The effort of searching an optimal solution for scheduling problems is important for real-world industrial applications especially for mission-time critical systems. In this paper, a parallel GA is employed to solve flowshopscheduling problems to minimize the makespan.According to our experimental results, the proposed parallelgeneticalgorithm (PPGA) considerably decreases the CPU time without adversely affecting the makespan.
investigating the problem of scheduling jobs on a single CNC machine to reduce the energy consumption and total completion time. They pointed out that there was a significant amount of energy savings when non-bottleneck machines were turned off until needed; such the relevant savings share on the total energy consumption would sum up to 80%. In addition, they reported that the inter-arrivals were forecasted and more energy-efficient dispatching rules could be adopted for scheduling. In further research, Mouzon and Yildirim proposed a greedy randomized adaptive search algorithm for solving a multi-objective optimization schedule that minimized the total energy consumption and the total tardiness on a machine. Fang et al. provided a new mixed integer linear programming model for scheduling a classical flowshop that combined the peak total power consumption and associated carbon footprint with the makespan. Bruzzone et al.  presented an energy-aware schedulingalgorithm based on a mixed integer programming formulation to realize energy savings for a given flexible flowshop which was required to keep fixed original jobs' assignment and sequencing.
The Multi-Objective GeneticAlgorithm (MOGA) of Murata et al. , being part of evolutionary algorithms, was developed to solve multi-objective ﬂow shopproblem. Other than a modiﬁed selection operator, this algorithm was a simple genetic approach to scheduling. Selection is interrelated with a set of weights assigned to the objectives, which allowed to distribute the search towards di ﬀerent criteria directions. Elitist preservation method was also incorporated, so that several solutions from the actual Pareto frontier were copied to the next generation. The MOGA was furthermore enhanced by Murata et al. , by changing the way of weight distribution between objectives. Using a cellular structure permitted a better weight selection, which in turn led to ﬁnding a ﬁner approximation of Pareto frontier. New algorithm was called CMOGA.
Genetic algorithms are a very popular heuristic which have been successfully applied to many optimization problems within the last 30 years. In this chapter, we give a survey on some genetic algorithms for shopscheduling problems. In a shopschedulingproblem, a set of jobs has to be processed on a set of machines such that a specific optimization criterion is satisfied. According to the restrictions on the technological routes of the jobs, we distinguish a flowshop (each job is characterized by the same technological route), a job shop (each job has a specific route) and an open shop (no technological route is imposed on the jobs). We also consider some extensions of shopscheduling problems such as hybrid or flexible shops (at each processing stage, we may have a set of parallel machines) or the inclusion of additional processing constraints such as controllable processing times, release times, setup times or the no-wait condition. After giving an introduction into basic genetic algorithms discussing briefly solution representations, the generation of the initial population, selection principles, the application of genetic operators such as crossover and mutation, and termination criteria, we discuss several genetic algorithms for the particular problem types emphasizing their common features and differences. Here we mainly focus on single-criterion problems (minimization of the makespan or of a particular sum criterion such as total completion time or total tardiness) but mention briefly also some work on multi-criteria problems. We discuss some computational results and compare them with those obtained by other heuristics. In addition, we also summarize the generation of benchmark instances for makespan problems and give a brief introduction into the use of the program package ’LiSA - A Library of Scheduling Algorithms’ developed at the Otto-von-Guericke-University Magdeburg for solvingshopscheduling problems, which also includes a geneticalgorithm.
simulated annealing, genetic algorithms etc. In recent years, the adoption of meta-heuristics like GA has led to better results than classical dispatching or heuristic algorithms . Solvingscheduling problems with GA methods have been introduced by many researchers.
In this paper a multi-objective schedulingproblem was studied for a two-stage production system including a hybrid flowshop and an assembly stage.In this production system it is assumed that several products of differentkinds are ordered to be produced.The parts are manufactured in the hybrid flowshop and then the products are assembled in the assembly stage after preparing the parts. Two objective functions are considered simultaneously that are: (1) to minimizing the completion time of all products (makespan), and (2) minimizing the sum of earliness and tardiness of all products ( ∑ -E d d ∕ T d ) . Since this problem is NP-hard, a new multi-objective algorithm based on GA was designed for searching locally Pareto-optimal frontier for the problem. Various test problems were designed and the reliability of the proposed algorithm was presented in comparison two algorithms WBGA, and NSGA-II. The computational results show that the performance of the proposed algorithms is good in both efficiency and effectiveness.
Tabu (also called Taboo) search (TS), which was proposed by Glover et al. , is a meta-heuristic algorithm used for combinatorial optimization problems. The motivation for TS comes from the visited solutions and repeated visits of local search approaches. TS creates a short-memory structure that records forbidden moves called a tabu list. The foundation of tabu search is described as follows. First, the initial solution is generated randomly. Second, a set of neighborhood (candidate) solutions is generated using the current solution. Third, the solution with the best admissibility is chosen (the solution with the best admissibility is the one in which the move satisfies the aspiration criterion) and the tabu list is updated. Finally, Steps 2 and 3 are repeated until the stopping criterion is reached.
Enumeration and heuristic methods have been applied for energy saving in previous studies . Integer programming, branch and bound programming, and MIP are the most widely used enumeration methods that can provide ap- propriate solutions. However, high computational times limit the applicability of enumeration methods to small-scale problems . Thus, heuristics such as the geneticalgorithm, simulated annealing algorithm, and ant colony optimization algorithm are commonly used for solving energy-saving problems. Lian  ob- tained the average relative error rates of −28.20% and 60.25% for a combined local and global PSO algorithm against PSO and genetic algorithms, respectively. Zhang et al.  presented an I-ATTPSO algorithm with an average effective- ness improvement rate of −14% in small-scale problems and 55% in large-scale problems. Liu et al.  obtained an average relative error rate of 0.65% for the PSO-EDA_PI algorithm against other algorithms. Zhao et al.  found the av- erage relative error rate of their proposed logistic dynamic PSO algorithm against other algorithms to be approximately 1.19% - 2.39%.
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
have been developed for TSP but here we are using the concept of geneticalgorithm. Other approximation techniques for finding near optimum solutions for TSP based on heuristics are proposed in the literature such as  simulated annealing , ant colonies , genetic algorithms (GA)  and . John Holland’s pioneering book “Adaptation in natural Artificial System (1975, 1992) showed how the evolutionary process can be applied to solve a wide variety of problems using a highly parallel technique that is now called geneticalgorithm. Genetic Algorithms have been applied to a large number of real world pro blems. One of the first such applications was a gas pipeline control system created by ,  mentions several GA applications including message routing, scheduling, and automated design. Entire conferences have been devoted to applications of Genetic Algorithms and evolutionary techniques to specific disciplines, such as Image Analysis, Signal Processing and Telecommunications .
After many reported experiments in the literature, genetic algorithms have been found to be efficient, effective and robust algorithm for complicated problems. Nevertheless, genetic algorithms also have their shortcomings. In fact, if the worst members are discarded after each generation, the population will tend to become homogeneous quickly. And then the crossovers and mutation may not produce offspring of large variation. For this reasons, some authors have suggested inserting another operator, namely, a Boltzmann- type operator, after the crossover and mutation operations. Therefore, it is called this new metaheuristic method as mixed simulated geneticalgorithm (MSGA). In MSGA, new chromosomes are chosen to produce the next generation from parents and offspring according to Boltzeman function. The selection criterion is based on the fitness values of parents and offspring. Chromosomes with higher fitness values have a greater probability of surviving into the next generation. Those with less fitness values are not necessarily discarded. Based on above discussion, the MSGA is now described as follows:
Since the occurrence of the industrial revolution, manufacturing and industrial construction are growing in size and complexity. Furthermore, timely delivering of products and services to customers is more significant during past decades. Therefore, in order to be more productive and profitable, the need for developing new principles, techniques, and research disciplines is remarkable to survive in this competitive market-place. Operation research (OR), as a systematic and analytical approach to decision-making and problem-solving, is one of the discipline that has been developed to respond to this challenge (Hillier and Lieberman, 2001). Over the years, many researchers used OR for improving factory layout design, facility location, utilization of resources, scheduling, inventory control etc. Among these topics, scheduling receives much attention from researchers due to the significant impact on productivity and successful of corporations in terms of reducing cycle time, reducing of cost (or increasing of profit), minimizing work in process (WIP), and so on (Rokni, 2010).
Journals: Gromicho, J. A. S., van Hoorn, J. J., Saldanha-da-Gama, F., & Timmer, G. T. (2012). “Solving the job-shopschedulingproblem optimally by dynamic programming”. Computers & Operations Research, 39(12), 2968-2977. doi:http://dx.doi.org/10.1016/j.cor.2012.02.024 Journals: Qing, R., & Wang, Y. (2012). “A new hybrid geneticalgorithm for job shopscheduling
The job shopschedulingproblem is a well known practical planning problem in the manufacturing sector. We have considered the JSSP with an objective of minimizing makespan. In this paper, a multi- population based hybrid geneticalgorithm is developed for solving the JSSP. The population is divided in several groups at first and the hybrid algorithm is applied to the disjoint groups. Then the migration operator is used. The proposed approach, MP-HGA, have been compared with other algorithms for job- shopscheduling and evaluated with satisfactory results on a set of JSSPs derived from classical job-shopscheduling benchmarks. We have solved 15 benchmark problems and compared results obtained with a number of algorithms established in the literature. The experimental results show that MP-HGA could gain the best known makespan in 13 out of 15 problems.
As organizations move from creating plans for individual production lines to entire supply chains, it is increasingly important to recognize that planning decisions impact the quality of products and the production output. Suboptimal planning give rise to increasing lead times, increased costs and also unsatisfied customers waiting for their products. In order to avoid all these operation issues, proper production planning and scheduling of the process is required. Usually GANTT charts and PERT/CPM network techniques are the basic tools used to solve these problems. Gantt charts were meant to help individual managers make better decisions. In practice, PERT and CPM scheduling techniques have proven to be only helpful when the project deadline is not fixed and the resources are not constrained by either availability or time (Eknarin Sriprasert and Nashwan Dawood, 2003) . For scheduling a process, such that the make span is minimized, the precedence constraints and the resource requirements of various activities of the process need to be considered. The scheduling with above mentioned constraints makes it a combinatorial problem and hence difficult to solve using traditional tools. Based on the works done by researchers in this area, the use of geneticalgorithm (GA) can result in an optimal solution.
Zuzana Čičková and Stanislav Števo wrote that flowshopscheduling processing systems with two machines, where the aim is to minimize the makespan, can be solved by a Johnsons algorithm, but there is no polynomial algorithm for solving the problem for three and more machines . A heuristic is used for deciding the number of blocks, Johnson’s and NEH algorithm for sequencing the parts and finally GeneticAlgorithm and Simulated Annealing for sizing the blocks. Four algorithms are presented by combination of this method. Three lower bounds presented and improved to evaluate the performance of algorithms . The algorithm of Johnson is a classic method which solves to optimum the problem of sequencing n jobs on two machines, in a polynomial time. Assume that there are n jobs on three machines, then the problems become NP-complete (which is cannot be solved optimally in polynomial time) and the Johnson’s algorithm can be applied only for some kind of cases that obey some primary conditions .
Nagar et al.  developed a distinct method for the minimization of mean flow time along with the minimization of make span in a flowshop environment. They used two very different methods to reach to the required objective. These two methods are branch and bound method and the evolutionary algorithm i.e. geneticalgorithm. Nowicki and Smutnicki  implemented tabu search to solve the flow-shopschedulingproblem. Neppalli et al.  used the basic evolutionary algorithm for solving the two machine problem. It used the genetic algorithms approach to carry out the same, which aimed at minimizing the make span.
impossible to directly solve the model of practical sizes within a reasonable amount of time, suitable decomposition can be applied to achieve good performance. In the first part of the decomposition, only the train type related constraints stay active. In the second part, the remaining constraints are satisfied using relaxation technique. This decomposition idea provides a cornerstone for an algorithm integrating cutting plane and branch-and-bound to optimise the railway networks in Germany and the Netherlands. Zhou and Zhong  dealt with a double-track train schedulingproblem with multiple objectives. Focusing on a high-speed passenger rail line in an existing network, the problem is to minimise both, 1) the expected waiting times for high-speed trains (efficiency criterion); and 2) the total travel times of high-speed and medium-speed trains (effectiveness criterion). By applying two practical priority rules to model acceleration and deceleration times, the problem is formulated as a multi-mode flow-shopschedulingproblem. A branch-and-bound algorithm with effective dominance rule is developed for the bicriteria schedulingproblem, and a beam search algorithm with utility evaluation rules is used to construct non-dominated solutions. The authors illustrated the methodology and evaluated the performances of the proposed algorithm by a case study based on Beijing-Shanghai high-speed railway in China.
If initial population is diverse enough then it is possible to choose best solutions for recombination operations and this may reduce the computational time required. Dispatching Rules (DRs) have been applied consistently to scheduling problems. They are procedures designed to provide good solutions to complex problems in real time. Many authors claim that priority dispatching rules can be successfully used in solving large JSSPs and even oth- er scheduling problems . Mahanim et al.  used GeneticAlgorithm (GA) with some modifications to deal with problem of job shopscheduling which generated an initial population randomly including the result ob- tained by some well-known priority rules such as shortest processing time and longest processing time. Kuc- zapski et al.  presented an efficient method of enhancing Genetic Algorithms (GAs) for solving the Job- ShopSchedulingProblem (JSSP), by generating near optimal initial populations.
We consider the N P-hard problem of scheduling n jobs in m two-stage parallel ﬂow shops so as to minimize the makespan. This problem decomposes into two subproblems: assigning the jobs to parallel ﬂow shops; and scheduling the jobs assigned to the same ﬂow shop by use of Johnson’s rule. For m = 2, we present a 3 2 -approximation algorithm, and for m = 3, we present a 12 7 -approximation algorithm. Both these algorithms run in O(n log n) time. These are the ﬁrst approximation algorithms with ﬁxed worst-case performance guarantees for the parallel ﬂow shopproblem.