Large Problem Instances Research Articles

Joint Design and Pricing Problem for Symbiotic Bioethanol Supply Chain Network: Model and Resolution Approach

To fight climate change, the Province of Quebec, Canada, has set targets to reduce greenhouse gas emissions by reducing fossil fuel consumption and integrating biofuel content into gasoline and diesel fuel. Motivated by a real-world case study, this paper presents a novel distributed decision model for designing a symbiotic supply chain network and supporting pricing decisions. A distributed decision-making problem is formulated as a game theoretic approach considering a Stackelberg–Nash equilibrium. A novel mathematical model is proposed to support the decisions of four actors: corn farms, processing depots, pig farms, and biorefineries. In addition to the configuration of a biofuel-based industrial symbiosis, the model offers the possibility of setting purchase prices and supply levels for biomass (corn stover supplied by farms), as well as determining sales prices and production levels for the main product (the cellulosic sugar used for the bioethanol production) and a coproduct (pig feed sold to pig farmers). A three-step optimization process involving the user is proposed to address the computational challenges posed by large design problem instances. The case study of the Province of Quebec is used to evaluate the performance of the proposed resolution approach.

Energy-aware scheduling in flow shops: a novel artificial neural network-driven multi-objective optimization

Group technology is a managerial strategy used to optimize production by reducing setup times, lead times, and work-in-process inventories. Research on flow-shop sequence-dependent group scheduling problems (FSDGSPs) has primarily focused on minimizing makespan and total flow time to improve efficiency. However, the need for energy-efficient scheduling in FSDGSPs remains underexplored despite increasing sustainability concerns. To address this, the energy-efficient flow-shop sequence-dependent group scheduling problem (EEFSDGSP) is introduced. A novel multi-objective optimization (MOO) technique, the artificial neural network-based multi-objective genetic algorithm (ANN-MOGA), is proposed to minimize makespan and energy consumption in EEFSDGSP. ANN-MOGA advances MOO by using a neural network to evaluate fitness and guide selection, reducing computational complexity versus traditional methods like NSGA-II and SPEA2. A post-processing step (PPANNS) further enhances solution diversity and distribution. Results show ANN-MOGA, especially with PPANNS, outperforms NSGA-II and competes effectively with SPEA2 in larger problem instances.

A multi-objective production scheduling model and dynamic dispatching rules for unrelated parallel machines with sequence-dependent set-up times

This study presents a production scheduling for unrelated parallel machines with machine and job sequence-dependent setup times. The system performance measures to minimize include makespan, total tardiness, and number of tardy jobs. The aim of the study is to develop a solution methodology that can solve the problem for the large scale. First, the problem is formulated as a mixed-integer linear programming model. The augmented ɛ-constraint method is applied to find Pareto solutions for small problem instances. The purpose is to demonstrate that Pareto solutions, which balance the trade-offs among three measures of performance, can be found for these instances. Dispatching rule-based heuristics is developed to solve large problem instances. The heuristics feature three dispatching rules that are designed to handle the dependent setup time. In addition, these rules are combined into six variants using a time-based rule-switching mechanism. The heuristics are tested with 18 problem instances, containing 244 to 298 jobs, in two demand scenarios derived from the monthly demand data from an industrial user. Under each demand scenario, a set of heuristics that provides the best performance with respect to the three measures is identified. The heuristics include combinations of the shortest completion time and due date-based rules. Finally, a multi-criteria decision-making analysis is performed to determine the conditions specified by the weight given to each measure, with which one heuristic is preferred over the others.

ε-Constraint Procedures for Pareto Front Optimization of Large Size Discrete Time/Cost Trade-Off Problem

The discrete time/cost trade-off problem (DTCTP) optimizes the project duration and/or cost while considering the trade-off between activity durations and their direct costs. The complete and non-dominated time-cost profile over the set of feasible project durations is achieved within the framework of Pareto front problem. Despite the importance of Pareto front optimization in project and portfolio management, exact procedures have achieved very limited success in solving the problem for large size instances. This study develops exact procedures based on combinations of mixed-integer linear programming (MILP), ε-constraint method, network and problem reduction techniques, and present new bounding strategies to solve the Pareto problem for large size instances. This study also provides new large size benchmark problem instances aiming to represent the size of real-life projects for the DTCTP. The new instances, therefore, are generated to include up to 990 activities and nine execution modes. Computational experiments reveal that the procedures presented herein can remarkably outperform the state-of-the-art exact methods. The new exact procedures enabled obtaining the optimal Pareto front for instances with serial networks that include more than 200 activities for the first time.

Making Formulog Fast: An Argument for Unconventional Datalog Evaluation

With its combination of Datalog, SMT solving, and functional programming, the language Formulog provides an appealing mix of features for implementing SMT-based static analyses (e.g., refinement type checking, symbolic execution) in a natural, declarative way. At the same time, the performance of its custom Datalog solver can be an impediment to using Formulog beyond prototyping—a common problem for Datalog variants that aspire to solve large problem instances. In this work we speed up Formulog evaluation, with some surprising results: while 2.2× speedups can be obtained by using the conventional techniques for high-performance Datalog (e.g., compilation, specialized data structures), the big wins come by abandoning the central assumption in modern performant Datalog engines, semi-naive Datalog evaluation. In the place of semi-naive evaluation, we develop eager evaluation, a concurrent Datalog evaluation algorithm that explores the logical inference space via a depth-first traversal order. In practice, eager evaluation leads to an advantageous distribution of Formulog’s SMT workload to external SMT solvers and improved SMT solving times: our eager evaluation extensions to the Formulog interpreter and Soufflé’s code generator achieve mean 5.2× and 7.6× speedups, respectively, over the optimized code generated by off-the-shelf Soufflé on SMT-heavy Formulog benchmarks. All in all, using compilation and eager evaluation (as appropriate), Formulog implementations of refinement type checking, bottom-up pointer analysis, and symbolic execution achieve speedups on 20 out of 23 benchmarks over previously published, hand-tuned analyses written in F ♯ , Java, and C++, providing strong evidence that Formulog can be the basis of a realistic platform for SMT-based static analysis. Moreover, our experience adds nuance to the conventional wisdom that traditional semi-naive evaluation is the one-size-fits-all best Datalog evaluation algorithm for static analysis workloads.

Approximate sequential optimization for informative path planning

We consider the problem of finding an informative path through a graph, given initial and terminal nodes and a given maximum path length. We assume that a linear noise corrupted measurement is taken at each node of an underlying unknown vector that we wish to estimate. The informativeness is measured by the reduction in uncertainty in our estimate, evaluated using several Gaussian process-based metrics. We present a convex relaxation for this informative path planning problem, which we can readily solve to obtain a bound on the possible performance. We develop an approximate sequential method where the path is constructed segment by segment through dynamic programming. This involves solving an orienteering problem, with the node reward acting as a surrogate for informativeness, taking the first step, and then repeating the process. The method scales to very large problem instances and achieves performance close to the bound produced by the convex relaxation. We also demonstrate our method’s ability to handle adaptive objectives, multimodal sensing, and multi-agent variations of the informative path planning problem.

A user-centric model of connectivity in street networks

Modelling street network connectivity is a fundamental research problem in transportation science. Here, we argue that the connectivity of a street network cannot be defined independently from the users of that street network. That is, different users will experience different levels of connectivity depending on their corresponding travel behaviour. In this work, we propose a model of connectivity that is defined with respect to a user’s travel behaviour within a given street network. We demonstrate that many real-world problems can be posed as instances of an optimisation problem defined with respect to this model. This includes optimising a user’s home location with respect to their connectivity and optimising the location of a facility with respect to the connectivity of its users. We prove the above optimisation problem is NP-hard and present an integer programming solution that scales to large problem instances.

On convergence of a q-random coordinate constrained algorithm for non-convex problems

We propose a random coordinate descent algorithm for optimizing a non-convex objective function subject to one linear constraint and simple bounds on the variables. Although it is common use to update only two random coordinates simultaneously in each iteration of a coordinate descent algorithm, our algorithm allows updating arbitrary number of coordinates. We provide a proof of convergence of the algorithm. The convergence rate of the algorithm improves when we update more coordinates per iteration. Numerical experiments on large scale instances of different optimization problems show the benefit of updating many coordinates simultaneously.

Scattered storage for retail e-commerce fulfillment warehouses with consideration for product turnover

Storage assignment policy of a warehouse controls how the stocks are assigned to various storage locations. Traditionally used storage policies, such as dedicated or random storage, do not address the specific needs of retail e-commerce fulfillment warehouses that store a wide assortment of products and service a large number of single-unit orders under strict timelines. This has led to the development of scattered storage assignment policy, which deliberately spreads the stocks of every product across the warehouse. However, the available approaches towards scattering have largely ignored product turnover, which is a significant determinant of order picking travel. To fill this research gap, we propose a new, turnover-incorporated scattered storage policy. More specifically, we develop a new measure of scattering of stocks and a mathematical model that optimizes the measure by scattering the stocks across the warehouse, while considering product turnover. Certain important properties of this measure are proved and eventually exploited in developing a heuristic approach to solve the proposed mathematical model for large problem instances. An upper bound for the objective function of the mathematical model is used as a benchmark to evaluate the performance and computation time of the proposed heuristic, as well as solutions obtained through genetic algorithms and surrogate optimization. We conduct a simulation study using the proposed heuristic to analyze the impact of the scattering of stocks on order picking performance in a single block, low level, picker-to-parts warehouse. We also present the impact of warehouse operating parameters on the performance of the proposed scattered storage policy.

Enhancing quantum annealing accuracy through replication-based error mitigation*

Abstract Quantum annealers like those manufactured by D-Wave Systems are designed to find high quality solutions to optimization problems that are typically hard for classical computers. They utilize quantum effects like tunneling to evolve toward low-energy states representing solutions to optimization problems. However, their analog nature and limited control functionalities present challenges to correcting or mitigating hardware errors. As quantum computing advances towards applications, effective error suppression is an important research goal. We propose a new approach called replication based mitigation (RBM) based on parallel quantum annealing (QA). In RBM, physical qubits representing the same logical qubit are dispersed across different copies of the problem embedded in the hardware. This mitigates hardware biases, is compatible with limited qubit connectivity in current annealers, and is well-suited for currently available noisy intermediate-scale quantum annealers. Our experimental analysis shows that RBM provides solution quality on par with previous methods while being more flexible and compatible with a wider range of hardware connectivity patterns. In comparisons against standard QA without error mitigation on larger problem instances that could not be handled by previous methods, RBM consistently gets better energies and ground state probabilities across parameterized problem sets.

An optimization framework for solving large scale multidemand multidimensional knapsack problem instances employing a novel core identification heuristic

By applying the core concept to solve a binary integer program (BIP), certain variables of the BIP are fixed to their anticipated values in the optimal solution. In contrast, the remaining variables, called core variables, are used to construct and solve a core problem (CP) instead of the BIP. A new approach for identifying CP utilizing a local branching (LB) alike constraint is presented in this article. By including the LB-like constraint in the linear programming relaxation of the BIP, this method transfers batches of variables to the set of core variables by analyzing changes to their reduced costs. This approach is sensitive to problem hardness because more variables are moved to the core set for hard problems compared to easy ones. This novel core identification approach is embedded in a multi-stage framework to solve the multidemand, multidimensional knapsack problems (MDMKP), where at each stage, more variables are added to the previous stage CP. The default branch and bound of CPLEX20.10 is used to solve the first stage, and a tabu search algorithm is used to solve subsequent stages until all variables are added to CP in the last stage. The new framework has shown equivalent to superior results compared to the state-of-the-art algorithms in solving large MDMKP instances having 500 and 1,000 variables.

A Model-Free Approach for Solving Choice-Based Competitive Facility Location Problems Using Simulation and Submodularity

This paper considers facility location problems in which a firm entering a market seeks to open facilities on a subset of candidate locations so as to maximize its expected market share, assuming that customers choose the available alternative that maximizes a random utility function. We introduce a deterministic equivalent reformulation of this stochastic problem as a maximum covering location problem with an exponential number of demand points, each of which is covered by a different set of candidate locations. Estimating the prevalence of these preference profiles through simulation generalizes a sample average approximation method from the literature and results in a maximum covering location problem of manageable size. To solve it, we develop a partial Benders reformulation in which the contribution to the objective of the least influential preference profiles is aggregated and bounded by submodular cuts. This set of profiles is selected by a knee detection method that seeks to identify the best tradeoff between the fraction of the demand that is retained in the master problem and the size of the model. We develop a theoretical analysis of our approach and show that the solution quality it provides for the original stochastic problem, its computational performance, and the automatic profile-retention strategy it exploits are directly connected to the entropy of the preference profiles in the population. Computational experiments on existing and new benchmark sets indicate that our approach dominates the classical sample average approximation method on large instances of the competitive facility location problem, can outperform the best heuristic method from the literature under the multinomial logit model, and achieves state-of-the-art results under the mixed multinomial logit model. We characterize a broader class of problems, which includes assortment optimization, to which the solving methodology and the analyses developed in this paper can be extended. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This research was supported by Fonds de Recherche du Québec-Nature et Technologies and Institut de Valorisation des Données through scholarships to R. Legault. E. Frejinger was partially supported by the Canada Research Chair program [Grant 950-232244]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/ijoc.2023.0280 .

A Scalable Accelerator for Local Score Computation of Structure Learning in Bayesian Networks

A Bayesian network is a powerful tool for representing uncertainty in data, offering transparent and interpretable inference, unlike neural networks’ black-box mechanisms. To fully harness the potential of Bayesian networks, it is essential to learn the graph structure that appropriately represents variable interrelations within data. Score-based structure learning, which involves constructing collections of potentially optimal parent sets for each variable, is computationally intensive, especially when dealing with high-dimensional data in discrete random variables. Our proposed novel acceleration algorithm extracts high levels of parallelism, offering significant advantages even with reduced reusability of computational results. In addition, it employs an elastic data representation tailored for parallel computation, making it FPGA-friendly and optimizing module occupancy while ensuring uniform handling of diverse problem scenarios. Demonstrated on a Xilinx Alveo U50 FPGA, our implementation significantly outperforms optimal CPU algorithms and is several times faster than GPU implementations on an NVIDIA TITAN RTX. Furthermore, the results of performance modeling for the accelerator indicate that, for sufficiently large problem instances, it is weakly scalable, meaning that it effectively utilizes increased computational resources for parallelization. To our knowledge, this is the first study to propose a comprehensive methodology for accelerating score-based structure learning, blending algorithmic and architectural considerations.

Strategic flood impact mitigation in developing countries’ urban road networks: Application to Hanoi

Due to climate change, the frequency and scale of flood events worldwide are increasing dramatically. Flood impacts are especially acute in developing countries, where they often revert years of progress in sustainable development and poverty reduction. This paper introduces an optimization-based decision support tool for selecting cost-efficient flood mitigation investments in developing countries’ urban areas. The core of the tool is a scenario-based, multi-period, bi-objective Mixed Integer Linear Programming model which minimizes infrastructure damage and traffic congestion in urban road networks. The tool was developed in collaboration with Vietnamese stakeholders (e.g., local communities and government authorities), and integrates data and inputs from other disciplines, including social science, transport economics, climatology and hydrology. A metaheuristic, combining a Greedy Randomized Adaptive Search Procedure with a Variable Neighborhood Descent algorithm, is developed to solve large scale problem instances. An extensive computational campaign on randomly generated instances demonstrates the efficiency of the metaheuristic in solving realistic problems with hundreds of interdependent flood mitigation interventions. Finally, the applicability of the interdisciplinary approach is demonstrated on a real case study to generate a 20-year plan of mitigation investments for the urban area of Hanoi. Policy implications and impacts of the study are also discussed.

Dispersed starting solutions in facility location: The case of the planar [formula omitted]-median problem

There are many planar multiple facilities location problems for which the optimal locations tend to be spread out. The most popular of these is the planar p-median problem. With this in mind, we propose several procedures to generate sparse configurations as starting solutions. The proposed procedures are easy to implement, and can be used as modules combined in different sequences within heuristics such as a recent trajectory-based procedure that we tested in this paper.The procedures are tested experimentally on a set of 24 large problem instances with up to 10,000 demand points and 100 facilities. We are able to demonstrate that the sparse starting solutions generated by the new procedures lead to significant improvements of final p-median solutions.

An efficient solver for large-scale onshore wind farm siting including cable routing

Existing planning approaches for onshore wind farm siting and grid integration often do not meet minimum cost solutions or social and environmental considerations. In this paper, we develop an exact approach for the integrated layout and cable routing problem of onshore wind farm planning using the Quota Steiner tree problem. Applying a novel transformation on a known directed cut formulation, reduction techniques, and heuristics, we design an exact solver that makes large problem instances solvable and outperforms generic MIP solvers. In selected regions of Germany, the trade-offs between minimizing costs and landscape impact of onshore wind farm siting are investigated. Although our case studies show large trade-offs between the objective criteria of cost and landscape impact, small burdens on one criterion can significantly improve the other criteria. In addition, we demonstrate that contrary to many approaches for exclusive turbine siting, grid integration must be simultaneously optimized to avoid excessive costs or landscape impacts in the course of a wind farm project. Our novel problem formulation and the developed solver can assist planners in decision-making and help optimize wind farms in large regions in the future.

CFLOBDDs: Context-Free-Language Ordered Binary Decision Diagrams

This article presents a new compressed representation of Boolean functions, called CFLOBDDs (for Context-Free-Language Ordered Binary Decision Diagrams). They are essentially a plug-compatible alternative to BDDs (Binary Decision Diagrams), and hence are useful for representing certain classes of functions, matrices, graphs, relations, and so forth in a highly compressed fashion. CFLOBDDs share many of the good properties of BDDs, but—in the best case—the CFLOBDD for a Boolean function can be exponentially smaller than any BDD for that function . Compared with the size of the decision tree for a function, a CFLOBDD—again, in the best case—can give a double-exponential reduction in size . They have the potential to permit applications to (i) execute much faster and (ii) handle much larger problem instances than has been possible heretofore. We applied CFLOBDDs in quantum-circuit simulation and found that for several standard problems, the improvement in scalability, compared to BDDs, is quite dramatic. With a 15-minute timeout, the number of qubits that CFLOBDDs can handle are 65,536 for Greenberger-Horne-Zellinger, 524,288 for Bernstein-Vazirani, 4,194,304 for Deutsch-Jozsa, and 4,096 for Grover’s algorithm, besting BDDs by factors of 128×, 1,024×, 8,192×, and 128×, respectively.

Wasserstein Robust Classification with Fairness Constraints

Problem definition: Data analytics models and machine learning algorithms are increasingly deployed to support consequential decision-making processes, from deciding which applicants will receive job offers and loans to university enrollments and medical interventions. However, recent studies show these models may unintentionally amplify human bias and yield significant unfavorable decisions to specific groups. Methodology/results: We propose a distributionally robust classification model with a fairness constraint that encourages the classifier to be fair in the equality of opportunity criterion. We use a type-[Formula: see text] Wasserstein ambiguity set centered at the empirical distribution to represent distributional uncertainty and derive a conservative reformulation for the worst-case equal opportunity unfairness measure. We show that the model is equivalent to a mixed binary conic optimization problem, which standard off-the-shelf solvers can solve. We propose a convex, hinge-loss-based model for large problem instances whose reformulation does not incur binary variables to improve scalability. Moreover, we also consider the distributionally robust learning problem with a generic ground transportation cost to hedge against the label and sensitive attribute uncertainties. We numerically examine the performance of our proposed models on five real-world data sets related to individual analysis. Compared with the state-of-the-art methods, our proposed approaches significantly improve fairness with negligible loss of predictive accuracy in the testing data set. Managerial implications: Our paper raises awareness that bias may arise when predictive models are used in service and operations. It generally comes from human bias, for example, imbalanced data collection or low sample sizes, and is further amplified by algorithms. Incorporating fairness constraints and the distributionally robust optimization (DRO) scheme is a powerful way to alleviate algorithmic biases. Funding: This work was supported by the National Science Foundation [Grants 2342505 and 2343869] and the Chinese University of Hong Kong [Grant 4055191]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2022.0230 .

Extension of CMSA with a Learning Mechanism: Application to the Far from Most String Problem

One of the problems with exact techniques for solving combinatorial optimization problems is that they tend to run into problems with growing problem instance size. Nevertheless, they might still be very usefully employed, even in the context of large problem instances, as a sub-ordinate method within so-called hybrid metaheuristics. “Construct, Merge, Solve and Adapt” (Cmsa) is a hybrid metaheuristic technique that allows the application of exact methods to large-scale problem instances through intelligent instance reduction. However, Cmsa does not make use of an explicit learning mechanism. In this work, an algorithm called LEARN_CMSA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsc {Learn}\\_\ extsc {Cmsa}$$\\end{document} is presented for the application to the far from most string problem (FFMSP), which is an NP-hard combinatorial optimization problem from the field of string consensus problems. LEARN_CMSA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsc {Learn}\\_\ extsc {Cmsa}$$\\end{document} results from hybridization between Cmsa and a population-based algorithm. By means of this hybridization, explicit learning is introduced to Cmsa. Even though the FFMSP is a well-studied problem, LEARN_CMSA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsc {Learn}\\_\ extsc {Cmsa}$$\\end{document} achieves superior performance when compared to current state-of-the-art solvers.

Route and charging planning for electric vehicles: a multi-objective approach

ABSTRACT Electric vehicle (EV) travel planning is a complex task that involves optimizing both the routes and the charging sessions for EVs. Existing algorithms rely on single-objective optimization, which limits their ability to consider EV users’ multiple, often conflicting objectives. In this paper, we introduce a new, genuinely multi-objective approach to EV travel planning, which can find Pareto sets containing multiple EV travel plans optimized simultaneously for multiple objectives. We focus on the bi-objective optimization for travel time and cost. To our knowledge, our algorithm is the first to perform such a genuine multi-objective optimization on realistically large country-scale problem instances involving 12,000 charging stations. We implemented our approach into a fully operational prototype application and extensively evaluated it on real-world data. Our results show that our approach can achieve practically usable planning times with only a minor loss of solution quality despite the very high computational complexity of the problem.