Brain Storm Optimization Algorithms for Flexible Job Shop Scheduling Problem

In this work Amplified Brain Storm Optimization (ABS) algorithm and Quantum based Brain Storm (QBS) Optimization Algorithm is used for solving optimal reactive power problem. In the projected amplified Brain storm optimization algorithm Hamiltonian cycle has been applied to improve the search abilities and also to avoid of trap in local optimal solution. A node is arbitrarily chosen from the graph as the preliminary point to form a Hamiltonian cycle. At generation t and t+1, L<sub>t</sub> and L<sub>t</sub><sub>+1</sub> are the length of Hamiltonian cycle correspondingly. In the QBS algorithm a Quantum state of an idea is illustrated by a wave function as an alternative of the position modernized only in Brain storm optimization algorithm. Monte Carlo simulation method<em> </em>is used, to measure the position for each idea from the<em> </em>quantum state to the traditional one. Proposed Amplified Brain Storm Optimization (ABS) algorithm and Quantum based Brain Storm (QBS) Optimization Algorithm has been tested in standard IEEE 57 bus test system and simulation results show the projected algorithms reduced the real power loss effectively.

Production scheduling is a critical requirement in today’s production systems. The production scheduling problem focuses on the rational allocation of production resources, determining the processing order of production tasks and operations, satisfying production constraints arising from the production environment such as the number of machines and task duration, and achieving optimal production goals, such as completing all tasks in the fastest way possible. The Flexible Job Shop Scheduling (FJSP) problem is a classical production scheduling issue, an extension of the Job Shop Scheduling (JSP) problem. The JSP problem involves allocating a set of jobs to a set of machines, where each job consists of multiple operations that must adhere to a precedence order. Each machine can process only one operation at a time for each job, and the time required for each operation on the corresponding machine is predetermined. The challenge in the JSP problem is to determine an appropriate order for processing operations or assignments, based on the production objective. FJSP represents a more complex and flexible variant of this problem, where at least one operation of a task can be performed on a set of alternative machines. Given that FJSP problems are NP-hard, solutions tend to be complex, varied, and often have limited applicability. Many FJSP scenarios require targeted modeling. In this paper, I propose a modeling approach for the static scheduling problem of job shops, considering low flexibility and demonstrating its usability by comparing it with other scheduling approaches, such as those based on genetic algorithm modeling. The paper is organized as follows:The first part of this paper offers a brief introduction to the FJSP problem, including background, research motivation, and main contributions, the second part provides a literature review,including a brief review and introduction of recent solutions to the FJSP problem, the third part describes a specific modeling approach, the fourth part details the test experiments and results of the modeling approach and includes comparisons with some other approaches, the fifth part analyzes the results from the fourth part and discusses the advantages and disadvantages of the modeling approach relative to others, and the sixth part concludes with a summary of findings and recommendations.

In this chapter, the human brainstorming process is modeled, based on which two versions of a Brain Storm Optimization (BSO) algorithm are introduced. Simulation results show that both BSO algorithms perform reasonably well on ten benchmark functions, which validates the effectiveness and usefulness of the proposed BSO algorithms. Simulation results also show that one of the BSO algorithms, BSO-II, performs better than the other BSO algorithm, BSO-I, in general. Furthermore, average inter-cluster distance Dc and inter-cluster diversity De are defined, which can be used to measure and monitor the distribution of cluster centroids and information entropy of the population over iterations. Simulation results illustrate that further improvement could be achieved by taking advantage of information revealed by Dc, which points at one direction for future research on BSO algorithms.

Recently, inspired by the human brainstorming process, a new kind of metaheuristic algorithm, called brain storm optimization (BSO) algorithm was proposed for global optimization. Experimental results have shown its excellent performance when solving optimization problems. In order to further improve the search ability of the BSO, this paper proposes an improved BSO (IBSO) algorithm by introducing graph theory into it. In IBSO, new individuals will be generated to replace some old individuals when the BSO algorithm is in a poor status. Whether a BSO algorithm is in a poor status is determined by the length of Hamiltonian cycle, which can be obtained by transferring all the individuals into an undirected weight graph. A Hamiltonian cycle and its length will be computed according to a modified cycle algorithm. The proposed IBSO algorithm is tested on twelve benchmarks, and the experimental results illustrate its effectiveness.

Using swarm intelligence to obtain multiple optima in a single run simultaneously proved efficient for solving multimodal optimization problems (MOPs). However, the existing studies fail to resolve the contradiction between the required solution accuracy and the number of solutions. In this paper, an improved brain storm optimization (BSO) algorithm based on knowledge learning (KLBSO) is proposed as a solution to the problem. The properties of the improved algorithm and the domain knowledge of the problem are combined during the search process. Two factors need to be taken into account to solve a MOP: the accuracy and the diversity of the solution set. In the proposed algorithm, there are two learning approaches. Firstly, improving the learning method by replacing the perturbation operator of the random solution with the inter-solution learning of the worst solutions, improves the optimization ability of the algorithm. Secondly, by analyzing the MOPs, adding an archive set guarantees the solution’s diversity. To assess the efficiency of KLBSO, eight benchmark functions with various sizes and complexities were used. Comparing the results of KLBSO with those of state-of-the-art methods which are brain storm optimization algorithm (BSO), brain storm optimization algorithm in objective space (BSOOS), two kinds of pigeon-inspired optimization algorithms (PIO, PIOr), the comparison results show that the KLBSO is able to solve the contradiction between required solution accuracy and the number of solutions, and improves the outcomes where BSO is ranked first followed by the test algorithms.

Flexible Job Shop Scheduling (FJSS) problem has many real-world applications such as manufacturing and cloud computing, and thus is an important area of study. In real world, the environment is often dynamic, and unpredicted job orders can arrive in real time. Dynamic FJSS consists of challenges of both dynamic optimisation and the FJSS problem. In Dynamic FJSS, two kinds of decisions (so-called routing and sequencing decisions) are to be made in real time. Dispatching rules have been demonstrated to be effective for dynamic scheduling due to their low computational complexity and ability to make real-time decisions. However, it is time consuming and strenuous to design effective dispatching rules manually due to the complex interactions between job shop attributes. Genetic Programming Hyper-heuristic (GPHH) has shown success in automatically designing dispatching rules which are much better than the manually designed ones. Previous works only focused on standard job shop scheduling with only the sequencing decisions. For FJSS, the routing rule is set arbitrarily by intuition. In this paper, we explore the possibility of evolving both routing and sequencing rules together and propose a new GPHH algorithm with Cooperative Co-evolution. Our results show that co-evolving the two rules together can lead to much more promising results than evolving the sequencing rule only.

In real scheduling problems, unexpected changes may occur frequently such as changes in task features. These changes cause deviation from primary scheduling. In this article, a heuristic model, inspired from Artificial Bee Colony algorithm, is proposed for a dynamic flexible job-shop scheduling (DFJSP) problem. This problem consists of n jobs that should be processed by m machines and the processing time of jobs deviates from estimated times. The objective is near-optimal scheduling after any change in tasks in order to minimise the maximal completion time (Makespan). In the proposed model, first, scheduling is done according to the estimated processing times and then re-scheduling is performed after determining the exact ones considering machine set-up. In order to evaluate the performance of the proposed model, some numerical experiments are designed in small, medium and large sizes in different levels of changes in processing times and statistical results illustrate the efficiency of the proposed algorithm.

A linguistic-based meta-heuristic modeling and solution approach for solving the flexible job shop scheduling problem (FJSSP) is presented in this study. FJSSP is an extension of the classical job-shop scheduling problem. The problem definition is to assign each operation to a machine out of a set of capable machines (the routing problem) and to order the operations on the machines (the sequencing problem), such that predefined performance measures are optimized. In this research, the scope of the problem is widened by taking into account the alternative process plans for each part (process plan selection problem). Probabilistic selection of alternative process plans and machines are also considered. The FJSSP is presented as a grammar and the productions in the grammar are defined as controls (Baykasoglu, 2002). Using these controls and Giffler and Thompson's (1960) priority rule-based heuristic along with the multiple objective tabu search algorithm of Baykasoglu et al. (1999) FJSSP is solved. This novel approach simplifies the modeling process of the FJSSP and enables usage of existing job shop scheduling algorithms for its fast solution. Instead of scheduling job shops with inflexible algorithms that cannot take into account the flexibility which is available in the job shop, the present algorithm is developed which can take into account the flexibility during scheduling. Such an approach will considerably increase the responsiveness of the job shops.

Flexible job shop scheduling problem (FJSP) is an extended formulation of the classical job shop scheduling problem, endowing great significance in the modern manufacturing system. The FJSP defines an operation that can be processed by any machine from a given set, which is a strong constrained NP-hard problem and intractable to be solved. In this paper, three recent proposed meta-heuristic optimization algorithms have been employed in solving the FJSP aiming to minimize the makespan, including moth-flame optimization (MFO), teaching-learning-based optimization (TLBO) and Rao-2 algorithm. Two featured FJSP cases are carried out and compared to evaluate the effectiveness and efficiency of the three algorithms, also associated with other classical algorithm counterparts. Numerical studies results demonstrate that the three algorithms can achieve significant improvement for solving FJSP, and MFO method appears to be the most competitive solver for the given cases.

The Flexible Job Shop scheduling Problem (FJSP) is a generalization of the classical Job Shop scheduling Problem (JSP) allowing to process operations on one machine out of a set of alternative machines. The FJSP is an NP-hard problem consisting of two sub-problems, which are the machine assignment and the operation scheduling problems. In this paper, we propose how to solve the FJSP by metaheuristics based on clustering in a holonic multiagent model. Firstly, a Neighborhood-based Genetic Algorithm (NGA) is applied by a scheduler agent for a global exploration of the search space. Secondly, a local search technique is used by a set of cluster agents to guide the research in promising regions of the search space and to improve the quality of the NGA final population. To evaluate our approach, numerical tests are made based on three sets of well known benchmark instances from the literature of the FJSP, which are Kacem, Brandimarte, Hurink. The experimental results show the efficiency of our approach in comparison to other approaches.

This chapter explains the mathematical formulation of brain storm optimization (BSO), conduct a comprehensive literature survey for the last 3 years, detail how BSO is applied to one real-world application, finally highlight promising future research directions. Since its introduction in 2011, different researchers have studied BSO behavior, proposed improvements to BSO, hybridized BSO with other techniques, developed cooperative BSO frameworks, applied BSO to real-world applications. Experimental results showed that simplex-BSO provided a better performance than BSO and Nelder-Mead simplex as well as being the best algorithm at any given computational cost. The term population-based metaheuristics refers to one large class of algorithms that has been successfully applied to solve continuous and discrete optimization problems. Reliability of the power supply is defined as the ability of a power system to supply customers in acceptable degree of adequacy and security. The work concluded that in lower dimensions, BSO produced good results as the population interaction of BSO follows a power law distribution.

Traditional planning and scheduling techniques still hold important roles in modern smart scheduling systems. Realistic features present in modern manufacturing systems need to be incorporated into these techniques. Flexible job-shop scheduling problem (FJSP) is one of the most challenging combinatorial optimization problems. FJSP is an extension of the classical job shop scheduling problem where an operation can be processed by several different machines. In this paper, we consider the FJSP with parallel operations (EFJSP) and we propose and compare a discrete firefly algorithm (FA) and a genetic algorithm (GA) for the problem. Several FJSP and EFJSP instances were used to evaluate the performance of the proposed algorithms. Comparisons among our methods and state-of-the-art algorithms are also provided. The experimental results demonstrate that the FA and GA achieved improvements in terms of efficiency and efficacy. Solutions obtained by both algorithms are comparable to those obtained by algorithms with local search. In addition, based on our initial experiments, results show that the proposed discrete firefly algorithm is feasible, more effective and efficient than our proposed genetic algorithm for the considered problem.

The brain storm optimization (BSO) algorithm has received increased attention in the field of evolutionary computation. While BSO has been applied in numerous industrial scenarios due to its effectiveness and accessibility, there are few theoretical analysis results about its running time. Running-time analysis can be conducted through the estimation of the upper bounds of the expected first hitting time to evaluate the efficiency of BSO. This study estimates the upper bounds of the expected first hitting time on six single individual BSO variants (BSOs with one individual) based on the average gain model. The theoretical analysis indicates the following results. (1) The time complexity of the six BSO variants is O(n) in equal coefficient linear functions regardless of the presence or absence of the disrupting operator, where n is the number of the dimensions. Moreover, the coefficient of the upper bounds on the expected first hitting time shows that the single individual BSOs with the disrupting operator require fewer iterations to obtain the target solution than the single individual BSOs without the disrupting operator. (2) The upper bounds on the expected first hitting time of single individual BSOs with the standard normally distributed mutation operator are lower than those of BSOs with the uniformly distributed mutation operator. (3) The upper bounds on the expected first hitting time of single individual BSOs with the U-12,12 mutation operator are approximately twice those of BSOs with the U(-1,1) mutation operator. The corresponding numerical results are also consistent with the theoretical analysis results.

The dual-resource constrained flexible job shop scheduling problem with variable sublots (DRCFJSP-VS) can be decomposed into four subproblems: the sublot splitting subproblem, the sublot sequencing subproblem, the machine assignment subproblem, and the worker assignment subproblem, which are difficult to solve efficiently using conventional methods. The introduction of variable-size batch splitting and the constraints of multiple levels and skills of workers further increase the complexity of the problem, making it difficult to solve efficiently using conventional methods. This paper proposes a mixed-integer linear programming (MILP) model to solve this complex problem and introduces a two-stage multi-objective evolutionary algorithm (TSMOEA). In the first stage of the algorithm, an improved multi-objective discrete difference evolutionary algorithm is used to optimize the dual-resource constrained flexible job shop scheduling problem; in the second stage, an adaptive simulated annealing algorithm is used to search for variable-size batch splitting strategies. To validate the feasibility of the model, the solution results are obtained using the CPLEX solver and compared with the results of TSMOEA. The performance of TSMOEA is compared with NSGA-II, PSO, DGWO, and WOA on improved instances. The results show that TSMOEA outperforms the other algorithms in both IGD and HV metrics, demonstrating its superior solution quality and robustness.

This paper researches on the flexible job shop scheduling problem (FJSP) with new job insertion. FJSP with new job insertion includes two phases: initializing schedules and rescheduling after new job(s) insertion. Initializing schedules is the standard FJSP problem while rescheduling is an FJSP with different job start time and different machine start time. The objective is to minimize maximum machine workload. A recently developed algorithm, so called Jaya, is employed to solve the FJSP with new job insertion and a discrete version of Jaya is proposed. Extensive computational experiments are carried out on eight real instances from remanufacturing enterprise. The discrete Jaya is compared to several existing heuristics and ensemble of them for FJSP with new job insertion. The results and comparisons verify that the discrete Jaya algorithm is superior over the existing methods. In future work, we will future improve the performance of discrete Jaya and compare it to more existing intelligent algorithms in literature.