An application of semi-Lagrangian relaxation to the generalised assignment problem

Online multi-dimensional generalized assignment problem with predictions

The generalized assignment problem with fixed processing times and uniform processing costs to minimize total cost

In practical supply chain operations, efficient order allocation significantly enhances the overall efficiency of the supply chain. Real production environments are plagued by numerous uncertainties, such as unpredictable customer orders, which greatly amplify the complexity of solving practical allocation problems. This study focuses on the problem of allocating orders to parallel machines with varying efficiencies under uncertain and high-dimensional conditions. To maximize the expected profit of order processing, a mathematical model for a high-dimensional stochastic optimization problem is developed, considering the uncertainty due to potential customer order cancellations in a real-world production. By integrating an intelligent optimization algorithm for the order assignment problem with a scenario generation approach, a novel framework for intelligent stochastic optimization is proposed. This framework employs an intelligent optimization algorithm suitable for the generalized assignment problem to search for improved solutions and utilizes the scenario generation method to produce the necessary scenarios for evaluating solutions in high-dimension. Experimental results demonstrate that the proposed approach effectively addresses the high-dimensional stochastic order allocation problem, outperforming the compared method in terms of efficiency and capability.

A real-time energy and cost efficient vehicle route assignment neural recommender system

In this paper, we develop a decision support system (DSS) aimed at solving a real-world supplier selection problem (SSP) for a global service provider (GSP) operating in the facility management (FM) industry. The GSP provides its customers with FM services, which are subcontracted to external suppliers selected on the basis of multiple criteria, like economic soundness, quality of service, capacity, and closeness. The SSP is formulated as a multi-objective generalized assignment problem, where the quality and the closeness of the selected suppliers are maximized, whereas a penalty produced by overcapacity assignments is minimized. The quality of each supplier is computed by applying a weighted sum method, resulting from a multi-criteria decision analysis in which the criteria weights are determined through an Analytic Hierarchy Process. The DSS is developed using a modular architecture with a relational database, a supplier evaluator, and a simulator, as well as an additional user-friendly interface. The simulator relies on a rolling horizon algorithm and three alternative configurations to assign contracts to suppliers. The effectiveness of the DSS is assessed by means of extensive computational experiments on historical data. The results show a significant average improvement of 25% compared to the solution adopted by the company.

Darboğaz çok kaynaklı genelleştirilmiş atama problemi (B-MRGAP) görevlerin, en büyük ajan yükünü enküçükleyecek şekilde ajanların kapasiteli kaynaklarına (dönemlerine) atanması problemidir. Bir firmanın temin etmesi gereken ürünleri (görevleri), birden çok dönemi göz önünde bulunduracak şekilde yan sanayilerine ataması problemi B-MRGAP’a bir örnektir. Bu problemde, talep edilen ürün miktarlarındaki her türlü değişim, görevlerin yan sanayilerdeki kaynak tüketim miktarlarını da değiştirecektir. Pek çok sektörde, üretim miktarlarının değişmesi sık yaşanan bir durum olduğundan kaynak tüketim miktarlarının deterministik değil, stokastik ele alınması daha gerçekçi çözümlere ulaşılmasını sağlayacaktır. Bu çalışmada B-MRGAP’da kaynak tüketim miktarları stokastik olarak ele alınmıştır. Bu problemin çözümü için iki aşamalı stokastik programlama modeli geliştirilmiştir. Önerilen yöntemin performansı rassal türetilen test problemleri kullanılarak gösterilmiştir. Test sonuçları incelendiğinde küçük boyutlu problemlerde bile, problemi stokastik ele almanın katkı sağladığı görülmüştür. Ayrıca ajan sayısı, görev sayısı ve kaynak tüketimi değişkenliği arttıkça sağlanan katkının da arttığı ortaya konmuştur.

On improvements of multi-objective branch and bound

It is a critical issue to allocate redundancy to critical smart grid infrastructure for disaster recovery planning. In this study, a framework to combine statistical prediction methods and optimization models for the optimal redundancy allocation problem is presented. First, statistical simulation methods to identify critical nodes of very large-scale smart grid infrastructure based on the topological features of embedding networks are developed, and then a linear integer programming model based on generalized assignment problem (GAP) for the redundancy allocation of critical nodes in smart grid infrastructure is presented. This paper aims to contribute to the field by employing a general redundancy allocation problem (GRAP) model from high-order nonlinear to linear model transformation. The model is specifically implemented in the context of smart grid infrastructure. The innovative linear integer programming model proposed in this paper capitalizes on the logarithmic multiplication property to reframe the inherently nonlinear resource allocation problem (RAP) into a linearly separable function. This reformulation markedly streamlines the problem, enhancing its suitability for efficient and effective solutions. The findings demonstrate that the combined approach of statistical simulation and optimization effectively addresses the size limitations inherent in a sole optimization approach. Notably, the optimal solutions for redundancy allocation in large grid systems highlight that the cost of redundancy is only a fraction of the economic losses incurred due to weather-related outages.

Optimization of Harvesting Priority of Sugarcane Farms by the Generalized Assignment Problem

Approximation algorithms for scheduling parallel machines with an energy constraint in green manufacturing

A three-phase matheuristic algorithm for the multi-day task assignment problem

The performance of optimization algorithms, and consequently of AI/machine learning solutions, is strongly influenced by the setting of their hyperparameters. Over the last decades, a rich literature has developed proposing methods to automatically determine the parameter setting for a problem of interest, aiming at either robust or instance-specific settings. Robust setting optimization is already a mature area of research, while instance-level setting is still in its infancy, with contributions mainly dealing with algorithm selection. The work reported in this paper belongs to the latter category, exploiting the learning and generalization capabilities of artificial neural networks to adapt a general setting generated by state-of-the-art automatic configurators. Our approach differs significantly from analogous ones in the literature, both because we rely on neural systems to suggest the settings, and because we propose a novel learning scheme in which different outputs are proposed for each input, in order to support generalization from examples. The approach was validated on two different algorithms that optimized instances of two different problems. We used an algorithm that is very sensitive to parameter settings, applied to generalized assignment problem instances, and a robust tabu search that is purportedly little sensitive to its settings, applied to quadratic assignment problem instances. The computational results in both cases attest to the effectiveness of the approach, especially when applied to instances that are structurally very different from those previously encountered.

The emerging paradigm of edge computing envisions to overcome the shortcomings of cloud-centric Internet of Things (IoT) by providing data processing and storage capabilities closer to the source of data. Accordingly, IoT edge devices, with the increasing demand of computation workloads on them, are prone to failures more than ever. Hard failures in hardware due to aging and reliability degradation are particularly important since they are irrecoverable, requiring maintenance for the replacement of defective parts, at high costs. In this article, we propose a novel dynamic reliability management (DRM) technique for multigateway IoT edge computing systems to mitigate degradation and defer early hard failures. Taking advantage of the edge computing architecture, we utilize gateways for computation offloading with the primary goal of maximizing the battery lifetime of edge devices, while satisfying the Quality of Service (QoS) and reliability requirements. We present a two-level management scheme, which work together to 1) choose the offloading rates of edge devices; 2) assign edge devices to gateways; and 3) decide multihop data flow routes and rates in the network. The offloading rates are selected by a hierarchical multitimescale distributed controller. We assign edge devices by solving a bottleneck generalized assignment problem (BGAP) and compute optimal flows in a fully distributed fashion, leveraging the subgradient method. Our results, based on real measurements and trace-driven simulation, demonstrate that the proposed scheme can achieve a similar battery lifetime and better QoS compared to the state-of-the-art approaches while satisfying reliability requirements, where other approaches fail by a large margin.

Sensitivity analysis in general deals with the question of how changes in input data of a model affect its output data. In the context of optimization problems, such an analysis could, for instance, address how changes in capacity constraints affect the optimal solution value. Although well established in the domain of linear programming, sensitivity analysis approaches for combinatorial optimization problems are model-specific, limited in scope and not applicable to practical optimization problems. To overcome these limitations, Schulte et al. developed the concept of bilevel innovization. By using evolutionary bilevel optimization in combination with data mining and visualization techniques, bilevel innovization provides decision-makers with deeper insights into the behavior of the optimization model and supports decision-making related to model building and configuration. Originally introduced in the field of evolutionary computation, most recently bilevel innovization has been proposed as an approach to sensitivity analysis for combinatorial problems in general. Based on previous work on bilevel innovization, our paper illustrates this concept as a tool for sensitivity analysis by providing a comprehensive analysis of the generalized assignment problem. Furthermore, it is investigated how different algorithms for solving the combinatorial problem affect the insights gained by the sensitivity analysis, thus evaluating the robustness and reliability of the sensitivity analysis results.

Dimension reduction for a multi-resource general assignment problem by decomposable costs for a vehicle compound

Mixed-Integer Linear Programming (MILP) plays an important role across a range of scientific disciplines and within areas of strategic importance to society. The MILP problems, however, suffer from combinatorial complexity. Because of integer decision variables, as the problem size increases, the number of possible solutions increases super-linearly thereby leading to a drastic increase in the computational effort. To efficiently solve MILP problems, a “price-based” decomposition and coordination approach is developed to exploit 1. the super-linear reduction of complexity upon the decomposition and 2. the geometric convergence potential inherent to Polyak’s stepsizing formula for the fastest coordination possible to obtain near-optimal solutions in a computationally efficient manner. Unlike all previous methods to set stepsizes heuristically by adjusting hyperparameters, the key novel way to obtain stepsizes is purely decision-based: a novel “auxiliary” constraint satisfaction problem is solved, from which the appropriate stepsizes are inferred. Testing results for large-scale Generalized Assignment Problems demonstrate that for the majority of instances, certifiably optimal solutions are obtained. For stochastic job-shop scheduling as well as for pharmaceutical scheduling, computational results demonstrate the two orders of magnitude speedup as compared to Branch-and-Cut. The new method has a major impact on the efficient resolution of complex Mixed-Integer Programming problems arising within a variety of scientific fields.

The parallel AGV scheduling problem with battery constraints: A new formulation and a matheuristic approach

Online generalized assignment problem with historical information

This study considers the team recommendation problem as a generalized assignment problem. Firstly, a formal description of the team recommendation problem is given; secondly, a team-recommended generalized assignment model (TRGAM) is established based on the work ability value of alternative members, the comprehensive work ability value of the team as the core concern index, the importance weight of team tasks and the energy allocation weight of team members as the fusion strategy of the data; thirdly, a solution method for the standard case of TRGAM is designed using the enumeration method and Hungarian algorithms (BEM⊕HM–TRGAMs) as local computational tools; fourthly, the alternative member set refinement methods and standardization measures for TRGAM are given; finally, BEM⊕HM–TRGAMs are analyzed using specific arithmetic examples. The theoretical analysis and experimental results show that TRGAM has good structural features and interpretability and BEM⊕HM–TRGAMs can effectively solve the TRGAM solving problem.