Minimizing Flow Time Research Articles

Matheuristic and learning-oriented multi-objective artificial bee colony algorithm for energy-aware flexible assembly job shop scheduling problem

With the increase of mass customization, flexible job shop scheduling problem considering assembly stage has widely existed in many manufacturing industries, such as die-casting mould factories. This problem is to find a reasonable machine assignment and operation sequence both in fabrication and assembly stages and simultaneously maximize production efficiency. In reality, energy shortages and environmental pollution have given an impetus to the development of energy-aware production scheduling problems. In this study, we address an energy-aware flexible assembly job shop scheduling problem (EFAJSP) with the objectives of minimizing flow time and energy consumption and first develop a mixed-integer linear programming (MILP) model to solve EFAJSP problem. Then, the model-specific characteristics are extracted and applied to a matheuristic decoding method for exploring the Pareto optimal solution. Due to the complexity of EFAJSP problem, a matheuristic and learning-oriented multi-objective artificial bee colony algorithm (MLABC), which combines the advantages of mathematical programming, reinforcement learning and meta-heuristic algorithm, is proposed. In addition, an initialization, destruction/construction operator and population update operator are proposed and work together to improve the exploration and exploitation performance of the proposed MLABC. Finally, numerical experimental results demonstrate the effectiveness of the proposed MILP model and the superiority of the MLABC over other algorithms in the literature.

Flow-Time Minimization for Timely Data Stream Processing in UAV-Aided Mobile Edge Computing

Unmanned Aerial Vehicle (UAV) has gained increasing attentions by both academic and industrial communities, due to its flexible deployment and efficient line-of-sight communication. Recently, UAVs equipped with base stations have been envisioned as a key technology to provide 5G network services for mobile users. In this paper, we provide timely services on the data streams of mobile users in a UAV-aided Mobile Edge Computing (MEC) network, in which each UAV is equipped with a 5G small-cell base station for communication and data processing. Specifically, we first formulate a flow-time minimization problem by jointly caching services and offloading tasks of mobile users to the UAV-aided MEC with the aim to minimize the flow-time, where the flow-time of a user request is referred to the time duration from the request issuing time point to its completion point, subject to resource and energy capacity on each UAV. We then propose a spatial-temporal learning optimization framework. We also devise an online algorithm with a competitive ratio for the problem based upon the framework, by leveraging the round-robin scheduling and dual fitting techniques. Finally, we evaluate the performance of the proposed algorithms through experimental simulation. The simulation results demonstrated that the proposed algorithms outperform their comparison counterparts, by reducing the flow-time no less than 19% on average.

Numerical modeling of the funnel multiphysical flow of fresh self-compacting concrete considering proportionate heterogeneity of aggregates

Filling ability is one of the prominent rheological properties of the self-compacting concrete (SCC), which has been studied in this research work deploying the functional behavior of the concrete through the studied funnel apparatus using the coupled ANSYS-SPH interface. Seven (7) model cases were studied and optimized. The aim of this numerical study is to propose a more sustainable mix of coarse and fine aggregates proportion that allows for most minimum flow time to enhance a more efficient filling of forms during concreting. The maximum size of the coarse aggregates considered is 20 mm and that of the fine aggregates is below 4 mm. The Bingham model properties for the multiphysics (SPH)-ANSYS models’ simulation are; viscosity = 20 ≤ μ ≤ 100 and the yield stress = 50 ≤τ0≤200\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\le {\ au }_{0}\\le 200$$\\end{document}, standard flow time, t (s) ranges; 6 ≤ t ≤ 25 and the funnel volume is 12 L. The minimum boundary flow time, which represents the time it takes for the SCC to completely flow through a specified distance, typically measured in seconds was modeled for in the seven (7) model cases. The second case with 40% coarse mixed with 60% fine completely flowed out in 16 s, thus fulfilling the minimum flow time. This minimum flow time was considered alongside other relevant parameters and tests, such as slump flow, passing ability, segregation resistance, and rheological properties (stresses), to comprehensively assess the filling ability of SCC in this model. By considering these factors and the optimized mix (40%C + 60%F:16s), engineers and researchers can optimize the SCC mix design to achieve the desired flowability and filling performance for their specific construction applications. The multiphase optimized mix was further simulated using the coupled interface of the ANSYS-SPH platform operating with the CFX command at air temperature of 25 °C. The results show energy reduction jump at the optimized flow time. Ideally, the mix, 40%C + 60%F:16s has been proposed as the mix with the most efficient flow to achieve the filling ability for sustainable structural concrete construction.

Effective Two-Phase Heuristic and Lower Bounds for Multi-Stage Flexible Flow Shop Scheduling Problem with Unloading Times

This paper addresses the flexible flow shop scheduling problem with unloading operations, which commonly occurs in modern manufacturing processes like sand casting. Although only a few related works have been proposed in the literature, the significance of this problem motivates the need for efficient algorithms and the exploration of new properties. One interesting property established is the symmetry of the problem, where scheduling from the first stage to the last or vice versa yields the same optimal solution. This property enhances solution quality. Considering the problem’s theoretical complexity as strongly NP-Hard, approximate solutions are preferable, especially for medium and large-scale instances. To address this, a new two-phase heuristic is proposed, consisting of a constructive phase and an improvement phase. This heuristic builds upon an existing efficient heuristic for the parallel machine-scheduling problem and extends it to incorporate unloading times efficiently. The selection of the two-phase heuristic is justified by its ability to generate high-quality schedules at each stage. Moreover, new efficient lower bounds based on estimating minimum idle time in each stage are presented, utilizing the polynomial parallel machine-scheduling problem with flow time minimization in the previous stage. These lower bounds contribute to assessing the performance of the two-phase heuristic over the relative gap performance measure. Extensive experiments are conducted on benchmark test problems, demonstrating the effectiveness of the proposed algorithms. The results indicate an average computation time of 9.92 s and a mean relative gap of only 2.80% for several jobs up to 200 and several stages up to 10.

Hardness of flow time minimization in a crossdock with a single door and asymmetric handover relations

We study the problem of sequencing trucks subject to handover relations. The objective is to minimize the total time pallets spend at the terminal. It has been shown that the problem is strongly NP-hard for two doors or with unrelated (un)loading durations. We show that it is strongly NP-hard even for a single door and (un)loading durations of trucks being proportional to the number of pallets (un)loaded.

Quickest Transshipment in the Prioritized Evacuation Network

Flow maximization, time minimization, and cost minimization are three main aspects of mathematical optimization problems. The evacuation planning problems are about flow maximization and/or time minimization problems in different dynamic evacuation networks. The quickest transshipment problem in such a network is to send exactly the right amount of flow out of each source and into each sink in the minimum overall time. In evacuation planning problems, the term flow stands for either the evacuees or the evacuees carrying vehicles. Here, we use the quickest transshipment strategy in a prioritized evacuation network. It consists of a collection and an assignment sub-network as the primary and secondary sub-networks, respectively. Pick-up locations are prioritized in the collection network. By treating such pick-up locations as sources, the available set of transit buses is assigned in the assignment sub-network to shift the evacuees to the sinks to achieve the quickest transshipment. Such an evacuation planning strategy is better suited for the simultaneous collection, assignment, and evacuation process in the prioritized evacuation network.

Sensitivity Analysis for the Single-Machine Preemptive Scheduling Problem of Minimizing Flow Time

Sensitivity Analysis for the Single-Machine Preemptive Scheduling Problem of Minimizing Flow Time

Flow simulation of self-consolidating concrete through V-funnel for sustainable buildings

Self-consolidating concrete (SCC) is one of the trending low-yield stress material innovations of the new age building industry due to its ability to flow through heavily reinforced structural members without segregation and without losing its moderate viscosity. In this research paper, a V-funnel simulation has been developed for the flow time to establish its validity with allowable design conditions according to the European standard. The Bernoulli’s equation and the continuity flow state conditions were adopted for the V-funnel of 515 mm upper width, 75 mm thick, and vertical dimensions (depth) of 450 mm and 150 mm for the V-section and funnel duct (75 mm × 65 mm) respectively. Concrete shear stress with the funnel wall was considered as a factor of concrete unit weight (ρ) and frictional force under downward velocity with respect to variational height (dh). The result of the V-funnel simulation for the flow time shows that the kinematic viscosity (η) of the concrete is bound within the limits of 0 and 1/64. This implies that ηmin ≈ 0 (no friction with walls), and the minimum flow time (Tmin) becomes 8.7 sec while minimum shear stress is zero (τmin ≈ 0 N/m2). However, for ηmax ≈ 1/64 (maximum friction with walls of τmax τ ρ/64 N/m2 is attained) and Tmax becomes 18.9 sec. These values fall within the flow time after 10 seconds of mixing, ranging between 8 and 10 seconds, and the flow time after 5 minutes of mixing of 11 to 25 seconds, according to the European Guidelines for self-consolidating concrete. These results for the flow simulation of the concrete placement during construction, are also consistent with the United Nations sustainable development goals (SDGs) for technological innovation, infrastructure, and sustainable cities.

Distributionally robust scheduling algorithms for total flow time minimization on parallel machines using norm regularizations

In this paper, we study a distributionally robust parallel machines scheduling problem, minimizing the total flow time criterion. The distribution of uncertain processing times is subject to ambiguity belonging to a set of distributions with constrained mean and covariance. We show that the problem can be cast as a deterministic optimization problem, with the objective function composed of an expectation and a regularization term given as an ℓp norm. The main question we ask and answer is whether the particular choice of the used ℓp norm affects the computational complexity of the problem and the robustness of its solution. We prove that if durations of the jobs are independent, the solution in terms of any ℓp norm can be solved in a pseudopolynomial time, by the reduction to a non-linear bipartite matching problem. We also show an efficient, polynomial-time algorithm for ℓ1 case. Furthermore, for instances with dependent durations of the jobs, we propose computationally efficient formulation and an algorithm that uses ℓ1 norm. Moreover, we identify a class of covariance matrices admitting a faster, polynomial-time algorithm. The computational experiments show that the proposed algorithms provide solutions with a similar quality to the existing algorithms while having significantly better computational complexities.

Complexity of flow time minimization in a crossdock truck scheduling problem with asymmetric handover relations

We address a novel truck scheduling problem arising in crossdocking logistics, in which inbound trucks carry items (pallets) which must be sorted and loaded onto outbound trucks. We minimize the utilisation of the warehouse by focusing on the synchronisation between the different related trucks. The problem is to assign the trucks to the doors of the warehouse and sequence them, in order to minimize the total time spent in the system by the pallets. We discuss the complexity of the problem, showing that even with a single door the problem is NP-hard in general, and discuss some special cases.

Iterative beam search algorithms for the permutation flowshop

We study an iterative beam search algorithm for the permutation flowshop (makespan and flowtime minimization). This algorithm combines branching strategies inspired by recent branch-and-bounds and a guidance strategy inspired by the LR heuristic. It obtains competitive results on large instances compared to the state-of-the-art algorithms, reports many new-best-so-far solutions on the VFR benchmark (makespan minimization) and the Taillard benchmark (flowtime minimization) without using any NEH-based branching or iterative-greedy strategy. The source code is available at: https://github.com/librallu/dogs-pfsp.

Optimal Job Scheduling With Resource Packing for Heterogeneous Servers

Jobs in modern computing clusters have highly diverse processing duration and heterogeneous resource requirements. In this paper, we consider the problem of job scheduling for a computing cluster comprised of multiple servers with heterogeneous computation resources, while taking the different resource demands of the jobs into account. Our focus is to achieve a low overall job response time for the system (which is also referred to as the job flowtime) while providing fairness between small and large jobs. Since the job flowtime minimization problem under multiple (even homogeneous) servers are known to be NP-hard, we propose an approximation algorithm to tackle the original online scheduling problem by adopting the recently-proposed notion of fractional job flowtime as a surrogate objective for minimization. For the general online job arrival case with multi-dimensional resource requirements, we apply Online Convex Optimization (OCO) techniques to design the corresponding scheduling algorithm with performance guarantees. In the single-dimensional resource setting, we show that the dynamic fit of the online version of our approximate algorithm grows only sublinearly with respect to time and derive a bound for its dynamic regret when comparing to its offline counterpart. While the baseline version of our proposed scheduling algorithm assumes the possibilities of job preemption and job migration across different servers, we show that the extent of job preemption and migration can be well controlled by augmenting the objective function with the corresponding switching costs.

Minimum Clearance Time on the Prioritized Integrated Evacuation Network

The evacuation planning problem can be viewed as different variants of dynamic flow maximization and time minimization problems. An optimal solution to the latter problem sends a given amount of flow from disaster zones to safe zones in minimum time. We solve this problem on an embedded integrated network of a prioritized primary and a bus-routed secondary sub-networks. For a lexicographically maximum (lex-max) dynamic flow problem, we are given a time horizon and a prioritized network, where we need a feasible dynamic flow that lexicographically maximizes the flow amount leaving each terminal respecting the priority. Here, we use the quickest transshipment partial arc reversal strategy to collect the evacuees in minimum time from the disaster zones to the pickup locations of the primary sub-network. By treating such pickup locations as sources, the available set of transit-buses is assigned in the secondary sub-network to shift the evacuees finally to the sinks on the first-come-first-serve basis. This novel approach proposed here is better suited for the simultaneous flow of evacuees with minimum waiting delay at such pickup locations in the integrated evacuation network topology. The lane reversal strategy significantly reduces the evacuation time, whereas reversing them only partially has an additional benefit that the unused road capacities can be used for supplying emergency logistics and allocating facilities as well.

A population-based iterated greedy algorithm for no-wait job shop scheduling with total flow time criterion

The no-wait job shop where no waiting time is allowed between two successive operations of a job has a strong industrial background, especially in steel-making industry and concrete manufacturing. This study formulates the no-wait job shop problem with a total flow time criterion based on time difference and decomposes the problem into timetabling and sequencing subproblems. Several timetabling methods are designed for the total flow time criterion to generate a sequence timetable. By adopting favourable features of the iterated greedy algorithm, the population-based iterated greedy (PBIG) algorithm for the sequencing subproblem is proposed. The individuals in the population evolve by means of a destruction and construction perturbator and an insertion-based local search. In each iteration, a tournament selection is designed to replace a relatively worse solution. In order to generate starting solutions with a certain quality and diversity, the Nawaz–Enscore–Ham-based heuristics for flow shop scheduling are extended in no-wait job shops. In computational experiments based on well-known benchmark instances, timetabling methods are investigated, and it is shown that the left timetabling is superior to other timetabling methods for the total flow time minimisation. Computational results also show that the proposed algorithm significantly outperforms several state-of-the-art metaheuristics, and it could be applicable to practical production environment.

Metaheuristic algorithms for the hybrid flowshop scheduling problem

The hybrid flowshop scheduling problem (HFSP) has been widely studied in the literature, as it has many real-life applications in industry. Even though many solution approaches have been presented for the HFSP with makespan criterion, studies on HFSP with total flow time minimization have been rather limited. This study presents a mathematical model, four variants of iterated greedy algorithms and a variable block insertion heuristic for the HFSP with total flow time minimization. Based on the well-known NEH heuristic, an efficient constructive heuristic is also proposed, and compared with NEH. A detailed design of experiment is carried out to calibrate the parameters of the proposed algorithms. The HFSP benchmark suite is used for evaluating the performance of the proposed methods. As there are only 10 large instances in the current literature, further 30 large instances are proposed as new benchmarks. The developed model is solved for all instances on CPLEX under a time limit, and the performances of the proposed algorithms are assessed through comparisons with the results from CPLEX and the two best-performing algorithms in literature. Computational results show that the proposed algorithms are very effective in terms of solution time and quality. Additionally, the proposed algorithms are tested on large instances for the makespan criterion, which reveal that they also perform superbly for the makespan objective. Especially for instances with 30 jobs, the proposed algorithms are able to find the current incumbent makespan values reported in literature, and provide three new best solutions.

Total flow time minimization in no-wait job shop using a hybrid discrete group search optimizer

The no-wait job shop scheduling problem is a well-known NP-hard problem and it is typically decomposed into timetabling subproblem and sequencing subproblem. By adopting favorable features of the group search technique, a hybrid discrete group search optimizer is proposed for finding high quality schedules in the no-wait job shops with the total flow time criterion. In order to find more promising sequences, the producer operator is designed as a destruction and construction (DC) procedure and an insertion-based local search, the scrounger operator is implemented by differential evolution scheme, and the ranger operator is designed by hybridizing best insert moves. An efficient initialization scheme based on Nawaz–Enscore–Ham (NEH) heuristic is designed to construct the initial population with both quality and diversity. A speed-up method is developed to accelerate the evaluation of the insertion neighborhood. Computational results based on well-known benchmark instances show that the proposed algorithm clearly outperforms a hybrid differential evolution algorithm and an iterated greedy algorithm. In addition, the proposed algorithm is comparable to a local search method based on optimal job insertion, especially for large-size instances.

A discrete gravitational search algorithm for the blocking flow shop problem with total flow time minimization

The blocking flow shop problem (BFSP) is one of the key models in the flow shop scheduling problem in the manufacturing systems. Gravitational Search Algorithm (GSA) is an algorithm based on the population for solving various optimization problems. However, GSA is scarcely applied to solve the BFSP as it is designed to solve the continuous problems. In this paper, a Discrete Gravitational Search Algorithm (DGSA) is presented for solving the BFSP with the total flow time minimization. A new variable profile fitting (VPF) combined with NEH heuristic, named VPF _ NEH(n), is introduced for balancing the quality and the diversity of the initial population to configure the DGSA. The three operators including the variable neighborhood operators (VNO), the path relinking and the plus operator are implemented during the location updating of the candidates. The objective of the operation is to prevent the premature convergence of the population and to balance the exploration and exploitation in the process of optimization. The expected runtime of the DGSA is analyzed by the level-based theorem. The simulated results indicate that the effectiveness and superiority of the DGSA.

Computational grid scheduling architecture using MapReduce model-based non-dominated sorting genetic algorithm

Computational grid (CG) environment has a group of autonomous dissimilar distributed computing systems to provide service to user tasks. To attain the auspicious usefulness of CG resources, basically best scheduling algorithms are important. The CG service users are very cautious in time needed for task completion. To meet multiple requirements of the user, the job allocation problem in CG is designed as a multi-objective problem. Evolutionary algorithms have an efficient meta-heuristic technique for optimization problem solving. This work introduces a MapReduce model for non-dominated sorting genetic algorithm (NSGA-II) for independent job scheduling in a CG. This research work attempts to find the optimal schedules by considering makespan and flowtime minimization. A fuzzy membership function is used to analyze the efficiency of the schedule. Set of benchmark instances is used to test the algorithm. Experimental results show that MapReduce model-based NSGA-II generated finer solutions in less time than the MapReduce model-based weighted sum multi-objective genetic algorithm (WMOGA) which is also implemented in this paper.

Minimizing flowtime in a flowshop scheduling problem with a biased random-key genetic algorithm

In this paper, we advance the state of the art for solving the Permutation Flowshop Scheduling Problem with total flowtime minimization. For this purpose, we propose a Biased Random-Key Genetic Algorithm (BRKGA) introducing on it a new feature called shaking. With the shaking, instead to full reset the population to escape from local optima, the shaking procedure perturbs all individuals from the elite set and resets the remaining population. We compare results for the standard and the shaking BRKGA with results from the Iterated Greedy Search, the Iterated Local Search, and a commercial mixed integer programming solver, in 120 traditional instances. For all algorithms, we use warm start solutions produced by the state-of-the-art Beam-Search procedure. Computational experiments show the efficiency of proposed BRKGA, in addition to identify lower and upper bounds, as well as some optimal values, among the solutions.

Heuristics for the mixed no-idle flowshop with sequence-dependent setup times and total flowtime criterion

This paper addresses the mixed no-idle flowshop scheduling problem with sequence-dependent setup times and total flowtime minimisation. In the mixed no-idle flowshop problem, machines that allow idleness coexist with stages that require uninterrupted processing. We studied an extension of this problem, which considers sequence-dependent setup times in machines where idleness is allowed. We present a mixed integer linear programming (MILP) model for the new problem. We also provide a method to evaluate the total flowtime of a permutation sequence. Furthermore, an acceleration method to calculate the total flowtime in an insertion neighbourhood is proposed. A new set of efficient heuristics were developed. In order to evaluate the proposed methods we adapted the best known heuristics available from related problems. The adapted heuristics, as well as the methods proposed here, were tested and compared through statistical and computational experimentation in an extensive benchmark with 4500 instances. We also compared the proposed heuristics with the optimal solutions found by the MILP formulation for small sized problems instances. The results demonstrate that the proposed heuristics perform extremely well in terms of solution quality and computational efficiency.