Small-scale Instances Research Articles

Unrelated Parallel Machine Scheduling with Job Splitting, Setup Time, Learning Effect, Processing Cost and Machine Eligibility

This work investigates an unrelated parallel machine scheduling problem in the shared manufacturing environment. Based on practical production complexity, five job and machine-related factors, including job splitting, setup time, learning effect, processing cost and machine eligibility constraint, are integrated into the considered problem. Parallel machines with uniform speed but non-identical processing capabilities are shared on a sharing service platform, and jobs with different types can only be processed by the machines with matching eligibilities. The platform pays an amount of processing cost for using any machine to process the jobs. To balance the processing cost paid and the satisfaction of customers, we aim to minimize the weighted sum of total processing cost and total completion time of jobs in the considered problem. We establish a mixed integer linear programming model, and provide a lower bound by relaxing the machine eligibility constraint. The CPLEX solver is employed to generate optimal solutions for small-scale instances. For large-scale instances, we propose an efficient heuristic algorithm. Experimental results demonstrate that for various instance settings, the proposed algorithm can always produce near optimal solutions. We further present several managerial insights for the shared manufacturing platform.

Mixed-model assembly line balancing problem considering preventive maintenance scenarios: MILP model and cooperative co-evolutionary algorithm

Considering preventive maintenance (PM) scenarios in assembly line balancing (ALB) problem has been proven to be an effective way to promote line efficiency. However, previous research only focused on the single-model assembly line and ignored the mixed-model assembly line, resulting in the line cannot meet the growing customization needs of customers. This paper addresses the mixed-model ALB considering PM scenarios (MALB_PMs). A mixed-integer mathematical formulation is proposed to optimize the cycle time and task alteration. The cooperative co-evolutionary algorithm is introduced to simplify the large-scaled cases via the powerful divide-and-conquer architecture and is enhanced with four improvements. An archive is generated to save complete solutions with better performance and evaluate the fitness of solutions. A mixed-model variable step-size decoding method is designed to speed up the decoding process of the algorithm. One inter-population crossover operator is designed to enhance the communication among sub-problems. Four objective-oriented neighbor search operators are proposed to promote the convergence performance of the algorithm. Finally, three small-scale instances are employed to illustrate the application of the mathematical model, and 39 cases are designed to test the performance of the developed algorithm. Experiment results demonstrate that the proposed mathematical formulation can obtain the Pareto solutions of small-scaled instances; The developed algorithm outperforms other algorithms on three criteria; The Pareto front obtained by this algorithm is closer to the True Pareto front.

Unrelated parallel machine scheduling with processing cost, machine eligibility and order splitting

Under the background of the emerging of shared manufacturing economics, this work addresses a new production order scheduling problem on unrelated parallel machines. Customer orders with release times are of various types depending on their specific product demands. Unrelated machines may be rented for processing orders via one cloud manufacturing service platform. It occurs a uniform processing cost once any machine is rented (via contract) for a given length time duration to process the orders. Each machine is generally able to process some but not all types of orders, i.e., machine eligibility is considered. Orders can be split into sub-orders and processed on their eligible machines simultaneously. For the objective of minimizing the weighted sum of total completion time of orders and total processing cost of machines being used, we establish a mixed integer linear programming model. We provide a lower bound of the considered problem by constraint relaxation, and present the pseudocode of an approach to obtain the lower bound. CPLEX is employed to generate optimal solutions for small-scale instances. For large-scale instances, two heuristic algorithms named Type-Based Greedy and Improved Differential Evolution are developed. The former algorithm selects a smallest set of machines to process the jobs and makes use of job splitting as much as possible, while the latter one is to acquire a best local optimal solution via finite times random global search in the feasible region. Computational experiments are carried out to demonstrate the efficiency and effectiveness of the proposed heuristics.

Solving the energy-efficient Robotic Mixed-Model Assembly Line balancing problem using a Memory-Based Cuckoo Search Algorithm

Minimizing energy consumption is an important issue in robotic assembly lines where a set of robots are assigned to a set of workstations to perform different tasks. When it is planned to assemble several models of one product in the same robotic assembly line, the minimization of energy consumption becomes more difficult since the best assignment of tasks and robots to workstations must be found, taking into consideration all models. The authors cannot find in the literature a work that aims to minimize energy consumption in robotic assembly lines that produce several models with one configuration. Furthermore, the introduction of the heterogeneity of models and robots makes the problem more complex and hard, even for small-scale instances, and for this reason, the authors propose in this paper a Memory-Based Cuckoo Search Algorithm (MBCSA) to tackle this problem. The principle of memory is used in this new Cuckoo Search Algorithm in order to escape from the local optima and discover new search zones. Six problems of different sizes are generated and solved by the proposed MBCSA, and to evaluate its performance, two comparisons are made with two meta-heuristics, the genetic algorithm and another version of the cuckoo search algorithm. Obtained results show that this new version of the Cuckoo search algorithm is promising and can obtain good solutions for problems of different sizes.

NukCP: An Improved Local Search Algorithm for Maximum k-Club Problem

The maximum k-club problem (MkCP) is an important clique relaxation problem with wide applications. Previous MkCP algorithms only work on small-scale instances and are not applicable for large-scale instances. For solving instances with different scales, this paper develops an efficient local search algorithm named NukCP for the MkCP which mainly includes two novel ideas. First, we propose a dynamic reduction strategy, which makes a good balance between the time efficiency and the precision effectiveness of the upper bound calculation. Second, a stratified threshold configuration checking strategy is designed by giving different priorities for the neighborhood in the different levels. Experiments on a broad range of different scale instances show that NukCP significantly outperforms the state-of-the-art MkCP algorithms on most instances.

Line-haul feeder location-routeing problem: mathematical model and heuristic algorithm

This study proposes a mathematical formulation and solution approach for a novel extension of the location-routeing problem (LRP), namely line-haul feeder LRP (LFLRP), where large vehicles (trucks) are synchronised with small vehicles (motorcycles) throughout delivery process. Customers are visited by site-dependent vehicles such that those not accessible by trucks must be served by motorcycles. The LFLRP is formulated as a mixed-integer linear programming model, and two efficient heuristic algorithms called EHA and Enhanced-EHA are developed to solve the problem. Experimental results show that the proposed algorithms can provide near-optimal solutions for 18 randomly generated small-scale LFLRP test instances and best-known solutions for 12 out of 19 large-scale standard LRP test instances in reasonable computation time. A cost-benefit analysis also indicates that the LFLRP model can considerably reduce total costs compared to equivalent standard LRP formulations. To provide managerial insights, a case study and sensitivity analysis of key parameters are conducted.

Modelling an Efficient Hybrid Optimizer for Handling Vehicle Routing Problem

Vehicle Routing Problem (VRP) like total routing distance, number of serve provisioning vehicles, and vehicles' waiting time are determined as the multi-objective constraints. Investigators pretend to handle these multi-constraint issues with the time window and fail to attain a prominent solution. Thus, there is a need for a global multi-objective vehicle routing solution. Here, a novel Particle Positioning Particle Swarm Optimization ( ) approach is designed to predict the robust route with the elimination of non-linearity measures. The linearity measure includes the movement of the vehicles, service time, and status of the move towards a particular direction. The lack of exploration and exploitation conditions during optimization is addressed with the inclusion of Grey Wolf Optimization (GWO). Therefore, the models attain a global solution with the least error rate. Simulation is done in MATLAB 2016b environment, and the experimental outcomes are compared with various approaches in large-scale and small-scale instances. The model intends to attain robustness and stability towards the measure in a linear manner. The model's time consumption and computational complexity are reduced with the adoption of a global routing-based optimization approach.

A Matheuristic Approach for the No-Wait Flowshop Scheduling Problem with Makespan Criterion

The No-wait Flowshop Scheduling Problem (NWFSP) has always been a research hotspot because of its importance in various industries. This paper uses a matheuristic approach that combines exact and heuristic algorithms to solve it with the objective to minimize the makespan. Firstly, according to the symmetry characteristics in NWFSP, a local search method is designed, where the first job and the last job in the symmetrical position remain unchanged, and then, a three-level neighborhood division method and the corresponding rapid evaluation method at each level are given. The two proposed heuristic algorithms are built on them, which can effectively avoid al-ready searched areas, so as to quickly obtain the local optimal solutions, and even directly obtain the optimal solutions for small-scale instances. Secondly, using the equivalence of this problem and the Asymmetric Traveling Salesman Problem (ATSP), an exact method for solving NWFSP is constructed. Importing the results of the heuristics into the model, the efficiency of the Mil-ler-Tucker-Zemlin (MTZ) model for solving small-scale NWFSP can be improved. Thirdly, the matheuristic algorithm is used to test 141 instances of the Tailard and Reeves benchmarks, and each optimal solution can be obtained within 134 s, which verifies the stability and effectiveness of the algorithm.

A knowledge-driven constructive heuristic algorithm for the distributed assembly blocking flow shop scheduling problem

The distributed flow shop scheduling problem (DFSP) has become widespread due to the increasing advantages of multi-factories manufacturing in recent years. The distributed assembly blocking flow shop scheduling problem (DABFSP), which aims at minimizing the maximum assembly completion time, is considered in this paper. A knowledge-driven constructive heuristic (KDH) algorithm is proposed to address the above problem. Three different kinds of neighborhood knowledge are refined by analyzing the characteristic of the problem and quantified to design the KDH algorithm. The jobs belonging to the same production are assigned to the different factories to advance the starting time of assembly, which is quantified as knowledge 1. The assembly sequence of the product is determined according to the processing sequence of the job in the processing factory, which is defined as knowledge 2. The jobs belonging to the same product are distributed together in each processing factory, which is quantified as knowledge 3. The performance of the KDH algorithm is verified on the benchmark instance, which comprises 900 small-scale instances and 810 large-scale instances. The experimental results demonstrate that the KDH algorithm is superior to state-of-the-art algorithms in the aspect of addressing DABFSP.

Discretization-Strategy-Based Solution for Berth Allocation and Quay Crane Assignment Problem

The continuous berth allocation and quay crane assignment problem considers the size of berths and ships, the number of quay cranes, the dynamic ships and non-crossing constraints of quay cranes. In this work, a mixed-integer linear programming model of this problem is established, aiming at minimizing the total stay time and delay penalty of ships. To solve the model, the continuous berth is separated into discrete segments via a proposed discretization strategy. Thereafter, a large neighborhood search algorithm composed of the random removal operator and relaxed sorting-based insertion operator and a backtracking comparison-based constraint repair strategy are proposed. The effectiveness of the model and algorithm presented is verified via real-life instances with different characteristics, and the performances of different combinations of removal operators and insertion operators in the large neighborhood search algorithmic framework are analyzed. Numerical results show that the large neighborhood search algorithm can optimally solve the small-scale instances in a reasonable time. Meanwhile, the results of large-scale instances show that the large neighborhood search algorithm incorporating the discretization strategy is more efficient than other genetic algorithms based on continuous optimization. With the proposed approach, high-quality berth and quay crane allocation results can be obtained efficiently.

An exact method for job sequencing in a mixed-model assembly line considering feeding lines based on the Benders decomposition approach

ABSTRACT The study proposes an exact method based on the Benders decomposition approach to solve the sequencing problem of the mixed-model assembly line considering feeding lines. A mathematical model is presented and linearized that is capable of solving the small-size scales of the problem. Since the problem is well known as a strongly NP-hard problem, appropriate methods can improve the effectiveness of the outcomes of the model. Therefore, we introduce a Benders decomposition method, which can solve the proposed problem on the medium and large scales. Moreover, a proper accelerator is presented to enhance the performance of the proposed method and to reduce computational time. The outcomes show that the proposed method can provide solutions with a maximum of 4.47% deviation from the optimal for small-scale instances. The result indicates the success of this exact method in solving the problem with different dimensions. In addition, comparing results emphasized that the accelerator used can reduce iterations up to 24% to provide the final solution.

Influence of the Linear Layer on the Algebraic Degree in SP-Networks

We consider SPN schemes, i.e., schemes whose non-linear layer is defined as the parallel application of t ≥ 1 independent S-Boxes over F2n and whose linear layer is defined by the multiplication with a (n · t) × (n · t) matrix over F2. Even if the algebraic representation of a scheme depends on all its components, upper bounds on the growth of the algebraic degree in the literature usually only consider the details of the non-linear layer. Hence a natural question arises: (how) do the details of the linear layer influence the growth of the algebraic degree? We show that the linear layer plays a crucial role in the growth of the algebraic degree and present a new upper bound on the algebraic degree in SP-networks. As main results, we prove that in the case of low-degree round functions with large S-Boxes: (a) an initial exponential growth of the algebraic degree can be followed by a linear growth until the maximum algebraic degree is reached; (b) the rate of the linear growth is proportional to the degree of the linear layer over Ft2n. Besides providing a theoretical insight, our analysis is particularly relevant for assessing the security of the security of cryptographic permutations designed to be competitive in applications like MPC, FHE, SNARKs, and STARKs, including permutations based on the Hades design strategy. We have verified our findings on small-scale instances and we have compared them against the currently best results in the literature, showing a substantial improvement of upper bounds on the algebraic degree in case of low-degree round functions with large S-Boxes.

Minimizing the sum of makespan on multi-agent single-machine scheduling with release dates

Competitive scheduling problems occur in integrated-services packet-switched networks, in which different applications compete for the same resource. Requests of each application arrive over time and contain multiple packets. This process can be described as a multi-agent single-machine scheduling (MSS) problem with release dates, where several packets (jobs) share a common network (processor) but are maintained by several competitive applications (agents) that optimize their criteria. The objective is to minimize the sum of makespans belonging to several agents individually. The NP-hardness of the model indicates that it cannot be optimally solved in polynomial time. For small-scale instances, an effective branch and bound (B&B) algorithm integrated with an elaborately designed pruning rule and a lower bound is developed to achieve exact solutions. Given the quality of service requirements and the periodical maintenance of networks, this problem is generalized to the weighted and periodic maintenance versions, respectively. For the weighted version, a hybrid discrete artificial bee colony (HDABC) algorithm integrated with effective improvement strategies is developed to achieve satisfactory solutions for medium-scale instances. For the periodic maintenance version, a deep reinforcement learning (DRL) method is introduced to obtain high-quality solutions in dynamic situation. Results of computational evaluation demonstrate the effectiveness of the proposed methods.

Collaborative multicenter vehicle routing problem with time windows and mixed deliveries and pickups

This study focuses on the collaborative multicenter vehicle routing problem with time windows and mixed deliveries and pickups (CMVRPTWMDP), which is a variant of the vehicle routing problem (VRP) with mixed deliveries and pickups, and VRP with simultaneous deliveries and pickups and time windows. Collaboration and transportation resource sharing are adopted to optimize vehicle routes in the CMVRPTWMDP, to integrate the delivery and pickup services with time windows, and to construct open–closed mixed vehicle routes. First, the CMVRPTWMDP is formulated as a mixed-integer programming model to minimize logistics operating costs. The effect of transportation resource sharing on reducing the number of needed vehicles and the maintenance cost is considered in the model formulation. Second, a two-stage hybrid algorithm combining customer clustering and vehicle routing optimization is designed to solve the CMVRPTWMDP. An improved 3D k-means clustering algorithm based on space–time distances and the customer demand is proposed to reassign customers to logistics facilities (e.g., delivery or pickup centers). Furthermore, a hybrid heuristic algorithm that combines the genetic algorithm (GA) and particle swarm optimization (PSO) algorithm, called GA–PSO, is designed to optimize the vehicle routes. A coordination operator between GA and PSO is designed to allow particles and chromosomes to interact, increasing the diversity of particle swarms and the possibility of finding a feasible solution. Third, the performance and effectiveness of the proposed approach are tested by comparing them with the CPLEX solver using 30 small-scale instances and other existing algorithms using 25 benchmark instances. Fourth, the minimum costs-remaining savings (MCRS) model is adopted to design a fair and reasonable profit allocation scheme for participants in the collaborative alliance and maintain alliance stability. Finally, the optimization results of a real-world case study from Chongqing, China, show that transportation resource misuse and logistics operating costs are significantly reduced, demonstrating the proposed approach’s effectiveness and applicability. This study provides insights for logistics enterprises and transportation departments on effectively allocating and utilizing the transportation resources and optimizing the local logistics network.

A branch-and-bound approach for AGV dispatching and routing problems in automated container terminals

The efficiency of automated container terminals primarily depends on the automated guided vehicle (AGV) scheduling scheme. This paper investigates the AGV dispatching and routing problem with multiple bidirectional paths to generate conflict-free routes. A mixed-integer programming (MIP) model is formulated to minimize the completion time of all jobs (i.e., minimize the makespan). A tailored branch-and-bound (B&B) algorithm is developed to solve the problem within a reasonable amount of time, where the B&B process is used to obtain job assignments and job sequences, and a heuristic algorithm is proposed to generate conflict-free routes. To expedite the proposed algorithm, some accelerating techniques are designed in view of the characteristics of the problem. Computational experiments indicate that the proposed algorithm can obtain near-optimal solutions in small-scale instances, and in large-scale instances, the B&B algorithm significantly outperforms the port scheduling strategies. The proposed algorithm can be applied to real-world cases and dynamic cases, and a two-stage greedy heuristic algorithm is also developed to obtain a satisfactory solution in a short amount of time. Some managerial insights into AGV scheduling are offered to guide terminal operations in this study.

Two-echelon vehicle routing problem with time windows and simultaneous pickup and delivery

This paper proposes a tabu search algorithm for the two-echelon vehicle routing problem with time windows and simultaneous pickup and delivery (2E-VRPTWSPD), which is a new variant of the two-echelon vehicle routing problem. 2E-VRPTWSPD involves three stages of routing: (1) the first-echelon vehicles start from the depot to deliver cargoes to satellites; (2) the second-echelon vehicles start from satellites to serve customers within time windows in a simultaneously pickup and delivery manner and finally return to their satellites with pickup cargoes; (3) the first-echelon vehicles start from the depot to collect cargoes on satellites. To solve this problem, we formulate it with a mathematical model. Then, we implement a variable neighborhood tabu search algorithm with a tailored solution representation to solve large-scale instances. Dummy satellites time windows are applied in our algorithm to speed up the search. Finally, we generate two benchmark instance sets to analyze the performance of our algorithm. Computational results show that our algorithm can obtain the optimal results for 10 out of 11 small-scale instances and produce promising solutions for 200-customer instances within a few minutes. Additional experiments indicate that the usage of dummy satellite time windows can save 19% computation time on average.

On Achilles Heel of some optical network designs and performance comparisons

This non-conventional paper represents the first attempt to uncover a possible vulnerability in some proposals for optical network designs and performance comparisons. While optical network designs and planning lie at the heart of achieving fiber capacity efficiency and/or operational efficiency, its combinatorial nature makes it computationally hard to reach optimal solutions for realistic scenarios. As a consequence, the well-established way that have been taken for granted by not-so-small number of research papers is that an optimization model based on mixed integer linear programming (MILP) formulation is first proposed and then due to the intractability of such combinatorial optimization model, a heuristic algorithm is offered as an approximation. The solution-quality comparison between the MILP and heuristic is then carried out on small-scale instances including topologies and traffic tests to verify the efficacy of the proposed heuristic. Next such allegedly verified heuristic are used for optical network designs of realistic scenarios. This approach may nevertheless leave a critical vulnerability as there is no guarantee that one performs well in small tests will generalize adequately for large-scale cases, a common pitfall widely referred as the peril of extrapolation and/or overfitting. Besides, it is not uncommon that in some research works, for benchmarking purpose, the comparison between a new design proposal whose performance is obtained from on one heuristic and a reference design based on another heuristic is carried out. As the consequence of lacking solution quality check, such performance comparison relied merely on heuristic solutions may be equally vulnerable, resulting to possibly unreliable conclusions. In this work, we pinpoint those issues and provide a realistic case study to highlight and demonstrate the impact of such vulnerabilities.

A MATHEMATICAL MODEL AND SOLUTION METHOD FOR THE BERTH ALLOCATION PROBLEM WITH VARIABLE HANDLING TIME AND CONTINUOUS TIME HORIZON

In this paper, we present the integration of two problems related to the operations in a port terminal: the Berth Allocation Problem (BAP) integrated with the Machine Assignment Problem. We present a mixed-integer linear programming (MILP) formulation, capable of assigning and scheduling incoming vessels to berthing positions and the assignment of machines for handling the vessels. The machines can be quay cranes, mobile cranes, straddle carriers, forklifts, trucks, and any other machine. The problem aims to minimize the waiting time plus the handling time of the vessels. To solve the problem, we developed a heuristic algorithm, capable of solving a problem instance in seconds. To compare the results, we generate several instance problems based on real data and solve them with our MILP formulation implemented in a solver, our heuristic, and a First In First Out (FIFO) algorithm. The solver was able to find solutions only in small-scale instances, and the heuristic was able to find good solutions for all instances.

Bi-objective optimization of identical parallel machine scheduling with flexible maintenance and job release times

This paper investigates an identical parallel machine scheduling problem with flexible maintenance and job release times and attempts to optimize two objectives: the minimization of the makespan and total tardiness simultaneously. A mixed-integer programming (MIP) model for solving small-scale instances is presented first, and then a modified NSGA-Ⅱ (M-NSGA-Ⅱ) algorithm is constructed for solving medium- and large-scale instances by incorporating several strategies. These strategies include: (ⅰ) the proposal of a decoding method based on dynamic programming, (ⅱ) the design of dynamic probability crossover and mutation operators, and (ⅲ) the presentation of neighborhood search method. The parameters of the proposed algorithm are optimized by the Taguchi method. Three scales of problems, including 52 instances, are generated to compare the performance of different optimization methods. The computational results demonstrate that the M-NSGA-Ⅱ algorithm obviously outperforms the original NSGA-II algorithm when solving medium- and large-scale instances, although the time taken to solve the instances is slightly longer.

An Adaptive Job Shop Scheduler Using Multilevel Convolutional Neural Network and Iterative Local Search

This manuscript proposed an effective hybrid method based on multi-level convolutional neural network (ML-CNN) and iterative local search (ILS) to solve job shop scheduling problems (JSSP) with small-scale training samples and less time. In the proposed method, ML-CNN is proposed to find the global path of JSSP instance from the genetic algorithm (GA); ML-CNN learned global path is fed into ILS to search for the best local path, it is the key to attach excellent adaptivity. In order to find the global path from optimal solutions, the proposed ML-CNN treated the JSSP as some sub-classification tasks first. Each subclass corresponding to one sub-operation prioritizes a particular machine according to the production environment. Significantly, the proposed ML-CNN designed two-level inputs to represent production statutes. The detailed-level input channel records fourteen detailed statutes, while the system-level input channel records four systematic statutes. Two-level inputs are fed into one dimensional (1-D) CNN to extract rich hidden features to predict the priority of each suboperation using a support vector machine (SVM) classifier. At last, the global path (priority sequences) could be obtained, which is encoded as the input of ILS to find the best local path. The authors trained and tested the proposed method on 82 public JSSP instances. The results indicated that the proposed method could obtain optimal solutions for small-scale instances and outperform others regarding makespan and computation time for large-scale JSSP instances.