult to control the penalty parameters. To overcome this shortcoming, this paper presents a new penalty function which has no parameter and can effectively handle constraint first, after which a hybrid-fitness function integrating this penalty function into the objective function is designed. The new fitness function can properly evaluate not only feasible solution, but also infeasible one, and distinguish any feasible one from an infeasible one. Meanwhile, a new crossover operator based on simplex crossover operator and a new PSO mutation operator are also proposed, which can produce high quality offspring. Based on these, a new evolutionary algorithm for constrained optimization problems is proposed. The simulations are made on ten widely used benchmark problems, and the results indicate the proposed algorithm is effective.

In this paper, a special nonlinear bilevel programming problem (nonlinear BLPP) is transformed into an equivalent single objective nonlinear programming problem. To solve the equivalent problem effectively, we first construct a specific optimization problem with two objectives. By solving the specific problem, we can decrease the leader's objective value, identify the quality of any feasible solution from infeasible solutions and the quality of two feasible solutions for the equivalent single objective optimization problem, force the infeasible solutions moving toward the feasible region, and improve the feasible solutions gradually. We then propose a new constraint-handling scheme and a specific-design crossover operator. The new constraint-handling scheme can make the individuals satisfy all linear constraints exactly and the nonlinear constraints approximately. The crossover operator can generate high quality potential offspring. Based on the constraint-handling scheme and the crossover operator, we propose a new evolutionary algorithm and prove its global convergence. A distinguishing feature of the algorithm is that it can be used to handle nonlinear BLPPs with nondifferentiable leader's objective functions. Finally, simulations on 31 benchmark problems, 12 of which have nondifferentiable leader's objective functions, are made and the results demonstrate the effectiveness of the proposed algorithm.

In this paper a hybrid adaptive genetic algorithm is proposed for solving constrained optimization problems. Genetic algorithm proposed here combines adaptive penalty method and smoothing technique in order to make the algorithm not needing parameters tuning and easily escaping from the local optimal solutions. Meanwhile, local line search technique is introduced and a new crossover operator is designed for getting much faster algorithm convergence. If there is no feasible solutions in the current population, finding feasible solutions is prior to finding optimal solution, otherwise the exploitation for global optimal solution based on a certain smoothing function at the best feasible solution in the current population and the exploration for whole search space are processing at the same time. The performance of the algorithm is tested on thirteen benchmark functions in the literature and the results indicate that the algorithm proposed here is robust and effective.

Approximate models have to be used in evolutionary optimization when the original fitness function is computationally very expensive. Unfortunately, the convergence property of the evolutionary algorithm is unclear when an approximate model is used for fitness evaluation because approximation errors are involved in the model. What is worse, the approximate model may introduce false optima that lead the evolutionary algorithm to a wrong solution. To address this problem, individual and generation based evolution control are introduced to ensure that the evolutionary algorithm using approximate fitness functions will converge correctly. A framework for managing approximate models in generation-based evolution control is proposed. This framework is well suited for parallel evolutionary optimization in which evaluation of the fitness function is time-consuming. Simulations on two benchmark problems and one example of aerodynamic design optimization demonstrate that the proposed algorithm is able to achieve a correct solution as well as a significantly reduced computation time.

Handling constraints in evolutionary algorithms (EAs) is a challenging issue, since an EA does not handle constraints directly. Thus, developing a heuristic that can guide the search toward feasible and good-performing solutions has become a topic of considerable interest in the field of evolutionary computation in recent years. If a heuristic is applied that is not appropriate or properly fine-tuned, the EA may converge on infeasible solutions, or on feasible solutions with poor objective function values. This paper presents a new constraint-handling technique based on stochastic tournament selection (STS). The performance of this technique is compared to various other constraint-handling techniques applied to a genetic algorithm(GA-) based irrigation canal management problem. The problem involves finding an efficient strategy of irrigation canal network operations that can minimize the total water consumed while preventing problems such as water shortage and flooding. The most common way to handle constraints in EAs is to incorporate penalty functions into the fitness criterion to degrade the fitness of solutions that violate one or more constraints. Alternative techniques have also been reported in the literature, including multiobjective optimization techniques that treat the constraints in single objective problems as additional objectives and stochastic techniques. This paper investigates the performance of five constraint-handling techniques (four techniques from the literature, and the new proposed STS technique). Three scenarios of the case study, with different levels of difficulty and different numbers of constraints, are tested. A comparison of the performances is made to help provide guidelines for the most promising constraint-handling techniques for EA-based management of water supply and irrigation canal operations, based on the level of difficulty of the problem. Copyright ASCE 2006 World Environmental and Water Resources Congress 2006 2

A Simplex Crossover based evolutionary algorithm including the genetic diversity as objective

The paper describes the comparison of three evolutionary algorithms for solving combinatorial optimization problems. In particular, a generational, a steady-state and a cellular genetic algorithm were applied to the maximum cut problem, the error correcting code design problem, and the minimum tardy task problem. The results obtained in this work are better than the ones previously reported in the literature in all cases except for one problem instance. The high quality results were achieved although no problem-specific changes of the evolutionary algorithms were made other than in the fitness function. The constraints for the minimum tardy task problem were taken into account by incorporating a graded penalty term into the fitness function. The generational and steady-state algorithms yielded very good results although they sampled only a tiny fraction of the search space.

The constrained optimization problem (COP) is converted into a biobjective optimization problem first, and then a new memetic differential evolution algorithm with dynamic preference is proposed for solving the converted problem. In the memetic algorithm, the global search, which uses differential evolution (DE) as the search scheme, is guided by a novel fitness function based on achievement scalarizing function (ASF). The novel fitness function constructed by a reference point and a weighting vector adjusts preference dynamically towards different objectives during evolution, in which the reference point and weighting vector are determined adapting to the current population. In the local search procedure, simplex crossover (SPX) is used as the search engine, which concentrates on the neighborhood embraced by both the best feasible and infeasible individuals and guides the search approaching the optimal solution from both sides of the boundary of the feasible region. As a result, the search can efficiently explore and exploit the search space. Numerical experiments on 22 well-known benchmark functions are executed, and comparisons with five state-of-the-art algorithms are made. The results illustrate that the proposed algorithm is competitive with and in some cases superior to the compared ones in terms of the quality, efficiency, and the robustness of the obtained results.

Evolutionary algorithms (EAs), as global search methods, are proved to be more robust than their counterpart local heuristics for detecting protein complexes in protein-protein interaction (PPI) networks. Typically, the source of robustness of these EAs comes from their components and parameters. These components are solution representation, selection, crossover, and mutation. Unfortunately, almost all EA based complex detection methods suggested in the literature were designed with only canonical or traditional components. Further, topological structure of the protein network is the main information that is used in the design of almost all such components. The main contribution of this paper is to formulate a more robust EA with more biological consistency. For this purpose, a new crossover operator is suggested where biological information in terms of both gene semantic similarity and protein functional similarity is fed into its design. To reflect the heuristic roles of both semantic and functional similarities, this paper introduces two gene ontology (GO) aware crossover operators. These are direct annotation-aware and inherited annotation-aware crossover operators. The first strategy is handled with the direct gene ontology annotation of the proteins, while the second strategy is handled with the directed acyclic graph (DAG) of each gene ontology term in the gene product. To conduct our experiments, the proposed EAs with GO-aware crossover operators are compared against the state-of-the-art heuristic, canonical EAs with the traditional crossover operator, and GO-based EAs. Simulation results are evaluated in terms of recall, precision, and F measure at both complex level and protein level. The results prove that the new EA design encourages a more reliable treatment of exploration and exploitation and, thus, improves the detection ability for more accurate protein complex structures.

Estimation of distribution algorithms (EDAs) are a class of evolutionary optimisation algorithms based on probability distribution model. This article extends the basic EDAs for tackling multi-objective optimisation problems by incorporating Archimedean copulas for constructing probability distribution model, and using the concept of Pareto dominance. In the algorithm, the marginal distributions from the current population are firstly estimated by kernel estimation method and are used to estimate the parameter of the Archimedean copula function generator by using the maximum likelihood method. Afterwards, the multivariate Archimedean copula sample algorithm is used to generate current offsprings population by sampling the n-dimensional Laplace transform Archimedean copula. The population with the current population and current offsprings population is sorted based on non-domination, and the best individuals are selected to form the next population based on rank and the crowding distance. The proposed algorithm is tested to compare with NSGA-II, PAES and SPEA2 using a set of benchmark functions. Both convergence and diversity metrics are used to evaluate the performance of the algorithm. The experimental results show that the algorithm outperforms NSGA-II, PAES and SPEA2 in two metrics.

Backtracking Search Optimization Algorithm for numerical optimization problems

Surrogate-assisted evolutionary algorithms provide an effective means for complex and computationally expensive optimization problems. However, due to the scarcity of training samples, the prediction accuracy of frequently-used regression surrogate models can hardly be guaranteed as the difficulty of the problem increases, resulting in performance degradation of the whole algorithm. Since real-world problems rarely exist in isolation, it is expected to alleviate the above issue by properly exploiting the knowledge shared across different problems. In this context, this study proposes a novel evolutionary multitasking optimization algorithm assisted by a classifier rather than a regression model for expensive multitasking problems, where the accuracy of the classifier is boosted by knowledge transfer. To be specific, a support vector classifier (SVC) is first developed and integrated into a classic evolutionary algorithm, i.e., covariance matrix adaptation evolution strategy (CMA-ES). With a low computational cost, it helps CMA-ES to prescreen parent solutions from the current population. Following that, a knowledge transfer strategy is designed to enrich the training samples for each task-oriented classifier by sharing high-quality solutions among different tasks, where a PCA-based subspace alignment technique is employed. Extensive experiments indicate that the SVC-assisted CMA-ES gains significant superiority over general CMA-ES in terms of both robustness and scalability, and the knowledge transfer strategy further helps it earn a competitive edge over some state-of-the-art algorithms on expensive multitasking optimization problems.

This chapter presents an evolutionary approach for solving the traveling salesman problem (TSP) and the TSP with backhauls (TSPB). We propose two evolutionary algorithms for solving the difficult TSPs. Our focus is on developing evolutionary operators based on conventional heuristics. We rely on a set of detailed computational experiments and statistical tests for developing an effective algorithm.The chapter starts with a careful survey of the algorithms for the TSP and the TSPB, with a special emphasis on crossover and mutation operators and applications on benchmark test instances. The second part addresses our first evolutionary algorithm. We explore the use of two tour construction heuristics, nearest neighbor and greedy, in developing new crossover operators.We focus on preserving the edges in the union graph constructed by edges of the parent tours.We let the heuristics exploit the building blocks found in this graph. This way, new solutions can inherit good blocks from both parents. We also combine the two crossover operators together in generating offspring to explore the potential gain due to synergy. In addition, we make use of 2-edge exchange moves as the mutation operator to incorporate more problem specific information in the evolution process. Our reproduction strategy is based on the generational approach. Experimental results indicate that our operators are promising in terms of both solution quality and computation time.In the third part of the chapter, we present the second evolutionary algorithm developed. This part can be thought of as an enhancement of the first algorithm. A common practice with such algorithms is to generate one child or two children from two parents. In the second implementation, we investigate the preservation of good edges available in more than two parents and generate multiple children.We use the steady-state evolution as a reproduction strategy this time and test the replacement of the worst parent or the worst population member to find the better replacement strategy. Our two mutation operators try to eliminate the longest and randomly selected edges and a third operator makes use of the cheapest insertion heuristic. The algorithm is finalized after conducting a set of experiments for best parameter settings and testing on larger TSPLIB instances. The second evolutionary algorithm is also implemented for solving randomly generated instances of the TSPB. Our experiments reveal that the algorithm is significantly better than the competitors in the literature. The last part concludes the chapter.KeywordsNetworks-GraphsTraveling Salesman ProblemsEvolutionary AlgorithmsCrossover OperatorMutation OperatorHeuristics

university is a complicated work so in the implementation it have violation of the constraints and it also takes a lot of time since it is created manually. In this paper evolutionary algorithm (EA) is used to create an effective and feasible schedules based on the real data input that is obtained from each department. The objective functions in EA contribute in gaining the fitness function to solve the constraints problem in the schedule by applying weighting for each hard constraints. The objective function is gained from the total of infringement in each soft constraints addition by score weighting. The genetic operator used in EA is stochastic variation Operator. As far as the reproduction operator is concerned, the tournament selection was used with size 3. Crossover operator is conducted after selection process with crossover probability equal to 0.05 and mutation rate is 0.1. The size of population was set to 9 and stopping criteria algorithm was left run for fitness value = 1. The simulation result shows that EA can create lecture schedules efficiently and feasibly. Moreover, it is also faster with the execution time of the proposed EA is less than 30 and easier than creating manually.

Crossover is the main genetic operator which influences the power of evolutionary algorithms. Among a variety of crossover operators, there has been a growing interest in multi-parent crossover operators in evolutionary computation. The main motivation of those schemes is establishing comprehensive collective collaboration of more than two chromosomes in the population to generate a new offspring. In this paper, a novel all-parent crossover operator called collective crossover for genetic algorithm is proposed. In this method, all individuals in the current population are involved in recombination part and one offspring is generated. The contribution of each individuals is defined based on its quality in terms of fitness value. The performance of the collective crossover operator is tested on CEC2017 benchmark functions. The results revealed that the proposed crossover operator performs better when compared to well-known two-parent crossover operators including one-point and two-point crossovers. In addition, the differences between collective crossover and the other crossover operators are statistically significant for the most cases.