Multilevel framework for large-scale global optimization

Mahdavi, Sedigheh; Rahnamayan, Shahryar; Shiri, Mohammad Ebrahim

doi:10.1007/s00500-016-2060-y

Cited by 31 publications

(16 citation statements)

References 14 publications

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“…One-dimension [31] Decompose N variables into N groups Easy to implement with low cost Lose efficacy on non-separable problems Random [32] Randomly decompose N variables into k groups Dependency on random technique Lose efficacy on non-separable problems Set-based [33] Random decompose N variables based on set Effective than one-dimension strategy Lose efficacy on non-separable problems Delta [28] Detect relationship based on the averaged difference More effective than random grouping Lose efficacy on non-separable problems K-means [34] Detect relationship based on K-means algorithm Effective on unbalanced grouping status High computational cost CCVIL [35] Detect relationship based on non-monotonicity method Effective than manual strategies Exist insurmountable benchmark IL [36] Detect relationship only once for each variable Lower computational cost than CCVIL Worse performance than CCVIL FII [37] Detect through fast interdependency identification Lower computational cost than CCVIL Worse performance for conditional variable DG [38] Detect relationship by the variance of fitness Better performance combined with PSO High computational cost EDG [39] Detect relationship by the variance of fitness Better performance compared with PSO High computational cost Probabilistic graphical models (PGMs) consist of Bayesian networks (BNs) and Markov random fields (MRFs). BNs are directed acyclic graphs which used for representing the causal relationship.…”

Section: Methodologies Advantage(s) Disadvantage(s)mentioning

confidence: 99%

Cooperative Co-Evolution Algorithm with an MRF-Based Decomposition Strategy for Stochastic Flexible Job Shop Scheduling

Sun

Lin

et al. 2019

Mathematics

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Flexible job shop scheduling is an important issue in the integration of research area and real-world applications. The traditional flexible scheduling problem always assumes that the processing time of each operation is fixed value and given in advance. However, the stochastic factors in the real-world applications cannot be ignored, especially for the processing times. We proposed a hybrid cooperative co-evolution algorithm with a Markov random field (MRF)-based decomposition strategy (hCEA-MRF) for solving the stochastic flexible scheduling problem with the objective to minimize the expectation and variance of makespan. First, an improved cooperative co-evolution algorithm which is good at preserving of evolutionary information is adopted in hCEA-MRF. Second, a MRF-based decomposition strategy is designed for decomposing all decision variables based on the learned network structure and the parameters of MRF. Then, a self-adaptive parameter strategy is adopted to overcome the status where the parameters cannot be accurately estimated when facing the stochastic factors. Finally, numerical experiments demonstrate the effectiveness and efficiency of the proposed algorithm and show the superiority compared with the state-of-the-art from the literature.Mathematics 2019, 7, 318 2 of 20 optimization problem with two sub-problems, i.e., operation sequence and machine assignment, and was proved as an NP-hard problem [9]. MotivationVarious researchers concentrated on the effective algorithms for minimizing the maximum completion time which named makespan of FJSP. Lin and Gen provided a survey in 2018 and presented the information of scheduling, e.g., mathematical formulation and graph representations [10]. Chaudhry and Khan reviewed solution techniques and methods published for flexible scheduling and presented an overview of the research trend of flexible scheduling in 2016 [11]. However, most of the existing research assumes that the processing time of each operation on the corresponding machine is fixed and given in advance. In actual, the stochastic factors in the real-world applications cannot be ignored. In addition, the processing time appears to be particularly important [12]. Therefore, in this paper, we consider the stochastic FJSP (S-FJSP), and the stochastic processing time is modeled as three probability distributions, i.e., the normal distribution, the Gaussian distribution and the exponential distribution.In recent years, various research was studied for stochastic scheduling problems. As listed in Table 1, Lei proposed a simplified multi-objective genetic algorithm (MOGA) for minimizing the expected makespan of JSP [13]. Hao et al. proposed an effective multi-objective estimation of distribution algorithm (moEDA) for minimizing the expected makespan and the total tardiness of JSP [14]. Kundakc and Kulak proposed a hybrid evolutionary algorithm for minimizing the expected of JSP makespan as well [15]. Represented by the above studies, some researchers modelled the stochastic processing timess by the unifor...

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Section: Methodologies Advantage(s) Disadvantage(s)mentioning

confidence: 99%

Cooperative Co-Evolution Algorithm with an MRF-Based Decomposition Strategy for Stochastic Flexible Job Shop Scheduling

Sun

Lin

et al. 2019

Mathematics

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“…The Multilevel Optimization Framework Based on Variables Effect (MOF-BVE) is one of the most recent attempts to address the imbalance problem [8]. The MOFBVE adopts a sensitivity analysis tool to measure the contributions of components at the early stage of the optimization.…”

Section: Contribution-aware CC Techniquesmentioning

confidence: 99%

“…A default option for CC regarding resource allocation is to allocate an equal portion of the computational budget to each subproblem. A large and growing body of literature is devoted to utilizing effective decomposition techniques with CC algorithms [5,6] and advancing the schemes for their computational budget allocation [7,8].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, a few techniques have been proposed to enable the traditional CC to handle the imbalance issue [7,8,10,12,13]. These techniques, which we refer to as contribution-aware CCs, keep track of the components' contributions to the improvement of the overall objective value.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, they seldom adapt to the dynamics of search process and their parameters are difficult to specify. Secondly, these techniques are often combinations of several other algorithms (e.g., [8,14]). This extra complexity brings lots of parameters into the framework such that the effects and contributions of each part to the overall outcome are difficult to identify.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bandit-based cooperative coevolution for tackling contribution imbalance in large-scale optimization problems

Kazimipour¹,

Omidvar

Qin

et al. 2019

Applied Soft Computing

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Fundamentals of Evolutionary Optimization: Single‐ and Multiobjective Problems

Coello

Gómez

Antonio

2018

Wiley Encyclopedia of Electrical and Electronics Engineering

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In this chapter, we describe the basics of evolutionary algorithms and their use in optimization. First, some generalities about evolutionary algorithms are provided, including a brief description of the components of the four main types of algorithms considered for the purposes of this chapter: (i) genetic algorithms, (ii) evolution strategies, (iii) evolutionary programming, and (iv) differential evolution. For the sake of brevity, this article focuses only on the use of evolutionary algorithms in numerical optimization. The discussion includes the use of evolutionary algorithms in both single‐ and multiobjective optimization and also includes aspects such as their variation operators, selection mechanism, and some of their applications.

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Multilevel framework for large-scale global optimization

Cited by 31 publications

References 14 publications

Cooperative Co-Evolution Algorithm with an MRF-Based Decomposition Strategy for Stochastic Flexible Job Shop Scheduling

Cooperative Co-Evolution Algorithm with an MRF-Based Decomposition Strategy for Stochastic Flexible Job Shop Scheduling

Bandit-based cooperative coevolution for tackling contribution imbalance in large-scale optimization problems

Fundamentals of Evolutionary Optimization: Single‐ and Multiobjective Problems

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