Hybrid Discrete Differential Evolution Algorithm Research Articles

Novel hybrid discrete differential evolution algorithm for the multi-stage multi-purpose batch plant scheduling problem

The multi-stage multi-product batch plant scheduling problem is an important part of batch chemical industry scheduling problems. Different from the multi-purpose batch scheduling problem, this problem can be characterized by multiple stages with non-identical parallel units, and multiple batches of customer orders. Numerous methodologies for this problem have been investigated to addressing scheduling cases of different production systems in the past two decades. This paper focus on the large-scale batch plant scheduling problem by minimizing the make-span in the scheduling horizon. And a novel hybrid discrete differential evolutionary algorithm is proposed to handle this problem. First, a novel two-line encoding scheme is constructed based on discrete and continuous variables. The sequence of orders is represented by a time-based representation method. Second, two novel mutation methods are proposed within the framework of encoding method. Two methods provide multiple search directions which helps improve the exploration ability and diversity of the population. At last, two local permutation methods are applied to improve the local optimal for the algorithm. The proposed work is tested through several real industrial instances with different sizes and characteristics by comparing with mixed integer linear programming method and meta-heuristic algorithms. The improvement of proposed work is also analyzed by the instances. The results report the efficiency and effectiveness of the novel proposed evolutionary algorithm in solving large scale multi-stage multi-product batch plant scheduling problem.

Exact and metaheuristic algorithms for flow-shop scheduling problems with release dates

Flow-shop scheduling is an extremely popular optimization model in industrial production, where each job must be scheduled on a series of machines following an identical process. The optimal criteria, makespan and maximum delivery–completion time, are investigated separately. A mixed integer programming model is built to evaluate the exact algorithm in simulation experiments. Given that these problems are NP hard and cannot be solved in polynomial time, exact and metaheuristic methods are proposed for different problem sizes. For small-scale instances, optimal schedules are achieved using an effective branch-and-bound algorithm, in which elaborately designed lower bound and branching rules significantly improve computational efficiency. For medium-scale instances, satisfactory solutions are obtained using a hybrid discrete differential evolution algorithm with improvement schemes to promote its performance. The experimental results show the effectiveness of the proposed algorithms.

Effective Heuristic Algorithms Solving the Jobshop Scheduling Problem with Release Dates

Manufacturing industry reflects a country’s productivity level and occupies an important share in the national economy of developed countries in the world. Jobshop scheduling (JSS) model originates from modern manufacturing, in which a number of tasks are executed individually on a series of processors following their preset processing routes. This study addresses a JSS problem with the criterion of minimizing total quadratic completion time (TQCT), where each task is available at its own release date. Constructive heuristic and meta-heuristic algorithms are introduced to handle different scale instances as the problem is NP-hard. Given that the shortest-processing-time (SPT)-based heuristic and dense scheduling rule are effective for the TQCT criterion and the JSS problem, respectively, an innovative heuristic combining SPT and dense scheduling rule is put forward to provide feasible solutions for large-scale instances. A preemptive single-machine-based lower bound is designed to estimate the optimal schedule and reveal the performance of the heuristic. Differential evolution algorithm is a global search algorithm on the basis of population, which has the advantages of simple structure, strong robustness, fast convergence, and easy implementation. Therefore, a hybrid discrete differential evolution (HDDE) algorithm is presented to obtain near-optimal solutions for medium-scale instances, where multi-point insertion and a local search scheme enhance the quality of final solutions. The superiority of the HDDE algorithm is highlighted by contrast experiments with population-based meta-heuristics, i.e., ant colony optimization (ACO), particle swarm optimization (PSO) and genetic algorithm (GA). Average gaps 45.62, 63.38 and 188.46 between HDDE with ACO, PSO and GA, respectively, are demonstrated by the numerical results with benchmark data, which reveals the domination of the proposed HDDE algorithm.

A Hybrid Discrete Differential Evolution Algorithm to Solve the Split Delivery Vehicle Routing Problem

For the split delivery vehicle routing problem in the distribution link of logistics where the optimization objective is to minimize the total distance of the transportation path, a hybrid discrete differential evolution (HDDE) algorithm is adopted in this study. The algorithm applies the encoding and decoding method based on the remaining vehicle capacity to split the demand of customer point and adjust the splitting node to the optimal position of its path. In order to avoid the prematurity of the algorithm, the perturbation mechanism is added, i.e. , the three-point insertion method is used in the crossover stage. To ensure the higher quality of the solution, the idea of tabu search is introduced in three cases: initial population generation, selection operation and local optimal situation. Finally, through the numerical experiments based on benchmark data, the HDDE algorithm is compared with other competitive algorithms to demonstrate its domination.

Quantum-inspired ant colony optimisation algorithm for a two-stage permutation flow shop with batch processing machines

This paper studied two-stage permutation flow shop problems with batch processing machines, considering different job sizes and arbitrary arrival times, with the optimisation objective of minimising the makespan. The quantum-inspired ant colony optimisation (QIACO) algorithm was proposed to solve the problem. In the QIACO algorithm, the ants are divided into two groups: one group selects the largest job in terms of job size as the initial job for each batch and the other group selects the smallest job as the initial job for each batch. Each group of ants has its own pheromone matrix. In the computational experiment, our novel algorithm was compared with the hybrid discrete differential evolution (HDDE) algorithm and the batch-based hybrid ant colony optimisation (BHACO) algorithm. Although the HDDE algorithm has a shorter run time, the quality of the solution for large-scale jobs is not good, while the BHACO algorithm always obtains a better solution but requires a longer run time. The computational results show that the QIACO algorithm embedded in the quantum information has advantages in terms of both solution quality and running time.

Ant colony optimisation algorithms for two-stage permutation flow shop with batch processing machines and nonidentical job sizes

This paper focuses on minimising the maximum completion time for the two-stage permutation flow shop scheduling problem with batch processing machines and nonidentical job sizes by considering blocking, arbitrary release times, and fixed setup and cleaning times. Two hybrid ant colony optimisation algorithms, one based on job sequencing (JHACO) and the other based on batch sequencing (BHACO), are proposed to solve this problem. First, max-min pheromone restriction rules and a local optimisation rule are embedded into JHACO and BHACO, respectively, to avoid trapping in local optima. Then, an effective lower bound is estimated to evaluate the performances of the different algorithms. Finally, the Taguchi method is adopted to investigate and optimise the parameters for JHACO and BHACO. The performances of the proposed algorithms are compared with that of CPLEX on small-scale instances and those of a hybrid genetic algorithm (HGA) and a hybrid discrete differential evolution (HDDE) algorithm on full-scale instances. The computational results demonstrate that BHACO outperforms JHACO, HDDE and HGA in terms of solution quality. Besides, JHACO strikes a balance between solution quality and run time.

Discrete differential evolution algorithm for distributed blocking flowshop scheduling with makespan criterion

This paper deals with a distributed blocking flowshop scheduling problem, which tries to solve the blocking flowshop scheduling in distributed manufacturing environment. The optimization objective is to find a suitable schedule, consisting of assigning jobs to at least two factories and sequencing the jobs assigned to each factory, to make the maximum completion time or makespan minimization. Two different mathematical models are proposed, and in view of the NP-hardness of the problem, a novel hybrid discrete differential evolution (DDE) algorithm is established. First, the problem solution is represented as several job permutations, each of which denotes the partial schedule at a certain factory. Second, four widely applied heuristics are generalized to the distributed environment for providing better initial solutions. Third, both operators of mutation and crossover are redesigned to perform the DDE directly based on the discrete permutations, and a biased section operator is used to increase the diversity of the searching information. Meanwhile, an effective local search based on distributed characteristics and an elitist retain strategy are integrated into the DDE framework to stress both local exploitation and global exploration. Taking into account the time cost, an effective speed-up technique is designed to enhance the algorithmic efficiency. In the experimental section, the parameters of DDE are calibrated by the Taguchi method. Experimental results derived from a wealth of test instances have demonstrated the algorithmic effectiveness, which further concludes that the proposed DDE algorithm is a suitable alternative approach for solving the problem under consideration.

A hybrid discrete differential evolution algorithm for deadlock-free scheduling with setup times of flexible manufacturing systems

This paper proposes an effective hybrid discrete differential evolution (DDE) algorithm for solving a scheduling problem of flexible manufacturing systems (FMSs), where sequence-dependent setup times are considered. The objective is to find a deadlock-free schedule that minimizes the makespan. Based on the timed Petri net models of FMSs, a possible solution of the scheduling problem is represented as an individual that is a permutation with repetition of jobs. For the existence of deadlocks, most of the individuals cannot be directly decoded into feasible (live) schedules. Therefore, a deadlock controller is applied in the decoding scheme, and infeasible individuals are amended into feasible ones. Moreover, in order to overcome the premature convergence of DDE algorithm and improve solution quality, a variable neighbourhood search algorithm, which performs a systematic change of neighbourhood in solution searching, is adopted. Then a hybrid scheduling algorithm that combines a DDE with a variable neighbourhood search is presented. Computational results and comparison based on a variety of instances show the feasibility and superiority of the proposed algorithm.

Hybrid discrete differential evolution algorithm for biobjective cyclic hoist scheduling with reentrance

Cyclic hoist scheduling problems in automated electroplating lines and surface processing shops attract many attentions and interests both from practitioners and researchers. In such systems, parts are transported from a workstation to another by a material handling hoist. The existing literature mainly addressed how to find an optimal cyclic schedule to minimize the cycle time that measures the productivity of the lines. The material handling cost is an important factor that needs to be considered in practice but seldom addressed in the literature. This study focuses on a biobjective cyclic hoist scheduling problem to minimize the cycle time and the material handling cost simultaneously. We consider the reentrant workstations that are usually encountered in real-life lines but inevitably make the part-flow more complicated. The problem is formulated as a biobjective linear programming model with a given hoist move sequence and transformed into finding a set of Pareto optimal hoist move sequences with respect to the bicriteria. To obtain the Pareto optimal or near-optimal front, a hybrid discrete differential evolution (DDE) algorithm is proposed. In this hybrid evolutional algorithm, the population is divided into several subpopulations according to the maximal work-in-process (WIP) level of the system and the sizes of subpopulations are dynamically adjusted to balance the exploration and exploitation of the search. We propose a constructive heuristic to generate initial subpopulations with different WIP levels, hybrid mutation and crossover operators, an evaluation method that can tackle infeasible individuals and a one-to-one greedy tabu selection method. Computational results on both benchmark instances and randomly generated instances show that our proposed hybrid DDE algorithm outperforms the basic DDE algorithm and can solve larger-size instances than the existing ε-constraint method.

Open shop scheduling problem to minimize total weighted completion time

ABSTRACTA given number of jobs in an open shop scheduling environment must each be processed for given amounts of time on each of a given set of machines in an arbitrary sequence. This study aims to achieve a schedule that minimizes total weighted completion time. Owing to the strong NP-hardness of the problem, the weighted shortest processing time block (WSPTB) heuristic is presented to obtain approximate solutions for large-scale problems. Performance analysis proves the asymptotic optimality of the WSPTB heuristic in the sense of probability limits. The largest weight block rule is provided to seek optimal schedules in polynomial time for a special case. A hybrid discrete differential evolution algorithm is designed to obtain high-quality solutions for moderate-scale problems. Simulation experiments demonstrate the effectiveness of the proposed algorithms.

A novel hybrid discrete differential evolution algorithm for workingsteps sequencing in multi-channel turn-milling complex machining

To address the problem of workingsteps sequencing in multi-channel turn-milling complex machining, a novel hybrid optimization algorithm titled hybrid discrete differential evolution has been proposed, which improves the algorithm to achieve better results for the workingsteps sequencing problem. The main thrust of this article is twofold: (1) to analyze the characteristics of synchronous machining in multi-channel turn-milling complex machining and their constraints, and to propose a zero-wait micro-resource allocation strategy; (2) to develop a hybrid discrete differential evolution algorithm for process planning in multi-channel turn-milling complex machining, and to describe in detail about the operation of crossover, mutation, and selection. Then, analysis of variance has been used to investigate the contribution and effects of variables (parameters) in hybrid discrete differential evolution, so the optimal parameters can be obtained. Finally, a comparison of the performance and efficiency between the proposed algorithm and the classical differential evolution algorithm is made. And experimental results show that the hybrid discrete differential evolution algorithm is good at solving the sequencing problem, and the results approximate the optimum expectation.

A hybrid differential evolution algorithm for a two-stage flow shop on batch processing machines with arbitrary release times and blocking

Batch processing machines (BPMs) have important applications in a variety of industrial systems. This paper considers the problem of scheduling two BPMs in a flow shop with arbitrary release times and blocking such that the makespan is minimised. The problem is formulated as a mixed integer programming model. Subsequently, a hybrid discrete differential evolution (HDDE) algorithm is proposed. In the algorithm, individuals in the population are first represented as discrete job sequences, and mutation and crossover operators are applied based on the representation. Second, after using the first-fit rule to form batches, a novel least idle/blocking time heuristic is developed to schedule the batches in the flow shop. Furthermore, an effective local search technique is embedded in the algorithm to enhance the exploitation ability. The performance of the proposed algorithm is evaluated by comparing its results to a commercial solver (CPLEX), a genetic algorithm and a simulated annealing algorithm. Computational experiments demonstrate the superiority of the HDDE algorithm in terms of solution quality, robustness and run time.

A hybrid discrete differential evolution algorithm to minimise total tardiness on identical parallel machines

This paper presents a hybrid discrete differential evolution (HDDE) algorithm to solve the Pm// problem. The coding and decoding scheme based on job permutation is applied in the algorithm. The algorithm employs several efficient heuristics in the initialisation phase and incorporates an insertion-based local search. To validate the proposed algorithm, computational experiments are conducted on a benchmark problem set from the literature. Computational results show that the HDDE algorithm outperforms the existing state-of-the-art algorithms for the Pm// problem.

Hybrid Discrete Differential Evolution Algorithm for Lot Splitting with Capacity Constraints in Flexible Job Scheduling

A two-level batch chromosome coding scheme is proposed to solve the lot splitting problem with equipment capacity constraints in flexible job shop scheduling, which includes a lot splitting chromosome and a lot scheduling chromosome. To balance global search and local exploration of the differential evolution algorithm, a hybrid discrete differential evolution algorithm (HDDE) is presented, in which the local strategy with dynamic random searching based on the critical path and a random mutation operator is developed. The performance of HDDE was experimented with 14 benchmark problems and the practical dye vat scheduling problem. The simulation results showed that the proposed algorithm has the strong global search capability and can effectively solve the practical lot splitting problems with equipment capacity constraints.

A Useful Metaheuristic for Dynamic Channel Assignment in Mobile Cellular Systems

The prime objective of a Channel Assignment Problem (CAP) is to assign appropriate number of required channels to each cell in a way to achieve both efficient frequency spectrum utilization and minimization of interference effects (by satisfying a number of channel reuse constraints). Dynamic Channel Assignment (DCA) assigns the channels to the cells dynamically according to traffic demand, and hence, can provide higher capacity (or lower call blocking probability), fidelity and quality of service than the fixed assignment schemes. Channel assignment algorithms are formulated as combinatorial optimization problems and are NP-hard. Devising a DCA, that is practical, efficient, and which can generate high quality assignments, is challenging. Though Metaheuristic Search techniques like Evolutionary Algorithms, Differential Evolution, Particle Swarm Optimization prove effective in the solution of Fixed Channel Assignment (FCA) problems but they still require high computational time and therefore may be inefficient for DCA. A number of approaches have been proposed for the solution of DCA problem but the high complexity of these proposed approaches makes them unsuitable/less efficient for practical use. Therefore, this paper presents an effective and efficient Hybrid Discrete Binary Differential Evolution Algorithm (HDB-DE) for the solution of DCA Problem.

A hybrid discrete differential evolution algorithm for the no-idle permutation flow shop scheduling problem with makespan criterion

This paper presents a hybrid discrete differential evolution (HDDE) algorithm for the no-idle permutation flow shop scheduling problem with makespan criterion, which is not so well studied. The no-idle condition requires that each machine must process jobs without any interruption from the start of processing the first job to the completion of processing the last job. A novel speed-up method based on network representation is proposed to evaluate the whole insert neighborhood of a job permutation and employed in HDDE, and moreover, an insert neighborhood local search is modified effectively in HDDE to balance global exploration and local exploitation. Experimental results and a thorough statistical analysis show that HDDE is superior to the existing state-of-the-art algorithms by a significant margin.

A multi-objective flow shop scheduling with resource-dependent processing times: trade-off between makespan and cost of resources

In traditional flow shop scheduling problems (FSSPs), the processing times are assumed to be pre-known and fixed parameters while in many practical environments, the processing times can be controlled by consumption of extra resources. In this paper, we propose resource-dependent processing times (RDPT) for permutation FSSP in which the processing time of a job depends on the amount of additional resources assigned to that job. To make a trade-off between makespan and required amount of resources, two conflict objective functions are considered: the minimisation of maximum completion time and the minimisation of total cost of resources. In order to solve the problem considered in this paper, a decomposition approach is suggested that strives to deal with the original model via two sub-problems: (i) sequencing problem; and (ii) resource allocation problem. A hybrid discrete differential evolution (HDDE) algorithm with an effective coordinate directions search and a variable neighbourhood search (VNS) are combined to solve two sub-problems. Furthermore, a statistical procedure is employed to adjust the significant parameters of the proposed HDDE and VNS algorithms. This procedure is based on the stepwise regression (SR) technique. The effectiveness of the suggested hybrid algorithm is investigated through a computational study and obtained results show the good performance of our approach with regard to the other algorithms.

An effective hybrid discrete differential evolution algorithm for the flow shop scheduling with intermediate buffers

In this paper, an effective hybrid discrete differential evolution (HDDE) algorithm is proposed to minimize the maximum completion time (makespan) for a flow shop scheduling problem with intermediate buffers located between two consecutive machines. Different from traditional differential evolution algorithms, the proposed HDDE algorithm adopted job permutation to represent individuals and applies job-permutation-based mutation and crossover operations to generate new candidate solutions. Moreover, a one-to-one selection scheme with probabilistic jumping is used to determine whether the candidates will become members of the target population in next generation. In addition, an efficient local search algorithm based on both insert and swap neighborhood structures is presented and embedded in the HDDE algorithm to enhance the algorithm’s local searching ability. Computational simulations and comparisons based on the well-known benchmark instances are provided. It shows that the proposed HDDE algorithm is not only capable to generate better results than the existing hybrid genetic algorithm and hybrid particle swarm optimization algorithm, but outperforms two recently proposed discrete differential evolution (DDE) algorithms as well. Especially, the HDDE algorithm is able to achieve excellent results for large-scale problems with up to 500 jobs and 20 machines.

A novel hybrid discrete differential evolution algorithm for blocking flow shop scheduling problems

This paper proposes a novel hybrid discrete differential evolution (HDDE) algorithm for solving blocking flow shop scheduling problems to minimize the maximum completion time (i.e. makespan). Firstly, in the algorithm, the individuals are represented as discrete job permutations, and new mutation and crossover operators are developed for this representation, so that the algorithm can directly work in the discrete domain. Secondly, a local search algorithm based on insert neighborhood structure is embedded in the algorithm to balance the exploration and exploitation by enhancing the local searching ability. In addition, a speed-up method to evaluate insert neighborhood is developed to improve the efficiency of the whole algorithm. Computational simulations and comparisons based on the well-known benchmark instances of Taillard [Benchmarks for basic scheduling problems. European Journal of Operational Research 1993;64:278–285], by treating them as blocking flow shop problem instances with makespan criterion, are provided. It is shown that the proposed HDDE algorithm not only generates better results than the existing tabu search (TS) and TS with multi-moves ( TS + M ) approaches proposed by Grabowski and Pempera [The permutation flow shop problem with blocking. A tabu search approach 2007;35:302–311], but also outperforms the hybrid differential evolution (HDE) algorithm developed by Qian et al. [An effective hybrid DE-based algorithm for multi-objective flow shop scheduling with limited buffers. Computers and operations research 2009;36(1):209–233] in terms of solution quality, robustness and search efficiency. Ultimately, 112 out of 120 best known solutions provided by Grabowski and Pempera [The permutation flow shop problem with blocking. A tabu search approach 2007;35:302–311] and Ronconi [A branch-and-bound algorithm to minimize the makespan in a flowshop problem with blocking. Annals of Operations Research 2005;138(1):53–65] are further improved by the proposed HDDE algorithm.