Exact Solution Method Research Articles

Beyond kemeny rank aggregation: A parameterizable-penalty framework for robust ranking aggregation with ties

Rank Aggregation has ubiquitous applications in operations research, artificial intelligence, computational social choice, and various other fields. Interest in this problem has increased due in part to the need to consolidate lists of rankings and scores output by different decision-making processes and algorithms. Although most attention has focused on the variant of this problem induced by the Kemeny-Snell distance, other robust rank aggregation problems have been proposed. This work delves into the rank aggregation problem under the generalized Kendall-tau distance —a parameterizable-penalty distance measure for comparing rankings with ties— which contains Kemeny aggregation as a special case. First, it derives exact and heuristic solution methods. Second, it introduces a social choice property (GXCC) that encloses existing variations of the Condorcet criterion as special cases, thereby expanding this seminal social choice concept beyond Kemeny aggregation for the first time. GXCC offers both computational and theoretical advantages. In particular, GXCC may help to divide the original problem into smaller subproblems, while still ensuring that solving them independently yields the optimal solution to the original problem. Experiments on two benchmark datasets conducted herein show that the featured exact and heuristic solution methods can benefit from GXCC. Finally, this work derives new theoretical insights into the effects of the generalized Kendall-tau distance penalty parameter on the optimal ranking and on the proposed social choice property.

Cost allocation of cooperative autonomous truck platooning: Efficiency and stability analysis

This study investigates the cost allocation of cooperative autonomous truck (AT) platooning among carriers. Motivated by the fuel consumption saving from truck platooning, carriers can collaborate for creating more platooning opportunities in an alliance. The formation of carrier alliance is associated with two key conditions: (i) efficiency: the total cost is allocated to each carrier without a budget deficit, and (ii) stability: all carriers find it beneficial to stay in the grand alliance and do not form sub-alliance. Since an alliance satisfying these two conditions may not always exist, we aim to find a cost allocation such that the violation of efficiency and stability conditions is minimized. We first propose a cooperative AT platooning problem for a trade-off between fuel consumption savings and schedule deviation cost. Then, we model the problem as a cooperative AT platooning game and formulate cost allocation models. The exact row-generation solution method is developed to computationally calculate the cost allocation. Extensive numerical experiments demonstrate the properties of proposed models and the effectiveness of solution methods. The results show that the developed row-generation solution method can solve the instances of up to 100 requests and 20 carriers within a two-hour time limit, and the schedule deviation coefficients significantly impact the performance of optimal cost allocation.

Introduction and verification of FEDM, an open-source FEniCS-based discharge modelling code

This paper introduces the finite element discharge modelling (FEDM) code, which was developed using the open-source computing platform FEniCS (https://fenicsproject.org). Building on FEniCS, the FEDM code utilises the finite element method to solve partial differential equations. It extends FEniCS with features that allow the automated implementation and numerical solution of fully coupled fluid-Poisson models including an arbitrary number of particle balance equations. The code is verified using the method of exact solutions and benchmarking. The physically based examples of a time-of-flight experiment, a positive streamer discharge in atmospheric-pressure air and a low-pressure glow discharge in argon are used as rigorous test cases for the developed modelling code and to illustrate its capabilities. The performance of the code is compared to the commercial software package COMSOL Multiphysics® and a comparable parallel speed-up is obtained. It is shown that the iterative solver implemented by FEDM performs particularly well on high-performance compute clusters.

Integration of blockchain-enabled closed-loop supply chain and robust product portfolio design

Blockchain technology is one of the latest financial concepts influencing international trades, which contributes to speeding the supply chains by managing faster and more accurate financial transactions. Moreover, the product portfolio is highly effective on the financial flow of the supply chain. Accordingly, in this research, a comprehensive framework is proposed to design a blockchain-enabled closed-loop supply chain (BCSC), considering the role of the product portfolio. First, a mathematical model for robust product portfolio design is proposed. Next, a closed-loop supply chain network is designed where the financial flow via blockchain is of concern. To optimize this supply chain, the change in equity, as well as satisfaction from the blockchain network, is maximized. An exact solution method using GAMS software is applied to optimize the proposed mathematical model. The results obtained by implementation and analysis of this proposed framework indicate that by designing a product portfolio based on a robust model, BCSC would achieve the ideal value for its financial indexes, the change in equity in specific. Comparison of this newly proposed framework with the integrated portfolio-supply chain model reveals a 0.33% average error and a 1.5% reduction in lost revenue. It is concluded that this proposed framework assists supply chain managers in reducing their inaccurate decisions in both the physical and financial flow considerably.

An analytical method for finding exact solutions of a nonlinear partial differential equation arising in electrical engineering

In this investigation, we aim to investigate the novel exact solutions of nonlinear partial differential equations (NLPDEs) arising in electrical engineering via the -expansion method. New acquired solutions are kink, particular kink, bright, dark, periodic combined-dark bright and combined-dark singular solitons, and hyperbolic functions solutions. The achieved distinct types of solitons solutions contain critical applications in engineering and physics. Numerous novel structures (3D, contour, and density plots) are also designed by taking the appropriate values of involved parameters. These solutions express the wave show of the governing models, actually.

A Meshfree Approach Based on Moving Kriging Interpolation for Numerical Solution of Coupled Reaction-Diffusion Problems

In this paper, a meshfree approach based on moving kriging interpolation is presented for numerical solution of coupled reaction-diffusion problems. The proposed approach is developed based upon local collocation using moving Kriging shape function. It is truly meshless and having the Kronecker delta property for accurate imposition of boundary conditions. In the proposed model, the weight function is used with correlation parameter treated as the model internal length factor. This produces a local moving kriging method with improved accuracy together with an ease to choose the weight function factor. The method can hence be used in an efficient manner without cumbersome effort for choosing its parameter. The meshless approach is presented for the first time for numerical solution of reaction-diffusion systems. Problems of Turing system and pattern formation in several 2D domains are solved in this study. The efficacy and accuracy of the proposed method for the reaction-diffusion systems in different problem domains are presented in comparison to available exact solution and other numerical methods. It is found that the present method is accurate and effective as a computational procedure for solving reaction-diffusion problems.

Hybridizing local searching with genetic algorithms for the job sequencing and tool switching problem with non-identical parallel machines

The job sequencing and tool switching problem (SSP) is an old and highly studied problem. However, the SSP with non-identical parallel machines (SSP-NPM) is a new generalization of this problem. Since the SSP-NPM has been very recently introduced, the number of solution methods for this problem is low. Additionally, exact solution methods are mostly insufficient to find a good solution within a reasonable computational time since this problem is NP-hard. Therefore, heuristic approaches are more appropriate, especially when solving large-size problems. Thus, this study presents a new hybrid algorithm that is a combination of a genetic algorithm (GA) and a local search (LS) technique. Both of these methods are greatly preferred by authors for solving job scheduling problems. Thereby, this study combines their strengths to solve the SSP-NPM. Two versions of the proposed method are tested with benchmark instances. These versions differ in terms of their tool optimization policies: the first uses the well-known “keep tool needed soonest” (KTNS) policy, while the second uses the “randomly remove tool” (RRT) policy. Computational experiments showed that combining some of the features of GA and LS methods for the SSP-NPM contributed greatly to the quality of the solution. Two versions of the proposed hybrid method were compared to a mixed-integer programming model and several schemes of an iterated local search algorithm. Our computational results show that both versions of the proposed hybrid method were significantly better than the other methods, and were able to find the solutions within a reasonable computational time.

The follower competitive facility location problem under the nested logit choice rule

Recently, more realistic customer choice rules based on the Multinomial Logit have been proposed for the follower competitive facility location problem, together with efficient exact solution methods based on cut generation approaches. We address this problem in the case in which a new chain, the entrant, decides to locate some stores in a market where there are already incumbent chains offering substitute products, which differ from the entrant's product in secondary features. The entrant's stores are very similar to each other, and this is also the case for the incumbent chains. In this case, for a given customer, purchases made at the stores of one of the chains are correlated, given the similitude between these stores. The Multinomial Logit rule does not capture this correlation. We propose using a Nested Logit rule which does capture this correlation and, in addition, represents a sequential decision process by the customer, who first chooses the chain and then the store. We prove the concavity of the objective function in the problem and find exact solutions using Branch and Cut over a generalized linear reformulation of the problem and four different types of cuts: submodular and an improvement of these, outer-approximation, and a set of new cuts. Our results show locations that fit better the intuition and practice. Furthermore, our computational times improve in many cases upon the known results for similar problems.

Aggregating disjoint partial sub-orders – an internal logistics application

The problematic addressed in this work concerns an internal logistics issue that arises in warehousing. It first concerns the aggregation of a several ordered flows of loads (cartons, totes, containers, etc.) into a single flow, called the load sequencing problem. Then, this flow should be injected into the system at a maximal throughput, which gives the load injection problem. From the theoretical perspective, the load sequencing problem belongs to the class of partial-order aggregation problems, known to be NP-Hard. We describe a use-case application in logistics and formulate it in mathematical terms as a specific partial-order aggregation problem, namely disjoint partial sub-orders aggregation. We then present two exact solution methods in detail, one based on integer linear programming and the other using dynamic programming combined with a Branch & Cut scheme. All methods perform very well for randomly generated industrial instances. At the end, we provide a heuristic based on the dynamic programming algorithm. This heuristic is implemented for industrial use and gives near-optimal solutions in a very short computation time. The load injection problem falls in the category of scheduling problem (Job shop problem). In practice, this comes to compute the injection dates of loads in the collector with goal of ensuring a maximal debit exit flow with respect to the capacity of the system. We provide the formula for the injection date which achieves maximal debit exit flow. With respect to the application in hand, the proposed method outperforms the existing used method in terms of flow management and brings in practice a significant increase (up to 20%) of a number of loads proceeded for the same amount of time. Our findings are supported by numerical results.

A general purpose exact solution method for mixed integer concave minimization problems

In this article, we discuss an exact algorithm for solving mixed integer concave minimization problems. A piecewise inner-approximation of the concave function is achieved using an auxiliary linear program that leads to a bilevel program, which provides a lower bound to the original problem. The bilevel program is reduced to a single level formulation with the help of Karush–Kuhn–Tucker (KKT) conditions. Incorporating the KKT conditions lead to complementary slackness conditions that are linearized using BigM, for which we identify a tight value for general problems. Multiple bilevel programs, when solved over iterations, guarantee convergence to the exact optimum of the original problem. Though the algorithm is general and can be applied to any optimization problem with concave function(s), in this paper, we solve two common classes of operations and supply chain problems; namely, the concave knapsack problem, and the concave production-transportation problem. The computational experiments indicate that our proposed approach outperforms the customized methods that have been used in the literature to solve the two classes of problems by an order of magnitude in most of the test cases.

Multiple allocation hub location with service level constraints for two shipment classes

In this paper, we study a hub network design problem arising in the context of a third-party logistics (3PL) service provider, which acts as an intermediary between shippers and carriers. A 3PL service provider usually caters to different classes of shipments that require different levels of service, e.g. two-day delivery, next-day delivery etc. We, therefore, study the problem under stochastic demand from two classes of shipments, with one class receiving priority over the other in service at the hubs to maintain the different service levels required by them. To this end, we present two models for designing a capacitated hub network with a service level constraint, defined using the distribution of time spent at hubs, for each shipment class. The models seek to design the hub network at the minimum total cost, which includes the total fixed cost of equipping open hubs with sufficient processing capacity and the variable transportation costs. The network of hubs, given their locations, is thus modeled as spatially distributed priority queues. The resulting model is challenging to solve, for which we propose a cutting plane-based exact solution method.

Metaheuristic optimizers to solve multi-echelon sustainable fresh seafood supply chain network design problem: A case of shrimp products

Seafood products are sought-after among communities all over the globe and are the main sources of essential nutrition for humans. Recently, the seafood supply chain networks have encountered obstacles that new sustainability regulations and the pandemic have brought forward. In this study, a novel supply chain network is developed for fresh seafood, considering sustainability aspects, to ideally balance the financial aspect of the network while enhancing the recycling of waste products. Moreover, four metaheuristics are employed to conquer the computational complexity of exact solution methods. To evaluate the performance of the algorithms in addressing the complexity of the proposed seafood supply chain model, some numerical examples in three different scales are designed. The obtained results from metaheuristic optimizers are assessed based on five effective measures. To facilitate the statistical analysis process, each measure is normalized using the relative deviation index indicator. According to the results obtained from the implementation of metaheuristic algorithms, it can be concluded that the multi-objective grey wolf and multi-objective golden eagle optimizers outperform the other two solution methods in terms of quality of solutions. Therefore, they can be applied efficiently in solving real-world seafood supply chain network problems.

An exact algorithm for linear integer programming problems with distributionally robust chance constraints

The distributionally robust chance constrained integer programming problems are notoriously hard to solve due to the stochastic feature and the discrete nature of integer variables. In this paper, an exact solution method is developed for linear integer programming problems with the distributionally robust chance constraint. By exploring the geometric properties, some domain cut techniques based on feasible points and infeasible points are derived. Thus cut off some sub-boxes which do not contain any optimal solution and the optimality gap is reduced successively in the solution iterations. Then the optimal solution will be found in a finite number of iterations. Encouraging computational results are also reported in the paper.

Responsiveness to sudden disturbances in manufacturing through dynamic job shop scheduling using Quantum Annealing

An efficient production planning and control is inevitable for the economic operation of a manufacturing system. As an essential part of production planning and control, process scheduling aims to assign processes to the available resources of a manufacturing system under consideration of its objectives. This forms an optimization problem also known as job shop scheduling which can be solved with computer aided techniques. Exact solution methods are only practical up to a certain number of functional units and processes, therefore, approximation methods are used in industry. However, as the problem size increases, the computational solving time increases significantly and the solution quality decreases in equal measure. In order to react to the current effects of global crises, such as disruptions in supply chains, approaches for fast and efficient rescheduling are needed. A dynamic shop job scheduling approach using Quantum Annealing bears the potential to close this research gap. Previous work has shown that Quantum Annealing is able to solve static job shop scheduling problems within seconds while finding good solutions. However, in a flexible environment such as a manufacturing system, the static approach is not suitable for process scheduling. Therefore, a dynamic Quantum Annealing based approach for job shop scheduling with consideration of machine breakdowns and new job arrivals is proposed. The approach monitors a manufacturing system and reacts to changes in the job pool or availabilities in functional units with rescheduling. The method is tested with several use cases involving small and large-scale problems and is compared with a simulated annealing approach. Thereby, the Quantum Annealing based computations show better results regarding solution quality and computing time. Moreover, the dynamic approach bears the potential for industrial application, especially as a supplement to a conventional advanced planning system.

Optimizing inland port scale and function decisions: A bilevel programming approach

With the implementation of the Belt and Road Initiative, the inland ports planning is receiving more and more attention. In this work, we aim to determine the scale and function of different potential inland ports in a certain region while considering the cargo flow allocation schemes for the inland ports and seaports in cross-border trade. Unlike previous studies, we consider the dynamic interaction between local government and manufacturing enterprises in the inland port planning process. Based on this, we formulate a bilevel programming model for the considered inland port planning problem, where the upper-level focuses on the local government and the lower-level concentrates on the manufacturing enterprise. To solve the proposed model, we develop a hybrid heuristic algorithm by combining a genetic algorithm and an exact solution method. Furthermore, we conduct a case study of the inland ports planning for the Huaihai Economic Zone in China to verify the applicability of the proposed model and algorithm. The computational results demonstrate that the proposed optimization approach can effectively increase the cross-border transportation market share of inland ports within a limited investment amount and reduce the competition among these inland ports. Our case study also provides valuable management insights on inland port planning in terms of manufacturing enterprises weights, investment limit amount, scale effect, and cargo value weights.

Numerical simulations of time-fractional PDES arising in mathematics and physics using the local Meshless differential quadrature method

The numerical solution of the 2-D time-fractional Sobolev equations is approximated using an efficient local differential quadrature method, in this paper. The time-fractional part of the model equations uses the Liouville-Caputo fractional derivative technique, however, the recommended meshless method is employed for the space derivatives. Test problems are used to undertake numerical experiments. In order to evaluate the effectiveness and accuracy of the suggested meshless method, we compared our outcomes with the exact solution and numerical methods presented in more recent literature. This comparison showed that the proposed method is more efficient computationally and yields excellent performance.

The data-driven time-dependent orienteering problem with soft time windows

In this paper, we study an extension of the orienteering problem where travel times are random and time-dependent and service times are random. Additionally, the service at each selected customer is subject to a soft time window; that is, violation of the window is allowed but subject to a penalty that increases in the delay. A solution is a tour determined before the vehicle departs from the depot. The objective is to maximize the sum of the collected prizes net of the expected penalty. The randomness of the travel and service times is modeled by a set of scenarios based on historical data that can be collected from public geographical information services. We present an exact solution method for the problem based on a branch-and-bound algorithm enhanced by a local search procedure at the nodes. A numerical experiment demonstrates the merits of the proposed solution approach. This study is the first to consider an orienteering problem with stochastic travel times and soft time windows, which are more relevant than hard time windows in stochastic settings.

Reformulation and exact solution method for <i>seru</i> scheduling problem with learning effect and job deterioration

Reformulation and exact solution method for <i>seru</i> scheduling problem with learning effect and job deterioration

Reformulation and exact solution method for seru scheduling problem with learning effect and job deterioration

Reformulation and exact solution method for seru scheduling problem with learning effect and job deterioration

Combinatorial Optimization Approach to Client Scheduling for Federated Learning

For machine learning in situations where data is scattered and cannot be aggregated, federated learning, in which aggregators and agents send and receive model parameters, is one of the most promising methods. The scheduling problem of deciding which agents to communicate with has been studied in various ways, but it is not easy to solve due to its combinatorial optimization nature. In this letter, we attempt to solve this scheduling problem using combinatorial optimization theory. Specifically, we propose an efficient exact solution method based on dynamic programming and a greedy method whose superiority is confirmed by numerical examples. We also discuss the applicability of the proposed methods to a more dynamic and uncertain environment.