Artificial chromosomes with genetic algorithm 2 (ACGA2) for single machine scheduling problems with sequence-dependent setup times

Artificial chromosomes with genetic algorithm (ACGA) is one of the latest versions of the estimation of distribution algorithms (EDAs). This algorithm has already been applied successfully to solve different kinds of scheduling problems. However, due to the fact that its probabilistic model does not consider variable interactions, ACGA may not perform well in some scheduling problems, particularly if sequence-dependent setup times are considered. This is due to the fact that the previous job will influence the processing time of the next job. Simply capturing ordinal information from the parental distribution is not sufficient for a probabilistic model. As a result, this paper proposes a bi-variate probabilistic model to add into the ACGA. This new algorithm is called the ACGA2 and is used to solve single machine scheduling problems with sequence-dependent setup times in a common due-date environment. A theoretical analysis is given in this paper. Some heuristics and local search algorithm variable neighborhood search (VNS) are also employed in the ACGA2. The results indicate that the average error ratio of this ACGA2 is half the error ratio of the ACGA. In addition, when ACGA2 is applied in combination with other heuristic methods and VNS, the hybrid algorithm achieves optimal solution quality in comparison with other algorithms in the literature. Thus, the proposed algorithms are effective for solving the scheduling problems.     

Continuous probabilistic model building genetic network programming using reinforcement learning

Recently, a novel probabilistic model-building evolutionary algorithm (so called estimation of distribution algorithm, or EDA), named probabilistic model building genetic network programming (PMBGNP), has been proposed. PMBGNP uses graph structures for its individual representation, which shows higher expression ability than the classical EDAs. Hence, it extends EDAs to solve a range of problems, such as data mining and agent control. This paper is dedicated to propose a continuous version of PMBGNP for continuous optimization in agent control problems. Different from the other continuous EDAs, the proposed algorithm evolves the continuous variables by reinforcement learning (RL). We compare the performance with several state-of-the-art algorithms on a real mobile robot control problem. The results show that the proposed algorithm outperforms the others with statistically significant differences.     

Using previous models to bias structural learning in the hierarchical BOA

Estimation of distribution algorithms (EDAs) are stochastic optimization techniques that explore the space of potential solutions by building and sampling explicit probabilistic models of promising candidate solutions. While the primary goal of applying EDAs is to discover the global optimum or at least its accurate approximation, besides this, any EDA provides us with a sequence of probabilistic models, which in most cases hold a great deal of information about the problem. Although using problem-specific knowledge has been shown to significantly improve performance of EDAs and other evolutionary algorithms, this readily available source of problem-specific information has been practically ignored by the EDA community. This paper takes the first step toward the use of probabilistic models obtained by EDAs to speed up the solution of similar problems in the future. More specifically, we propose two approaches to biasing model building in the hierarchical Bayesian optimization algorithm (hBOA) based on knowledge automatically learned from previous hBOA runs on similar problems. We show that the proposed methods lead to substantial speedups and argue that the methods should work well in other applications that require solving a large number of problems with similar structure.     

The continuous artificial bee colony algorithm for binary optimization

Artificial bee colony (ABC) algorithm, one of the swarm intelligence algorithms, has been proposed for continuous optimization, inspired intelligent behaviors of real honey bee colony. For the optimization problems having binary structured solution space, the basic ABC algorithm should be modified because its basic version is proposed for solving continuous optimization problems. In this study, an adapted version of ABC, ABC_bin for short, is proposed for binary optimization. In the proposed model for solving binary optimization problems, despite the fact that artificial agents in the algorithm works on the continuous solution space, the food source position obtained by the artificial agents is converted to binary values, before the objective function specific for the problem is evaluated. The accuracy and performance of the proposed approach have been examined on well-known 15 benchmark instances of uncapacitated facility location problem, and the results obtained by ABC_bin are compared with the results of continuous particle swarm optimization (CPSO), binary particle swarm optimization (BPSO), improved binary particle swarm optimization (IBPSO), binary artificial bee colony algorithm (binABC) and discrete artificial bee colony algorithm (DisABC). The performance of ABC_bin is also analyzed under the change of control parameter values. The experimental results and comparisons show that proposed ABC_bin is an alternative and simple binary optimization tool in terms of solution quality and robustness.     

A Self-guided Genetic Algorithm for permutation flowshop scheduling problems

In this paper we develop a Self-guided Genetic Algorithm (Self-guided GA), which belongs to the category of Estimation of Distribution Algorithms (EDAs). Most EDAs explicitly use the probabilistic model to sample new solutions without using traditional genetic operators. EDAs make good use of the global statistical information collected from previous searches but they do not efficiently use the location information about individual solutions. It is recently realized that global statistical information and location information should complement each other during the evolution process. In view of this, we design the Self-guided GA based on a novel strategy to combine these two kinds of information. The Self-guided GA does not sample new solutions from the probabilistic model. Instead, it estimates the quality of a candidate offspring based on the probabilistic model used in its crossover and mutation operations. In such a way, the mutation and crossover operations are able to generate fitter solutions, thus improving the performance of the algorithm. We tested the proposed algorithm by applying it to deal with the NP-complete flowshop scheduling problem to minimize the makespan. The experimental results show that the Self-guided GA is very promising. We also demonstrate that the Self-guided GA can be easily extended to treat other intractable combinatorial problems.     

A genetic algorithm with genes-association recognition for flowshop scheduling problems

In this paper, we consider a flowshop scheduling problem with a special blocking RCb (Release when Completing Blocking). This flexible production system is prevalent in some industrial environments. Genetic algorithms are first proposed for solving these flowshop problems and different initial populations have been tested to find which is best adapted. Then, a method is proposed for further improving genetic algorithm found solutions, which consists in marking out recurrent genes association occurrences in an already genetic algorithm optimized population. This idea directly follows Holland’s first statement about nature observations. Here, proposed idea is that populations well adapted to a problem have an adapted genetic code with common properties. We propose to mark out these properties in available genetic code to further improve genetic algorithm efficiency. Implementation of this method is presented and obtained results on flowshop scheduling problems are discussed.     

Biasing Bayesian Optimization Algorithm using Case Based Reasoning

Studies show that application of the prior knowledge in biasing the Estimation of Distribution Algorithms (EDAs), such as Bayesian Optimization Algorithm (BOA), increases the efficiency of these algorithms significantly. One of the main advantages of the EDAs over other optimization algorithms is that the former provides a trail of probabilistic models of candidate solutions with increasing quality. Some recent studies have applied these probabilistic models, obtained from previously solved problems in biasing the BOA algorithm, to solve the future problems. In this paper, in order to improve the previous works and reduce their disadvantages, a method based on Case Based Reasoning (CBR) is proposed for biasing the BOA algorithm. Herein, after running BOA for solving optimization problems, each problem, the corresponding solution, as well as the last Bayesian network obtained from the BOA algorithm, will be stored as an entry in the case-base. Upon introducing a new problem, similar problems from the case-base are retrieved and the last Bayesian networks of these solved problems are combined according to the degree of their similarity with the new problem; hence, a compound Bayesian network is constructed. The compound Bayesian network is sampled and the initial population for the BOA algorithm is generated. This network will be applied efficiently for biasing future probabilistic models during the runs of BOA for the new problem. The proposed method is tested on three well-known combinatorial benchmark problems. Experimental results show significant improvements in algorithm execution time and quality of solutions, compared to previous methods.     

Exploiting Bivariate Dependencies to Speedup Structure Learning in Bayesian Optimization Algorithm

Bayesian optimization algorithm (BOA) is one of the successful and widely used estimation of distribution algorithms (EDAs) which have been employed to solve different optimization problems. In EDAs, a model is learned from the selected population that encodes interactions among problem variables. New individuals are generated by sampling the model and incorporated into the population. Different probabilistic models have been used in EDAs to learn interactions. Bayesian network (BN) is a well-known graphical model which is used in BOA. Learning a proper model in EDAs and particularly in BOA is distinguished as a computationally expensive task. Different methods have been proposed in the literature to improve the complexity of model building in EDAs. This paper employs bivariate dependencies to learn accurate BNs in BOA efficiently. The proposed approach extracts the bivariate dependencies using an appropriate pairwise interaction-detection metric. Due to the static structure of the underlying problems, these dependencies are used in each generation of BOA to learn an accurate network. By using this approach, the computational cost of model building is reduced dramatically. Various optimization problems are selected to be solved by the algorithm. The experimental results show that the proposed approach successfully finds the optimum in problems with different types of interactions efficiently. Significant speedups are observed in the model building procedure as well.     

A comparison of two chromosome representation schemes used in solving a family-based scheduling problem

Meta-heuristic algorithms have been widely used in solving scheduling problems; previous studies focused on enhancing existing algorithmic mechanisms. This study advocates a new perspective—developing new chromosome (solution) representation schemes may improve the performance of existing meta-heuristic algorithms. In the context of a scheduling problem, known as permutation manufacturing-cell flow shop (PMFS), we compare the effectiveness of two chromosome representation schemes (S_old and S_new) while they are embedded in a meta-heuristic algorithm to solve the PMFS scheduling problem. Two existing meta-heuristic algorithms, genetic algorithm (GA) and ant colony optimization (ACO), are tested. Denote a tested meta-heuristic algorithm by X_Y, where X represents an algorithmic mechanism and Y represents a chromosome representation. Experiment results indicate that GA_ S_new outperforms GA_S_old, and ACO_S_new also outperforms ACO_S_old. These findings reveal the importance of developing new chromosome representations in the application of meta-heuristic algorithms.     

Effects of different chromosome representations in developing genetic algorithms to solve DFJS scheduling problems

This paper attempts to compare the effect of using different chromosome representations while developing a genetic algorithm to solve a scheduling problem called DFJS (distributed flexible job shop scheduling) problem. The DFJS problem is strongly NP-hard; most recent prior studies develop various genetic algorithms (GAs) to solve the problems. These prior GAs are similar in the algorithmic flows, but are different in proposing different chromosome representations. Extending from this line, this research proposes a new chromosome representation (called S_OP) and develops a genetic algorithm (called GA_OP) to solve the DFJS problem. Experiment results indicate that GA_OP outperforms all prior genetic algorithms. This research advocates the importance of developing appropriate chromosome representations while applying genetic algorithms (or other meta-heuristic algorithms) to solve a space search problem, in particular when the solution space is high-dimensional.     

构建在最大熵原理上的分布估计算法及其应用研究

分布估计算法是进化计算领域的一个新方向.它主要用概率模型来建造进化计算中的遗传算法,它不再依赖于交叉与变异,而是估计较好个体的概率分布,用概率分布来引导对搜寻空间的探索.本文提出一类基于最大熵的分布估计算法.实验结果表明,在解决某些较复杂问题时,本文算法比遗传算法更具优势.     

Security Driven Scheduling Model for Computational Grid Using NSGA-II

Number of software applications demands various levels of security at the time of scheduling in Computational Grid. Grid may offer these securities but may result in the performance degradation due to overhead in offering the desired security. Scheduling performance in a Grid is affected by the heterogeneities of security and computational power of resources. Customized Genetic Algorithms have been effectively used for solving complex optimization problems (NP Hard) and various heuristics have been suggested for solving Multi-objective optimization problems. In this paper a security driven, elitist non-dominated sorting genetic algorithm, Optimal Security with Optimal Overhead Scheduling (OSO₂S), based on NSGA-II, is proposed. The model considers dual objectives of minimizing the security overhead and maximizing the total security achieved. Simulation results exhibit that the proposed algorithm delivers improved makespan and lesser security overhead in comparison to other such algorithms viz. MinMin, MaxMin, SPMinMin, SPMaxMin and SDSG.     

Optimisation of distributed manufacturing flexible job shop scheduling by using hybrid genetic algorithms

In contrast to traditional job-shop scheduling problems, various complex constraints must be considered in distributed manufacturing environments; therefore, developing a novel scheduling solution is necessary. This paper proposes a hybrid genetic algorithm (HGA) for solving the distributed and flexible job-shop scheduling problem (DFJSP). Compared with previous studies on HGAs, the HGA approach proposed in this study uses the Taguchi method to optimize the parameters of a genetic algorithm (GA). Furthermore, a novel encoding mechanism is proposed to solve invalid job assignments, where a GA is employed to solve complex flexible job-shop scheduling problems (FJSPs). In addition, various crossover and mutation operators are adopted for increasing the probability of finding the optimal solution and diversity of chromosomes and for refining a makespan solution. To evaluate the performance of the proposed approach, three classic DFJSP benchmarks and three virtual DFJSPs were adapted from classical FJSP benchmarks. The experimental results indicate that the proposed approach is considerably robust, outperforming previous algorithms after 50 runs.     

Environment identification-based memory scheme for estimation of distribution algorithms in dynamic environments

In estimation of distribution algorithms (EDAs), the joint probability distribution of high-performance solutions is presented by a probability model. This means that the priority search areas of the solution space are characterized by the probability model. From this point of view, an environment identification-based memory management scheme (EI-MMS) is proposed to adapt binary-coded EDAs to solve dynamic optimization problems (DOPs). Within this scheme, the probability models that characterize the search space of the changing environment are stored and retrieved to adapt EDAs according to environmental changes. A diversity loss correction scheme and a boundary correction scheme are combined to counteract the diversity loss during the static evolutionary process of each environment. Experimental results show the validity of the EI-MMS and indicate that the EI-MMS can be applied to any binary-coded EDAs. In comparison with three state-of-the-art algorithms, the univariate marginal distribution algorithm (UMDA) using the EI-MMS performs better when solving three decomposable DOPs. In order to understand the EI-MMS more deeply, the sensitivity analysis of parameters is also carried out in this paper.     

A modified genetic algorithm with fuzzy roulette wheel selection for job-shop scheduling problems

The job-shop scheduling problem is one of the most difficult production planning problems. Since it is in the NP-hard class, a recent trend in solving the job-shop scheduling problem is shifting towards the use of heuristic and metaheuristic algorithms. This paper proposes a novel metaheuristic algorithm, which is a modification of the genetic algorithm. This proposed algorithm introduces two new concepts to the standard genetic algorithm: (1) fuzzy roulette wheel selection and (2) the mutation operation with tabu list. The proposed algorithm has been evaluated and compared with several state-of-the-art algorithms in the literature. The experimental results on 53 JSSPs show that the proposed algorithm is very effective in solving the combinatorial optimization problems. It outperforms all state-of-the-art algorithms on all benchmark problems in terms of the ability to achieve the optimal solution and the computational time.     

Model accuracy in the Bayesian optimization algorithm

Evolutionary algorithms (EAs) are particularly suited to solve problems for which there is not much information available. From this standpoint, estimation of distribution algorithms (EDAs), which guide the search by using probabilistic models of the population, have brought a new view to evolutionary computation. While solving a given problem with an EDA, the user has access to a set of models that reveal probabilistic dependencies between variables, an important source of information about the problem. However, as the complexity of the used models increases, the chance of overfitting and consequently reducing model interpretability, increases as well. This paper investigates the relationship between the probabilistic models learned by the Bayesian optimization algorithm (BOA) and the underlying problem structure. The purpose of the paper is threefold. First, model building in BOA is analyzed to understand how the problem structure is learned. Second, it is shown how the selection operator can lead to model overfitting in Bayesian EDAs. Third, the scoring metric that guides the search for an adequate model structure is modified to take into account the non-uniform distribution of the mating pool generated by tournament selection. Overall, this paper makes a contribution towards understanding and improving model accuracy in BOA, providing more interpretable models to assist efficiency enhancement techniques and human researchers.     

一种基于递增估计GMM的连续优化算法

目前的分布估计算法(estimation of distribution algorithms)中概率模型的学习或多或少存在着对先验知识的依赖,而这些先验知识往往是不可预知的.针对这一问题,文中提出采用集成学习(ensemble learning)的思想实现EDAs中概率模型结构和参数的自动学习,并提出了一种基于递增学习策略的连续域分布估计算法,该算法采用贪心EM算法来实现高斯混合模型(GMM)的递增学习,在不需要任何先验知识的情况下,实现模型结构和参数的自动学习.通过一组函数优化实验对该算法的性能进行了考查,并与其它同类算法进行了比较.实验结果表明该方法是有效的,并且,相比其它同类EDAs,该算法用相对少的迭代,可以得到同样或者更好的结果.     

Evolutionary based hybrid GA for solving multi-objective grid scheduling problem

The grid computing aims at bringing computing capacities together in a manner that can be used to find solutions for complicated problems of science. Conventional algorithms like first come first serve (FCFS), shortest job first (SJF) has been used for solving grid scheduling problem (GSP), but the increased complexity and job size led to the poor performance of these algorithms especially in the grid environment due to its dynamic nature. Previously, researchers have used a genetic algorithm (GA) to schedule jobs in the grid environment. In this paper, a multi-objective GSP is solved and optimized using the proposed algorithm. The proposed algorithm enhances the way the genetic algorithm performs and incorporate significant changes in the initialization step of the algorithm. The proposed algorithm uses SJF during its initialization step for producing the initial population solution. The proposed GA has three key features which are discussed in this paper: It executes jobs with minimum job completion time. It performs load balancing and improves resource utilization. Lastly, it supports scalability. The proposed algorithm is tested using a standard workload (given by Czech National Grid Infrastructure named Metacentrum) which can be a benchmark for further research. A performance comparison shows that the proposed algorithm has got better scheduling results than other scheduling algorithms.

     

A linkage mining in block-based evolutionary algorithm for permutation flowshop scheduling problem

A genetic algorithm is a type of heuristic algorithm used to solve permutation flowshop scheduling problems (PFSPs). Producing an optimal offspring with a variety of genes is difficult because of the evolution of the gene selection and a crossover mechanism that leads to local optima. This study proposes a linkage mining in block-based evolutionary algorithm (LMBBEA) for solving the PFSP, in which the association rule extracts various good genes and increases gene diversity. These genes are used to generate various blocks for artificial chromosome combinations. The generated blocks not only improve the chance of finding optimal solutions but also enhance the efficiency of convergence. The proposed LMBBEA is compared with other algorithms through numerical experiments, namely the Taillard and Reeves experiments in the OR-Library. To compare with other algorithms, the solutions produced by the proposed LMBBEA are closest to the optimal solution. The LMBBEA has a high convergence speed and a better solution quality due to an increase in the diversity of solutions.     

An efficient genetic algorithm for job-shop scheduling problems with fuzzy processing time and fuzzy duedate

In this paper, by considering the imprecise or fuzzy nature of the data in real-world problems, job-shop scheduling problems with fuzzy processing time and fuzzy duedate are formulated and a genetic algorithm which is suitable for solving the formulated problems is proposed. On the basis of the agreement index of fuzzy duedate and fuzzy completion time, the formulated fuzzy job-shop scheduling problems are interpreted so as to maximize the minimum agreement index. For solving the formulated fuzzy job-shop scheduling problems, an efficient genetic algorithm is proposed by incorporating the concept of similarity among individuals into the genetic algorithms using the Gannt chart. As illustrative numerical examples, both 6×6 and 10×10 job-shop scheduling problems with fuzzy duedate and fuzzy processing time are considered. Through the comparative simulations with simulated annealing, the feasibility and effectiveness of the proposed method are demonstrated.