A multi-population genetic algorithm to solve multi-objective scheduling problems for parallel machines

In modern ship manufacturing, a ship is divided into hundreds of blocks in the design stage, and the productivity of the block manufacturing process is vital to ship delivery. This paper investigates the production scheduling problem of ship blocks with the parent-child relationship; this relationship is characterised by the fact that sibling jobs at the same BOM layer must be processed on adjacent machines at their assembly stages. We formulate this problem as a multi-objective hybrid flow shop scheduling problem: the first objective is to minimise the total deviation from the target time of the jobs and the second one is to minimise the total processing time. To solve this problem, we propose a heuristic method based on the multi-objective genetic algorithm, in which an adjacent machine priority method is first proposed to generate feasible solutions that satisfy the space constraints. Then, we improve the individual quality in crossover and mutation of the algorithm via tabu search. We verify the performance of our algorithm by test instances generated from real manufacturing data of a shipbuilding company. Results show that the proposed method outperforms the existing algorithms when identifying the Pareto optimal solutions, especially for large-sized problems.

Many optimization problems encountered in practice are multi-objective by nature, i.e., different objectives are conflicting and equally important. Many times, it is not desirable to drop some of them or to optimize them in a composite single objective or hierarchical manner. Furthermore, cost parameters change over time which makes optimization problems harder. For instance, in the transport sector, travel costs are a function of travel time which changes depending on the time of the day a vehicle is travelling (e.g., due to road congestion). Road congestion results in tremendous delays which lead to a decrease in the service quality and the responsiveness of logistic service providers. In Chapter 2, we develop a generic approach to deal with Multi-Objective Scheduling Problems (MOSPs) with State-Dependent Cost Parameters. The aim is to determine the set of Pareto solutions that capture the trade offs between the different conflicting objectives. Due to the complexity of MOSPs, an efficient approximation based on dynamic programming is developed. The approximation has a provable worse case performance guarantee. Even though the generated approximate Pareto front consist of fewer solutions, it still represents a good coverage of the true Pareto front. Furthermore, considerable gains in computation times are achieved. In Chapter 3, the developed methodology is validated on the multi-objective timedependent knapsack problem. In the classical knapsack problem, the input consists of a knapsack with a finite capacity and a set of items, each with a certain weight and a cost. A feasible solution to the knapsack problem is a selection of items such that their total weight does not exceed the knapsack capacity. The goal is to maximize the single objective function consisting of the total pro t of the selected items. We extend the classical knapsack problem in two ways. First, we consider time-dependent profits (e.g., in a retail environment profit depends on whether it is Christmas or not).

This paper investigates a multi-objective parallel machine scheduling problem under fully fuzzy environment with fuzzy job deterioration effect, fuzzy learning effect and fuzzy processing times. Due dates are decision variables for the problem and objective functions are to minimise total tardiness penalty cost, to minimise earliness penalty cost and to minimise cost of setting due dates. Due date assignment problems are significant for Just-in-Time (JIT) thought. A JIT company may want to have optimum schedule by minimising cost combination of earliness, tardiness and setting due dates. In this paper, we compare different approaches for modelling fuzzy mathematical programming models with a local search algorithm based on expected values of fuzzy parameters such as job deterioration effect, learning effect and processing times.

Multi-objective parallel machine scheduling problem with job deterioration and learning effect under fuzzy environment

This chapter considers a dynamic multi-objective machine scheduling problem in response to continuous arrival of new jobs with deterioration effect, under the assumption that jobs can be rejected and job processing time is controllable by allocating extra resources. By deterioration effect, we mean that each job’s processing time may be subject to change due to the capability deterioration with machine’s usage, i.e., the actual processing time of a job becomes longer if the job starts processing later. The operational cost and the disruption cost need to be optimized simultaneously. To solve these dynamic scheduling problems, a directed search strategy (DSS) is introduced into the elitist non-dominated sorting genetic algorithm (NSGA-II) to enhance its capability of tracking changing optimums while maintaining fast convergence. The DSS consists of a population re-initialization mechanism (PRM) to be adopted upon the arrival of new jobs and an offspring generation mechanism (OGM) during evolutionary optimization. PRM re-initializes the population by repairing the non-dominated solutions obtained before the disturbances occur, modifying randomly generated solutions according to the structural properties, as well as randomly generating solutions. OGM generates offspring individuals by fine-tuning a few randomly selected individuals in the parent population, employing intermediate crossover in combination with Gaussian mutations to generate offspring, and using intermediate crossover together with differential evolution based mutation operator. Both PRM and OGM aim to strike a good balance between exploration and exploitation in solving the dynamic multi-objective scheduling problem. Comparative studies are performed on a variety of problem instances of different sizes and with different changing dynamics. Experimental results demonstrate that the proposed DSS is effective in handling the dynamic scheduling problems under investigation.

Multi-objective flow shop scheduling plays a key role in real-life scheduling problem which attract the researcher attention. The primary concern is to find the best sequence for flow shop scheduling problem. Estimation of Distribution Algorithms (EDAs) has gained sufficient attention from the researchers and it provides prominent results as an alternate of traditional evolutionary algorithms. In this paper, we propose the pareto optimal block-based EDA using bivariate model for multi-objective flow shop scheduling problem. We apply a bivariate probabilistic model to generate block which have the better diversity. We employ the non-dominated sorting technique to filter the solutions. To check the performance of proposed approach, we test it on the benchmark problems available in OR-library and then we compare it with non-dominated sorting genetic algorithm-II (NSGA-II). Computational results show that pareto optimal BBEDA provides better result and better convergence than NSGA-II.

This paper presents the comparative use of Simulated Annealing (SA) and Genetic Algorithm (GA) in a scheduling problem of unrelated parallel machines with set-up times. The problem accounts for allotting batched work parts to the unrelated parallel machines, where each batch is composed of a fixed number of identical jobs. Processing time of each job of a batch is determined according to the machine group as well as the batch group to which the job belongs. Major or minor set-up times are required between two subsequent batches, depending on the batch sequence but yet independent of machines. The objective of the problem is to minimise the Total Weighted Tardiness (TWT) for the unrelated parallel machine scheduling. SA and GA algorithms are proposed to obtain near-optimal solutions of the problem. The performance of proposed heuristics is compared through computational experiments with real data from dicing operations of a compound semiconductor manufacturing facility.

This paper presents a two-stage genetic algorithm (2S-GA) for multi-objective Job Shop scheduling problems. The 2S-GA is proposed with three criteria: Minimize makespan, Minimize total weighted earliness, and Minimize total weighted tardiness. The proposed algorithm is composed of two Stages: Stage 1 applies parallel GA to find the best solution of each individual objective function with migration among populations. In Stage 2 the populations are combined. The evolution process of Stage 2 is based on Steady-State GA using the weighted aggregating objective function. The algorithm developed can be used with one or two objectives without modification. The genetic algorithm is designed and implemented with the GALIB object library. The random keys representation is applied to the problem. The schedules are constructed using a permutation with m-repetitions of job numbers. Performance of the proposed algorithm is tested on published benchmark instances and compared with results from other published approaches for both the single objective and multi-objective cases. The experimental results show that 2S-GA is effective and efficient to solve job shop scheduling problem in term of solution quality.

In this paper, we discuss scheduling problems in semiconductor manufacturing. Starting from describing the manufacturing process, we identify typical scheduling problems found in semiconductor manufacturing systems. We describe batch scheduling problems, parallel machine scheduling problems, job shop scheduling problems, scheduling problems with auxiliary resources, multiple orders per job scheduling problems, and scheduling problems related to cluster tools. We also present important solution techniques that are used to solve these scheduling problems by means of specific examples, and report on known implementations. Finally, we summarize some of the challenges in scheduling semiconductor manufacturing operations.

This paper addresses the problem of scheduling n jobs on a single machine and on m identical parallel machines to minimize the completion time variance of jobs. This problem of scheduling jobs on parallel machines is motivated by a case study in an automobile ancillary unit. First, a heuristic to solve the single-machine scheduling problem is proposed. The parallel-machine scheduling problem is solved in two phases: job-allocation phase and job-sequencing phase. Two heuristics are proposed in the job-allocation phase, whereas in the job-scheduling phase, the single-machine scheduling approach is used. In this paper, both versions of parallel-machine scheduling problem (restricted and unrestricted) are considered. A good upper bound is obtained using a genetic algorithm, to evaluate the performance of the proposed heuristics for the parallel-machine scheduling problem. An extensive computation evaluation of the proposed heuristics is presented for both single-machine scheduling problem and the parallel-machine scheduling problem (especially considering the case study), along with the comparison of performances with the existing heuristics in the literature.

The flexible open shop scheduling problem is the combination of two classical open shop and a parallel machine scheduling problems. Due to the computational complexity of solving the open shop scheduling problem, so far, limited research has considered the assumption of flexibility in this problem. In this study, a bi-objective flexible open shop scheduling with independent setup time is considered. The considered objective functions are to minimize the maximum completion time of jobs and total tardiness. Using the first objective function, an attempt is made to balance the amount of workloads on the machines so that the completion time of the last job is minimized, while using the second one, from the customers' point of view, an attempt is made to reduce the amount of tardiness in delivery of jobs to the customers. Here, firstly, a mixed-integer nonlinear programming model is proposed. Then, to deal with the multi-objective problem, the weighted Lp-metric method is used. Since, this problem is a non-deterministic polynomial-time hard problem (NP-hard), a scatter search algorithm is developed to obtain near-optimal solutions in a reasonable time. In this regard, for the first time, a novel solution representation method is also presented. To ensure the efficiency of the proposed algorithm, the results were compared with NSGA-II using several instances. After analyzing the results using four evaluation metrics, it is observed that the scatter search algorithm performs better than the NSGA-II.

In this paper, a hybrid discrete particle swarm algorithm based on maximum fitness function is proposed for a dual-resources constrained flexible job shop scheduling problem with multiple optimisation objectives. An improved position updating mechanism of particles is used to effectively avoid the occurrence of infeasible solution. Additionally, a novel dynamic search strategy is designed to enhance the local exploiting search ability of discrete particle swarms. Finally, simulation results demonstrate that the proposed algorithm effectively decreases both the production time and production cost.

Scheduling problems, as one of the classic combinatorial optimization problems are essential issues in many fields. Various meta-heuristic algorithms have been adopted to solve scheduling problems. However, parameter control problem is still crucial to the performance of algorithms. In this paper, we propose a self-adaptive parameter control method based on entropy and security market line, fully considering the characteristics scheduling problems. It consists of two key parts: locus-entropy strategy and parameter-control strategy. Firstly, the entropy on each genetic locus is calculated to accurately evaluate the population status of scheduling algorithms. Then, a parameter-control strategy based on the conception of security market line is proposed to address the issue that the nature of multipeak in scheduling problems makes algorithms fall into local optimal solutions. The strategy maintains the solutions of good quality and eliminate the solutions of poor quality by using locus-entropy as feedback. Through our method, the balance between exploitation and exploration is kept in algorithms to perform well in scheduling problems with different dimensions and characteristics. These strategies are tightly linked to adjust parameters adaptively without introducing new parameters, so that meta-heuristic algorithms equipped with the proposed approach are able to find a better solution. Moreover, our parameter control method is universal for meta-heuristic algorithms. The proposed approach is hybrid with genetic algorithm and particle swarm optimization. The hybrid algorithms are first compared with the standard algorithms in multipeak benchmark functions, then with other variants of the standard algorithms in real-world single and multi-objective scheduling problems. The results demonstrate that the proposed approach is valid for different kinds of algorithms to enhance the performance of solving a variety of scheduling problems.

Identical parallel machine scheduling problem for minimizing the makespan is a very important production scheduling problem which has been proven to be NP-hard. The problem further compounds with additional constraints. Genetic algorithms (GA) have shown great advantages in solving the combinatorial optimization problem in view of its characteristic that has high efficiency and that is fit for practical application. In this chapter we present a spreadsheet based GA approach for minimizing the makespan for scheduling of a set of tasks for identical parallel machines and worker assignment to machines. The results obtained from the proposed approach are compared with two sets of benchmark problems consisting of 100 problems each. It has been demonstrated that the performance of proposed approach is superior to the results that have been obtained earlier. The proposed approach produces optimal solution for almost 95% of the problems demonstrating the effectiveness of the proposed approach. An empirical analysis of GA parameters has also been carried out to see the effect on the performance of the proposed algorithm.

We consider the parallel-machine flexible-resource scheduling (PMFRS) problem in which a set of jobs must be scheduled over a set of parallel machines, where the processing time of each job is a function of the amount of allocated resource. Resource flexibility provides the capability to dynamically reassign a renewable resource across machines to break processing bottlenecks and improve system performance as measured by schedule makespan. The PMFRS problem has many important applications, including production scheduling of manufacturing cells where a cross-trained work force can be dynamically reallocated among cells. The problem is also NP-hard, motivating the development of effective heuristics that approximately determine the allocation of resource to jobs, the sequence of jobs on each machine, and the associated job start times that minimize system makespan. This paper explores heuristics for the PMFRS problem, and in particular the application of tabu-search methodology to this problem setting. We review an existing heuristic (SBH), define two tabu-search heuristics, and discuss extensive computational experience with the procedures. The computational results indicate that the heuristics are effective in obtaining approximate solutions to the PMFRS problem. In particular, the approach that uses tabu-search methodology in tandem with SBH consistently yields high-quality solutions with modest computational effort.