Medium-scale Problems Research Articles

A parallel social spider algorithm based on population mining

The social spider algorithm is a meta-heuristic algorithm inspired by the foraging behavior of biological social spiders, and is initially used to solve optimization problems with continuous functions. There exist many challenges when dealing with discrete combinatorial optimization problems. Therefore, a novel parallel social spider algorithm based on population mining is proposed. Its starting point is to mine dynamic heuristic information from the population of social spiders that cause vibrations to guide the spider’s next walk. It proposes the concept of vibration candidate sets and enhances the behavior of artificial spiders. Furthermore, it is implemented in parallel on the graphics processing unit. According to our investigation, it is the first parallel social spider algorithm. The classical traveling salesman problem is solved as an example. By solving 30 small-scale and medium-scale problems and comparing with other algorithms, it shows that its solution quality is significantly better. By solving 17 large-scale problems, compared with the parallel ant colony system and parallel iterative hill climbing algorithm on the GPU, it is found that both the solution quality and performance are also significantly better. Codes are available at https://github.com/BuptCIAGroup/P-SSA.

DUGKS-GPU: An efficient parallel GPU code for 3D turbulent flow simulations using Discrete Unified Gas Kinetic Scheme

This paper presents a parallel implementation of the Discrete Unified Gas Kinetic Scheme (DUGKS) on the GPU system using the CUDA Fortran and CUDA C++ programming languages. Firstly, we conducted an extensive revision of our original CPU-based code, resulting in a threefold decrease in memory usage. This new implementation is also paired with a novel approach to compute cell face flux using trilinear interpolation. It is shown analytically that the interpolation-based approach to flux calculation is more accurate compared to the one used in the original DUGKS. The initial simulation results using this new approach suggest that trilinear interpolation can reduce numerical errors on a coarse mesh. For example, in the case of the decaying Taylor-Green vortex flow at a 1283 mesh resolution, the relative numerical error in the energy dissipation rate at t⁎=2, using the spectral simulation result as the benchmark, is approximately 30% lower than that of the original implementation. The improved GPU DUGKS method is applied to laminar and turbulent flows in periodic and wall-bounded boundary configurations. A performance comparison of the GPU implementation is also presented and compared to the previous CPU implementation. A maximum speedup of 7.64x was achieved on a desktop-level GPU compared to a 32-core CPU. The strong scaling test, conducted on an eight-GPU node, demonstrated the efficient utilization of available multiple GPU resources by the code. Program summaryProgram Title: DUGKS-GPUCPC Library link to program files:https://doi.org/10.17632/yykv5s9g2n.1Developer's repository link:https://github.com/kairzhan/DUGKS-GPUCode Ocean capsule:https://codeocean.com/capsule/3b1e4f74-cdd3-4781-8923-8514d5923dfb/Licensing provisions: GNU General Public License 3Programming language: CUDA C++, CUDA FortranSupplementary material:Nature of problem: DUGKS-GPU is an advanced numerical code designed to accelerate the simulation of turbulent fluid flows through the application of the kinetic method known as the Discrete Unified Gas Kinetic Scheme (DUGKS). This computational tool comprises a CUDA Fortran version, tailored for a single GPU, as well as a CUDA C++ version developed for multi-GPU platforms.Solution method: The code employs a second-order finite-volume discretization of the discrete velocity Boltzmann equation with the BGK collision model. It can be used to simulate small to medium-scale problems on modern multi-GPU platforms with CUDA architecture.

Surrogate-Assisted Evolutionary Multi-Objective Optimization of Medium-Scale Problems by Random Grouping and Sparse Gaussian Modeling

Surrogate-Assisted Evolutionary Multi-Objective Optimization of Medium-Scale Problems by Random Grouping and Sparse Gaussian Modeling

High-speed train timetable optimization based on space–time network model and quantum simulator

Timetable scheduling is a combinatorial optimization problem that presents formidable challenges for classical computers. This paper introduces a pioneering methodology for addressing the high-speed train timetabling problem through quantum computing. Initially, a comprehensive binary integer programming model, grounded in the space–time network, is proposed (M1). To manage the intricacy of model M1, a knapsack problem reformulation is employed to establish a simplified binary integer programming model (M2). Both M1 and M2 are subsequently converted into quadratic unconstrained binary optimization (QUBO) models to harness the potential of quantum computing. Several techniques, including the Gurobi solver, simulated annealing, and the coherent Ising machine (CIM) quantum simulator, are deployed to solve the model across four distinct scenarios of varying complexity. The findings indicate that CIM quantum simulator outperforms the simulated annealing method in terms of solution quality for medium-scale problems.

Solution of discrete time–cost trade-off problem with adaptive search domain

PurposeExact solution of time–cost trade-off problem (TCTP) by the state-of-the-art meta-heuristic algorithms can be obtained for small- and medium-scale problems, while satisfactory results cannot be obtained for large construction projects. In this study, a hybrid heuristic meta-heuristic algorithm that adapts the search domain is developed to solve the large-scale discrete TCTP more efficiently.Design/methodology/approachMinimum cost slope–based heuristic network analysis algorithm (NAA), which eliminates the unfeasible search domain, is embedded into differential evolution meta-heuristic algorithm. Heuristic NAA narrows the search domain at the initial phase of the optimization. Moreover, activities with float durations higher than the predetermined threshold value are eliminated and then the meta-heuristic algorithm starts and searches the global optimum through the narrowed search space. However, narrowing the search space may increase the probability of obtaining a local optimum. Therefore, adaptive search domain approach is employed to make reintroduction of the eliminated activities to the design variable set possible, which reduces the possibility of converging into local minima.FindingsThe developed algorithm is compared with plain meta-heuristic algorithm with two separate analyses. In the first analysis, both algorithms have the same computational demand, and in the latter analysis, the meta-heuristic algorithm has fivefold computational demand. The tests on case study problems reveal that the developed algorithm presents lower total project costs according to the dependent t-test for paired samples with α = 0.0005.Research limitations/implicationsIn this study, TCTP is solved without considering quality or restrictions on the resources.Originality/valueThe proposed method enables to adapt the number of parameters, that is, the search domain and provides the opportunity of obtaining significant improvements on the meta-heuristic algorithms for other engineering optimization problems, which is the theoretical contribution of this study. The proposed approach reduces the total construction cost of the large-scale projects, which can be the practical benefit of this study.

Multi-objective time–cost trade-off optimization for the construction scheduling with Rao algorithms

Determining the time and cost of activities is one of the most important stages of construction project planning. Measures taken to shorten the time, such as the need for more or more qualified employees, equipment and machinery, increase project direct cost. The process of deciding which option to use in activities with more than one time–cost option has revealed the time–cost trade-off problem which is discrete optimization. Within the scope of this study, the non-dominant sorting (NDS) method is integrated into the Rao-1 and Rao-2 algorithms and applied to small and medium-scale problems. The numerical results show that the NDS-Rao-2 algorithm has found a better result with a significant number of function evaluations compared to algorithms such as PSO, ACO, GA and TLBO used in previous studies. In addition, the NDS-based Rao-2 algorithm not only find optimal /near results, but also suggest more than one pareto result to the decision maker for time–cost trade-off problem. For this reason, the developed multi-objective Rao-2 algorithm can be considered as a very good alternative for time–cost trade-off problems which are combinatorial problems.

Mixed integer linear programming formulations for the permutation flow shop scheduling problem with preventive maintenance activities

Integrating the maintenance activities into the production process allows for keeping/restoring the good functional state of machines and improving the system productivity. According to the maintenance strategy adopted by a company, maintenance activities can be carried out in fixed positions/intervals or can be flexible, with an optimised maintenance approach being the key to efficient production maintenance. Consequently, the scheduling problems with maintenance activities (machine availability constraints) have received an increasing attention for both cases of fixed and flexible maintenance activities. This paper investigates the flow shop scheduling problem in the non-resumable case using an arbitrary number of preventive maintenance activities on each machine, with the optimised criterion being the makespan. Three mixed integer linear programming (MILP) models are proposed for three different problem types with respect to the considered maintenance policies within fixed-time windows, after a fixed number of finished jobs, and within an optimal preventive maintenance period. The computational results based on the randomly generated test problems demonstrate the high performance of the proposed MILP models in solving a wide range of instances, particularly, in small- and medium-scale problems.

A bi-objective hybrid vibration damping optimization model for synchronous flow shop scheduling problems

Flow shop scheduling deals with the determination of the optimal sequence of jobs processing on machines in a fixed order with the main objective consisting of minimizing the completion time of all jobs (makespan). This type of scheduling problem appears in many industrial and production planning applications. This study proposes a new bi-objective mixed-integer programming model for solving the synchronous flow shop scheduling problems with completion time. The objective functions are the total makespan and the sum of tardiness and earliness cost of blocks. At the same time, jobs are moved among machines through a synchronous transportation system with synchronized processing cycles. In each cycle, the existing jobs begin simultaneously, each on one of the machines, and after completion, wait until the last job is completed. Subsequently, all the jobs are moved concurrently to the next machine. Four algorithms, including non-dominated sorting genetic algorithm (NSGA II), multi-objective simulated annealing (MOSA), multi-objective particle swarm optimization (MOPSO), and multi-objective hybrid vibration-damping optimization (MOHVDO), are used to find a near-optimal solution for this NP-hard problem. In particular, the proposed hybrid VDO algorithm is based on the imperialist competitive algorithm (ICA) and the integration of a neighborhood creation technique. MOHVDO and MOSA show the best performance among the other algorithms regarding objective functions and CPU Time, respectively. Thus, the results from running small-scale and medium-scale problems in MOHVDO and MOSA are compared with the solutions obtained from the epsilon-constraint method. In particular, the error percentage of MOHVDO’s objective functions is less than 2% compared to the epsilon-constraint method for all solved problems. Besides the specific results obtained in terms of performance and, hence, practical applicability, the proposed approach fills a considerable gap in the literature. Indeed, even though variants of the aforementioned meta-heuristic algorithms have been largely introduced in multi-objective environments, a simultaneous implementation of these algorithms as well as a compared study of their performance when solving flow shop scheduling problems has been so far overlooked.

A Bi-population Cooperative Optimization Algorithm Assisted by an Autoencoder for Medium-scale Expensive Problems

This study presents an autoencoder-embedded optimization (AEO) algorithm which involves a bi-population cooperative strategy for medium-scale expensive problems (MEPs). A huge search space can be compressed to an informative low-dimensional space by using an autoencoder as a dimension reduction tool. The search operation conducted in this low space facilitates the population with fast convergence towards the optima. To strike the balance between exploration and exploitation during optimization, two phases of a tailored teaching-learning-based optimization (TTLBO) are adopted to coevolve solutions in a distributed fashion, wherein one is assisted by an autoencoder and the other undergoes a regular evolutionary process. Also, a dynamic size adjustment scheme according to problem dimension and evolutionary progress is proposed to promote information exchange between these two phases and accelerate evolutionary convergence speed. The proposed algorithm is validated by testing benchmark functions with dimensions varying from 50 to 200. As indicated in our experiments, TTLBO is suitable for dealing with medium-scale problems and thus incorporated into the AEO framework as a base optimizer. Compared with the state-of-the-art algorithms for MEPs, AEO shows extraordinarily high efficiency for these challenging problems, thus opening new directions for various evolutionary algorithms under AEO to tackle MEPs and greatly advancing the field of medium-scale computationally expensive optimization.

Efficient differentiable quadratic programming layers: an ADMM approach

Recent advances in neural-network architecture allow for seamless integration of convex optimization problems as differentiable layers in an end-to-end trainable neural network. Integrating medium and large scale quadratic programs into a deep neural network architecture, however, is challenging as solving quadratic programs exactly by interior-point methods has worst-case cubic complexity in the number of variables. In this paper, we present an alternative network layer architecture based on the alternating direction method of multipliers (ADMM) that is capable of scaling to moderate sized problems with 100–1000 decision variables and thousands of training examples. Backward differentiation is performed by implicit differentiation of a customized fixed-point iteration. Simulated results demonstrate the computational advantage of the ADMM layer, which for medium scale problems is approximately an order of magnitude faster than the state-of-the-art layers. Furthermore, our novel backward-pass routine is computationally efficient in comparison to the standard approach based on unrolled differentiation or implicit differentiation of the KKT optimality conditions. We conclude with examples from portfolio optimization in the integrated prediction and optimization paradigm.

Accelerated boundary element method for direct current interference of cathodic protections systems

The use of cathodic protection (CP) is a widely used practice to mitigate the corrosion of metals. In certain circumstances, stray-current induced corrosion can occur on a structure when it interacts with the CP system of another nearby structure. Due to the locality of the phenomenon, stray-current induced corrosion is one of the most severe types of corrosion. The boundary element method (BEM) is ideal for solving CP problems. In the present work, two accelerated BEM formulations are presented to treat direct current interference problems. The first formulation is more efficient in solving small and medium scale problems, while the second one is more suitable for large scale problems. Furthermore, the stray current induced corrosion in an offshore platform due to its interaction with a nearby moored oil tanker is studied utilizing the above methodologies. The obtained numerical results are extensively discussed, and interesting conclusions are outlined.

A new humanitarian relief logistic network for multi-objective optimization under stochastic programming.

Millions of affected people and thousands of victims are consequences of earthquakes, every year. Therefore, it is necessary to prepare a proper preparedness and response planning. The objectives of this paper are i) minimizing the expected value of the total costs of relief supply chain, ii) minimizing the maximum number of unsatisfied demands for relief staff and iii) minimizing the total probability of unsuccessful evacuation in routes. In this paper, a scenario based stochastic multi-objective location-allocation-routing model is proposed for a real humanitarian relief logistics problem which focused on both pre- and post-disaster situations in presence of uncertainty. To cope with demand uncertainty, a simulation approach is used. The proposed model integrates these two phases simultaneously. Then, both strategic and operational decisions (pre-disaster and post-disaster), fairness in the evacuation, and relief item distribution including commodities and relief workers, victim evacuation including injured people, corpses and homeless people are also considered simultaneously in this paper. The presented model is solved utilizing the Epsilon-constraint method for small- and medium-scale problems and using three metaheuristic algorithms for the large-scale problem (case study). Empirical results illustrate that the model can be used to locate the shelters and relief distribution centers, determine appropriate routes and allocate resources in uncertain and real-life disaster situations.

Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimization.

We propose the first general and scalable framework to design certifiable algorithms for robust geometric perception in the presence of outliers. Our first contribution is to show that estimation using common robust costs, such as truncated least squares (TLS), maximum consensus, Geman-McClure, Tukey's biweight, among others, can be reformulated as polynomial optimization problems (POPs). By focusing on the TLS cost, our second contribution is to exploit sparsity in the POP and propose a sparse semidefinite programming (SDP) relaxation that is much smaller than the standard Lasserre's hierarchy while preserving empirical exactness, i.e., the SDP recovers the optimizer of the nonconvex POP with an optimality certificate. Our third contribution is to solve the SDP relaxations at an unprecedented scale and accuracy by presenting [Formula: see text], a solver that blends global descent on the convex SDP with fast local search on the nonconvex POP. Our fourth contribution is an evaluation of the proposed framework on six geometric perception problems including single and multiple rotation averaging, point cloud and mesh registration, absolute pose estimation, and category-level object pose and shape estimation. Our experiments demonstrate that (i) our sparse SDP relaxation is empirically exact with up to 60%- 90% outliers across applications; (ii) while still being far from real-time, [Formula: see text] is up to 100 times faster than existing SDP solvers on medium-scale problems, and is the only solver that can solve large-scale SDPs with hundreds of thousands of constraints to high accuracy; (iii) [Formula: see text] safeguards existing fast heuristics for robust estimation (e.g., [Formula: see text] or Graduated Non-Convexity), i.e., it certifies global optimality if the heuristic estimates are optimal, or detects and allows escaping local optima when the heuristic estimates are suboptimal.

Minimizing the maximum flow time for flexible job shop problem with parallel machines

ABSTRACT This paper studies a flexible job shop problem with parallel machines considering release time. The objective aims to minimize the maximum flow time. Based on the specific characteristics of the problem, we find a property which can reduce the dimension of solution space to dimension, where is the total number of operations. To solve the small-scale problem, a branch-and-bound algorithm is proposed. For the medium-scale problem, a heuristic based on a differential evolution algorithm is proposed. The LSPT-DS heuristic is tried to solve the large-scale problem. Through computational experiments, the proposed algorithms are proved to be both effective and efficient in solving this flexible job shop problem. Besides experiments are also conducted to verify that the objective to minimize the maximum flow time is reasonable.

The container drayage problem for heterogeneous trucks with multiple loads: A revisit

In this study, we revisit the container drayage problem for heterogeneous trucks with multiple loads in view of its practical significance. We first propose a tailored mixed-integer linear programming (MILP) model explicitly to reflect the reality of container drayage operations. To solve medium-scale problems more effectively, two relaxed MILP models are built to provide a solution that is close to optimal with less computational time. These two relaxed models are proven to work as intended and provide optimal solutions under certain conditions. Moreover, an effective hybrid heuristic method incorporating the cheapest feasible insertion mechanism and the variable neighborhood search scheme is designed to solve large-scale problems. Extensive numerical experiments demonstrate the scalability of the heuristic method in real-world applications.

Optimization for a Multi-Constraint Truck Appointment System Considering Morning and Evening Peak Congestion

Gate and yard congestion is a typical type of container port congestion, which prevents trucks from traveling freely and has become the bottleneck that constrains the port productivity. In addition, urban traffic increases the uncertainty of the truck arrival time and additional congestion costs. More and more container terminals are adopting a truck appointment system (TAS), which tries to manage the truck arrivals evenly all day long. Extending the existing research, this work considers morning and evening peak congestion and proposes a novel approach for multi-constraint TAS intended to serve both truck companies and container terminals. A Mixed Integer Nonlinear Programming (MINLP) based multi-constraint TAS model is formulated, which explicitly considers the appointment change cost, queuing cost, and morning and evening peak congestion cost. The aim of the proposed multi-constraint TAS model is to minimize the overall operation cost. The Lingo commercial software is used to solve the exact solutions for small and medium scale problems, and a hybrid genetic algorithm and simulated annealing (HGA-SA) is proposed to obtain the solutions for large-scale problems. Experimental results indicate that the proposed TAS can not only better serve truck companies and container terminals but also more effectively reduce their overall operation cost compared with the traditional TASs.

Two meta-heuristic algorithms for optimizing a multi-objective supply chain scheduling problem in an identical parallel machines environment

Optimizing the trade-off between crucial decisions has been a prominent issue to help decision-makers for synchronizing the production scheduling and distribution planning in supply chain management. In this article, a bi-objective integrated scheduling problem of production and distribution is addressed in a production environment with identical parallel machines. Besides, two objective functions are considered as measures for customer satisfaction and reduction of the manufacturer’s costs. The first objective is considered aiming at minimizing the total weighted tardiness and total operation time. The second objective is considered aiming at minimizing the total cost of the company’s reputational damage due to the number of tardy orders, total earliness penalty, and total batch delivery costs. First, a mathematical programming model is developed for the problem. Then, two well-known meta-heuristic algorithms are designed to spot near-optimal solutions since the problem is strongly NP-hard. A multi-objective particle swarm optimization (MOPSO) is designed using a mutation function, followed by a non-dominated sorting genetic algorithm (NSGA-II) with a one-point crossover operator and a heuristic mutation operator. The experiments on MOPSO and NSGA-II are carried out on small, medium, and large scale problems. Moreover, the performance of the two algorithms is compared according to some comparing criteria. The computational results reveal that the NSGA-II performs highly better than the MOPSO algorithm in small scale problems. In the case of medium and large scale problems, the efficiency of the MOPSO algorithm was significantly improved. Nevertheless, the NSGA-II performs robustly in the most important criteria.

Optimizing the Strategic Decisions for One-Way Station-Based Carsharing Systems: A Mean-CVaR Approach

The study focuses on the strategic decisions including on the location and capacity of stations and the fleet size for designing the one-way station-based carsharing systems. Under demand uncertainty, we introduce a two-stage risk-averse stochastic model to maximize the mean return and minimize the risk, where the conditional value-at-risk (CVaR) is specified as the risk measure. To solve the problem efficiently, a branch-and-cut algorithm and a scenario decomposition algorithm are developed. We conduct computational experiments based on historical use data and generate efficient frontiers so that the system operator can make a trade-off between return and risk. We then utilize an evaluation method to analyze the necessity of introducing risk. Finally, the efficiency of the proposed algorithms is elaborated through comparative experiments. Both branch-and-cut algorithm and scenario decomposition algorithm can tackle the small- and medium-scale problems well. For large-scale problems that cannot be solved by using an optimization solver or the branch-and-cut algorithm, scenario decomposition method can provide favorable solutions within a reasonable time.

Integrated Decisions on Online Product Image Configuration and Inventory Planning Using DPSO

Integrated decisions on merchandise image display and inventory planning are closely related to operational performance of online stores. A visual-attention-dependent demand (VADD) model has been developed to support online stores make the decisions. In the face of evolving products, customer needs, and competitors in an e-commerce environment, the benefits of using VADD model depend on how fast the model runs on the computer. As a result, a discrete particle swarm optimization (DPSO) method is employed to solve the VADD model. To verify the usability and effectiveness of DPSO method, it was compared with the existing methods for large-scale, medium-scale, and small-scale problems. The comparison results show that both GA and DPSO method perform well in terms of the approximation rate, but the DPSO method takes less time than the GA method. A sensitivity is conducted to determine the model parameters that influence the above comparison result.

Time-Varying Convex Optimization: Time-Structured Algorithms and Applications

Optimization underpins many of the challenges that science and technology face on a daily basis. Recent years have witnessed a major shift from traditional optimization paradigms grounded on batch algorithms for medium-scale problems to challenging dynamic, time-varying, and even huge-size settings. This is driven by technological transformations that converted infrastructural and social platforms into complex and dynamic networked systems with even pervasive sensing and computing capabilities. This article reviews a broad class of state-of-the-art algorithms for time-varying optimization, with an eye to performing both algorithmic development and performance analysis. It offers a comprehensive overview of available tools and methods and unveils open challenges in application domains of broad range of interest. The real-world examples presented include smart power systems, robotics, machine learning, and data analytics, highlighting domain-specific issues and solutions. The ultimate goal is to exemplify wide engineering relevance of analytical tools and pertinent theoretical foundations.