This paper presents a MemeticChickenswarm optimization (MeCSO) to solve jobshopschedulingproblem (JSSP). The aim is to find a better solution which minimizes the maximum of the completion time also called Makespan. In this paper, we adapt the chickenswarmalgorithm which take into consideration the hierarchical order of chickenswarm while seeking for food. Moreover, we integrate 2-opt method to im- prove the movement of the rooster. The new algorithm is applied on some instances of OR-Library. The empirical results show the forcefulness of MeCSO comparing to other metaheuristics from literature in term of run time and quality of solution.
have high efficiency in solving small-scale FJSP prob- lems, but they have the same flaws as the exact solution algorithms, and their application scope is limited . Artificial intelligence algorithm is mainly used to simulate the behavior of biological groups in nature. It has the advantages of parallelism, fast search speed, etc. It is the most widely used in FJSP problem solving and has become the main research direction . Some scholars proposed the use of genetic algorithm, simulated annealing, particle swarm optimization algorithm, ant colony algorithm, and firefly algorithm to solve the FJSP problem and obtained better results [7–9]. However, in practical applications, these artificial intelligence algorithms all have their own deficiencies, such as the late con- vergence speed is slow, easy to obtain local optimal solution . Artificial immune algorithm (AIA) is a kind of evolutionary algorithm that simulates the biological immune system. It is a multi-point ran- dom search algorithm. It has self-learning, self- organization, and memory under the premise of maintaining the excellent characteristics of the gen- etic algorithm. Such characteristics, so compared with other evolutionary algorithms, have better glo- bal search capabilities; have been successfully applied in cloud computing resource scheduling, robot path planning, and other fields; and provide a new re- search tool for solving FJSP problems .
Since the PSO algorithm is used basically for continuous optimization problems and the GS problem is a discrete problem (the optimal solution is the sequence of groups, as well as jobs, which is a discrete problem), it is required to perform several changes in the standard PSO algorithm to make it applicable for such discrete problems. Therefore, a novel encoding scheme, based on the Ronked Order Value (ROV) rule, is developed. The ROV rule converts the continuous position value of the particles to job and group sequences. Then a neighborhood search strategy named Individual Enhancement (IE), composed of PSO, is developed to enhance the searching ability and to balance exploration and exploitation. This algorithm is called PSOIE. A meta-heuristic algorithm based on the extended PSO algorithm is developed to solve FSDGS problems as follows.
Mousakhani (2013) formulate the SDST-FJSP as a mixed integer linear programming model to minimize total tardiness and present a meta-heuristic based on iterated local search for the same problem. Oddi et al. (2011) considers the SDST-FJSP to minimize the makespan using the iterative flattering search (IFS) and propose a new benchmark which is denoted SDST-HUdata. It consists of 20 instances produced as an extension of the existing well- known benchmarks of FJSP of Hurink et al. (1994). Gonzàlez et al. (2013) develop memeticalgorithm to minimize the makespan which the tabu search was applied to every chromosome generated by the genetic algorithm. In order to evaluate their model, they used the same benchmark as in Oddi et al. (2011) and prove that the memeticalgorithm has obtained a better result than the IFS. Recently, Rossi (2014) investigate the SDST-FJSP with transportation times using ant-colony algorithm with reinforced pheromone. The most recent comprehensive survey of schedulingproblem with setup times is given by Allahverdi (2015).
Because of the diculty in solving combinatorial optimization problems in real-size by an exact method, most studies on the IPPS problem focused on the use and development of meta-heuristics to nd high quality solutions for the problem. In a review study, Tan and Khoshnevis  investigated the capability of development of various methods to solve the mentioned problem. The study was focused on introducing process planning systems based on articial intelligence. Ima- nipour et al.  modeled the problem as a non-linear mixed integer programming model with the objective of minimizing maximum lateness, and solved it by two new versions of the tabu search algorithm. They also considered transportation times in their model. Ima- nipour  proposed a non-linear mixed integer pro- gramming for the IPPS problem considering sequence dependent setup times and developed a tabu search algorithm to solve the problem. Li and McMahon  proposed an approach based on the simulated anneal- ing algorithm in order to solve the IPPS problem. Moon and Seo  developed a mathematical model for solving the problem in a multi plant chain, considering transportation times. In addition, they presented an evolutionary algorithm for solving the proposed model. Moon et al.  presented a mixed integer programming model and an evolutionary algorithm, based on a topological type, to solve the IPPS problem in a supply chain. Guo et al.  used a modied Particle Swarm Optimization (PSO) algorithm to solve the problem in single objective mode. Shao et al.  proposed a modied approach based on the genetic algorithm for the IPPS problem. Li et al.  proposed a new hybrid algorithm to solve the problem. They devised a collection of new genetic representations and genetic operators in the algorithm. They also used the tabu search algorithm for local search. In addition, Li et al.  presented a mathematical model for the IPPS problem and proposed an evolutionary based algorithm to solve it. Wang et al.  proposed a new solution representation to use in the PSO algorithm for this problem and devised a local search approach to improve solution quality.
In (Lin et al., 2010) an efficient pool-based procedure has been presented that combines genetic algorithms, particle swarm optimization, and simulated annealing. In this hybrid, a multi-type individual enhancement scheme has been used as the base of the employed local search. A random key representation has also been employed as the encoding scheme. The multi-type individual enhancement scheme consists of three operations of swapping, insertion, and inversion. The enhancement, which is performed to find better neighbors, does not use any information about the critical path at all. These three operations are done with their corresponding probabilities and change random keys on the encoding. A main point of this method is that despite not using any information about critical paths, it produces very good results.
ABC algorithm  is a swarm based meta-heuristic algorithm that imitates a foraging behavior of honey bees. In ABC, there are two types of bee: employed and unemployed foraging bees. The employed bees search for new food sources within the neighborhood of the food source in their memory. Thereafter, they return to the hive with loads of nectar and with information about the food source, its distance and direction from the hive. They share the above information with unemployed bees by dancing in the designated dance area inside the hive. The second type is unemployed foraging bees. The unemployed bees consist of two groups of bees: onlooker bees and scouts. The onlooker bees wait in the hive and decide a food source to exploit depending on the information shared by the employed bees. The employed bees whose food sources are abandoned are converted into scout bees. The scout bees randomly search the environment surrounding the hive for new food sources.
Combining the chaos particle swarm optimization with genetic algorithm, Tang et al. (2011) proposed a hybrid algorithm. Chen et al. (2012) developed a schedulingalgorithm for jobshopschedulingproblem with parallel machines and reentrant process. A real weapons production factory is used as a case study to evaluate the performance of the proposed algorithm. Karimi et al. (2012) proposed a knowledge-based meta-heuristic algorithm, called knowledge-based variable neighborhood search (KBVNS) to solve FJSSP. Wang et al. (2012) applied the artificial bee colony (ABC) algorithm and estimation of distribution algorithm (EDA) to the FJSSP, both of which stress the balance between global exploration and local exploration. Zhang et al. (2012) proposed a model for Flexible JobShopSchedulingProblem (FJSSP) with transportation constraints and bounded processing times. A genetic algorithm with tabu search procedure is proposed to solve both assignment of resources and sequencing problems on each resource. Chiang and Lin (2013) addressed the multi objective flexible jobshopschedulingproblem (MOFJSSP) regarding minimizing the makespan, total workload, and maximum workload. Huang et al. (2013) considered the due window and the sequential dependent setup time.
The present paper extends the idea of jobshopschedulingproblem with resting constraints to the train schedulingproblem with the Muslim praying considerations. For this purpose, after proposing the new mathematical model, a heuristic algorithm based on the Electromagnetism-Like algorithm (EM) which is well adjusted to scheduling problems is employed to solve the large-size practical cases. The effectiveness of the proposed algorithm is then validated by comparing with optimum solution using small-size instances and simulated annealing algorithm, and Particle swarm Optimization (PSO) using medium and large-size instances. At the end, a practical case from Iranian railway network is studied and the results are reported. The results indicate that in the case of considering the Muslim praying constraint, the ratios of total tardiness of trains, and the total praying times are 14.5%, and 3.5%, respectively, while in the case of relaxing this constraint; the first ratio reduces to 12.3%. This result demonstrates that the proposed algorithm is able to schedule the praying times so that in many cases the trains with different directions meet each other during the praying times.
Recently, Artificial Immune System (AIS) is used to solve problems from different fields such as Robotic , Anomaly Detection , Combinatory Optimization , Learning , etc. One type of optimization problems is scheduling, and one of the very most common models in field of scheduling is that of the Job-shopscheduling. This problem belongs to NP-hard problems, whose optimal solution is difficult to achieve . Some evolutionary methods such as Genetic Algorithms (GAs), Ant Colony Optimization (ACO), Partial Swarm Optimization (PSO), Tabu Search (TS) etc. must be used to solve this problem. But these algorithms have a few lacks. For example GAs have two main drawbacks. One of them is lack of local search ability and the other is the premature
The MPSO algorithm is presented in this section, which includes global search and local search. An encoding scheme and a mixed particle initialization way are given first. Then global search updates particles in discrete domain directly. Finally, a VNS with variable neighborhood is introduced to improve the local search ability.
Particle Swarm Optimization (PSO) is one of the population based optimization technique inspired by social behavior of bird flocking and fish schooling. PSO inventers were inspired of such natural process based sce- narios to solve the optimization problems. In PSO, each single solution, called a particle, is considered as a bird, the group becomes a swarm (population) and the search space is the area to explore. Each particle has a fitness value calculated by a fitness function, and a velocity of flying towards the optimum, food. All parti- cles fly across the problem space following the particle nearest to the optimum. PSO starts with initial popu- lation of solutions, which is updated iteration-by-iteration. Therefore, PSO can be counted as an evolution- ary algorithm besides being a metaheuristics method, which allows exploiting the searching experience of a single particle as well as the best of the whole swarm. In this paper, A PSO model for the jobshop schedul- ing problem is proposed. In addition, a simple but efficient local search method called Variable Neighbor- hood Search (VNS) is embedded to the PSO model and applied to several hardest benchmark suites. The re- sults for the PSO algorithm with VNS are also presented and compared with many efficient meta-heuristic algorithms in literature. As a final result, PSO with VNS results are generally found to be better than other results.
Rui Zhang (2011) presented a PSO algorithm based on Local Perturbations for the JSSP. In his work, a local search procedure based on processing time perturbations is designed and embedded into the framework of PSO for MSSP model. In this paper, we attempt to introduce a new customized GA algorithm which has the strength of improving optimality obtained through satisfaction of multi soft constraints where crossover and mutation operators are designed according to the problem structure. To improve the outcome of GA operators, proposed to apply SAHC local search.
included [33-36]) since they allow exploring in an efficient way the solution space; nevertheless, they may converge prematurely. That is why recent researches have aimed to combine the GA with other techniques that ameliorate its efficiency by developing hybrid methods as the MemeticAlgorithm (MA). The MA was first introduced by Moscato and Norman . The basis of the MA lays on individual enhancements of the solutions of agents that interrelate one to another in a process that contains stages of cooperation and population competition. The MA has been successfully used in different areas and combinatorial problems, such as the knapsack problem [38-40], routing problems [41-43], quadratic assignment [44-45], and spanning tree [32, 46], among others. In order to give a solution to the JSP, some studies [1, 47-50] have proposed a MA, where the global search given by the GA is combined with a neighborhood structure based on Nowicki and Smutnicki , which allows the leading of the local search and the efficient exploitation of the solution space with the generation of three adjacent solutions for each initial solution; all of this with the final goal of minimizing the makespan. Here, we review the literature related to solve sequence problems with evolutionary “metaheuristics” algorithms, taking into account the JSP and the MA. In addition, we designed an algorithm to minimize the makespan, and studied the representation of the solution with chromosome, based on operations, and various ways of starting and building the solutions. Likewise, we fixed and established the genetic operators, as well as the searching algorithm, and designed an experiment to measure the effect of the algorithm parameters on the outputs. Finally, we evaluated the algorithm efficiency with reference problems from the OR-Library.
ticularity of the k-coloring problem is that its constraints are very simple, whereas FJSP has multiple complex con- straints. Consequently, HEAD and MAE have to be very dif- ferent: HEAD uses the greedy partition crossover to generate the child solutions, because it works in the space of infea- sible solutions to search for a feasible k-coloring, whereas MAE uses a recombination operator based on path relink- ing with a novel distance definition to generate child solu- tions, because it works in the space of feasible solutions to search for an optimal feasible solution. In fact, a crossover operator often generates infeasible child solutions for FJSP, and repairing these solutions then results in poor solutions, whereas a recombination operator based on path relinking can be more easily controlled to generate feasible child so- lutions. Besides, the diversity in the search of HEAD is also maintained by the crossover operator, whereas MAE main- tains the diversity by directly replacing one individual with a random feasible solution as soon as the two individuals be- come close to each other. Similar attempts of two-individual memeticalgorithm hybridized with regular re-initialization can be found in (Duarte et al. 2005).
Tabu Search merupakan salah satu metode pemecahan permasalahan optimasi kombinatorial yang tergabung ke dalam local search methods. Metode ini bertujuan untuk mengefektifkan proses pencarian solusi terbaik dari suatu permasalahan optimasi kombinatorial yang berskala besar (bersifat np-hard), contohnya permasalahan penjadwalan jobshop, dengan waktu komputasi yang relatif lebih kecil, namun tanpa ada jaminan akan tercapainya solusi yang optimal. Dalam penelitian ini, Tabu search diterapkan pada sebuah permasalahan penjadwalan jobshop dengan tujuan untuk meminimalkan waktu proses total atau makespan (C max ). Penjadwalan menggunakan algoritma Tabu Search ini
Artificial Intelligence amid the most recent decades. Because of its high unpredictability, as it were little cases can be fathomed by correct strategies, while examples with a size of down to earth intrigue ought to be settled by methods for surmised techniques guided by heuristic learning. In this paper we stand up to the JobShopScheduling with Sequence Dependent Setup Times (SDJSS). The SDJSS issue models numerous genuine circumstances superior to the JSS. Our approach comprises in expanding a hereditary calculation and a neighborhood look strategy that showed to be proficient in tackling the JSS issue. We report comes about because of a test think about demonstrating that the proposed approaches are more effective than other hereditary algorithm proposed in the writing, and that it is very focused with a state-of-the-art approaches.
The paper is organized as follows: In section 2, a general background is presented and the JSSP formulation and the disjunctive graph representation are explained. In section 3, the sequential and the parallel variants of the proposed algorithm are presented. These algorithms are a hybridization of Ant Colony System, GA, and SA. In section 4 the proposed algorithms are evaluated using a set of benchmark instances. In this section, sequential and parallel versions are compared considering the state-of-art algorithms as a reference. Finally, general conclusions are presented at the end of the paper.
In order to give a rough idea about the quality achieved, we confine to the 15 famous problems of Lawrence . MP-HGA is tested on Lawrence's data set (LA01-LA15). Applied instances of this data set consist of 15 problems with 10, 15 or 20 jobs, 5 machines, and 5 operations. We ran the proposed approach five times on the same instance to obtain meaningful results. The results appear in Table2. It respectively lists problem name, problem size (number of jobs × number of operations), the best known solution (BKS), and the best solution obtained in this paper (MP-HGA). The solutions obtained by the following literatures: Park et al. , Gao et al. , and Yang et al.  along with the relative deviations, Dev (%), are shown in the next columns of the table. Dev (%) columns refer to the relative deviation of those algorithms with respect to MP-HGA. The relative deviation is defined in Eq. (2).
However, a considerable number of recently published papers address real-life scheduling cases. Vieira et al.  described the development of a global scheduling system for a semiconductor test area. Gilkinson et al.  tackled the schedulingproblem of a company that produces laminated paper and foil products. Hamada et al.  approached a complex schedulingproblem in a steel-making company using a hybrid system based on evolutionary algorithms and expert systems. Shaw and Fleming  and Kumar and Srinivasan  proposed evolutionary computation methods for the solution of scheduling problems in companies that produce ready-chill meals and defense products, respectively. Sakawa et al.  considered the schedulingproblem of a machining center using an evolutionary algorithm. Shah et al.  developed knowledge based dynamic scheduling for Steel Plant. Finally, Suh et al. 1998  implemented ordering strategies for constraint satisfaction in steel industry. A scheduling expert system was developed to implement these strategies for the reactive adjustment of hot-rolling schedules in a hot strip mill.