Linear Programming Formulation Research Articles

Assessing and Improving Automated Viewpoint Planning for Static Laser Scanning Using Optimization Methods

Abstract. The preparation of laser scanning missions is important for efficiency and data quality. Furthermore, it is a prerequisite for automated data acquisition, which has numerous applications in the built environment, including autonomous inspections and monitoring of construction progress and quality criteria. The scene and potential scanning locations can be discretized to facilitate the analysis of visibility and quality aspects. The remaining mathematical problem to generate an economic scan strategy is the Viewpoint Planning Problem (VPP), which asks for a minimum number of scanning locations within the given scene to cover the scene under pre-defined requirements. Solutions for this problem are most commonly found using heuristics. While these efficient methods scale well, they cannot generally return globally optimal solutions. This paper investigates the VPP based on a problem description that considers quality-constrained visibility in 3D scenes and suitable overlaps between individual viewpoints for targetless registration of acquired point clouds. The methodology includes the introduction of a preprocessing method designed to simplify the input data without losing information about the problem. The paper details various solution methods for the VPP, encompassing conventional heuristics and a mixed-integer linear programming formulation, which is solved using Benders decomposition. Experiments are carried out on two case study datasets, varying in specifications and sizes, to evaluate these methods. The results show the actual quality of the obtained solutions and their deviation from optimality (in terms of the estimated optimality gap) for instances where exact solutions can not be achieved.

Mathematical programming models for order picking in warehouses with decoupling of picker and cart

As a special Travelling Salesman Problem (TSP), the Single-Picker Routing Problem (SPRP) in warehouses is of important theoretical and practical significance. In manual order picking, the items are usually picked up by a picker with a cart. To speed up the picking process, the picker is allowed to stop the cart to pick up the items individually and return to the location of the cart. This paper proposes a mixed integer linear programming formulation for an order picking problem with the decoupling of the picker and the cart in a multi-block warehouse, where the picker capacity is at most four. And based on this model, order batching problem is also analysed. Through numerical experiments, the cost of above decoupling problems is computed under different settings of the speed ratio and the capacity of the picker while he/she is travelling alone. The results indicate how the decoupling of picker and cart leads to cost reduction. Our model shows good performance for orders of small and medium scale and hence has great potential to improve the order picking operation which is executed by decoupling containers and robots/vehicles in modern digital warehouse systems.

Optimizing modular equipment in the design of multi-product reconfigurable production lines

This work addresses the problem of the design and balancing of a modular multi-product line in a reconfigurable environment. The study emphasizes the importance of modularity in the reconfigurable manufacturing systems (RMS), which allows fast, efficient, and cost-effective adaptation to changes by rearranging, moving, or removing modules. The line consists of a fixed number of modular machines arranged linearly and connected by a material handling system. Each machine has a limited number of slots for modules. The line can handle several product types per batch, and each batch requires a specific line configuration to be produced. The objective consists in identifying the minimum number of modules needed and their arrangement in different configurations to produce each product type. To solve this problem, a compact integer linear programming (ILP) formulation is initially investigated. Then an ILP reformulation, based on a decomposition approach, as well as a heuristic that uses this ILP reformulation are developed. The results demonstrate the effectiveness of the proposed methods.

Ride-Hailing Matching with Uncertain Travel Time: A Novel Interval-Valued Fuzzy Multi-Objective Linear Programming Approach

This study introduces an innovative approach to tackle multi-objective linear programming (MOLP) problems amidst uncertainty, employing interval-valued fuzzy numbers. The method is tailored to resolve ride-hailing matching challenges encompassing uncertain travel times. Findings reveal that managing uncertainty parameters within interval-valued fuzzy MOLP is achieved through strategic reformulations, focusing on constraint coefficients, resulting in streamlined linear programming formulations conducive to solution simplicity. The efficacy of the proposed model in efficiently handling ride-hailing matching quandaries is demonstrated. Moreover, this study delves into the prospective applications of the developed method, including its potential for generalization to address non-linear programming (NLP) issues pertinent to the ride-hailing domain. This research advances decision-making processes under uncertainty and paves the way for broader applications beyond ride-hailing.

Cost minimization of multi-class demands groomed over multi-rate OTN interfaces considering WDM-layer constraints

This paper introduces a practical comprehensive approach to optimize the cost of installed Optical Transport Network (OTN) interfaces, as well as the required number of wavelengths in the substrate Wavelength Division Multiplexing (WDM) optical network. The approach assumes grooming variable-bit-rate traffic demands on multi-rate OTN interfaces. We propose an Integer Linear Programming (ILP) formulation to address the combined problem of OTN interface deployment, virtual-network formation, traffic grooming on the established distinct-capacity virtual paths, and virtual network embedding on the WDM physical substrate. The presented model focuses on mitigating the capital expenditure required to deploy OTN interfaces, usually the most costly element in the network, as well as minimizing the required number of wavelengths in the Routing and Wavelength Assignment (RWA) problem, contributing to the overall reduction in network costs and ensuring open capacity for future expansions. As the RWA problem is NP-hard and involves significant computational costs, we also propose a multi-step heuristic approach to tackle larger network instances more efficiently. In this approach, the optimization steps for the OTN design and the RWA solutions are conducted independently. For the OTN-layer planning, the optimum ILP formulation (OTN-ILP) is maintained, so that the optimum solution for the cost of installed interfaces on the OTN layer is guaranteed. The RWA problem is proposed through either an ILP formulation (RWA-ILP) or a heuristic approach. The RWA-ILP model can find the same or slightly superior number of wavelengths compared to the optimum solution of the Integrated ILP formulation, but it can provide results in reasonable times only for small networks. On the other hand, the heuristic RWA is able to run any network size, but it requires more wavelengths compared to the RWA-ILP model.

A blockchain-based optimal peer-to-peer energy trading framework for decentralized energy management with in a virtual power plant: Lab scale studies and large scale proposal

The integration of distributed energy resources (DERs) such as wind, solar, batteries, etc. into the grid presents opportunities as well as challenges with regard to efficient coordination and trading. Virtual power plants (VPPs) have emerged as an important paradigm for aggregating and managing numerous DERs. This paper proposes a decentralized blockchain-based peer-to-peer (P2P) multilayer energy trading framework to facilitate optimized coordination of DERs within a VPP context. A control center, prosumers, and service operators constitute the model’s multi-layered architecture. Profits from feed-in tariffs, ancillary services, and P2P sales are optimized for revenue while expenses are minimized using a mixed-integer linear programming formulation. Smart contracts enable prosumers to trade energy units in the Ethereum blockchain with ease via a participatory web platform. The effectiveness of the framework in synchronizing power supply and demand within the VPP by coordinating the charging and discharging of storage systems in accordance with consumption patterns is demonstrated through performance evaluation. In contrast to conventional centralized architectures, the proposed framework utilized decentralized architecture efficiently consolidates and optimizes distributed energy resources (DERs) to improve grid stability and renewable energy utilization.

Management of a post-disaster emergency scenario through unmanned aerial vehicles: Multi-Depot Multi-Trip Vehicle Routing with Total Completion Time Minimization

One of the most valuable and promising applications for Unmanned aerial vehicles (UAVs) is in natural disaster management, where these aircraft can operate autonomously without any need for human intervention during their flights.In this paper, we foster the interface of Operational Research with computer science in general and sensor networking in particular by focusing on managing a post-disaster emergency scenario where the use of a fleet of UAVs helps rescue teams identify people needing help inside an affected area. We model this situation as an original graph theoretical problem called Multi-Depot Multi-Trip Vehicle Routing Problem with Total Completion Time minimization (MDMT-VRP-TCT). The main novelty of the MDMT-VRP-TCT is the combination of the following three features: multi-depot, multi-trip, and completion time minimization.We propose a mixed-integer linear programming (MILP) formulation, develop a matheuristic framework to address large instances, and present an extended set of experiments to test the performance of the proposed matheuristic: first, we compare the matheuristic with the MILP formulation on a set of small instances (up to 30 nodes); then, we compare our matheuristic with two heuristics from networking literature, showing that it outperforms the existing algorithms.

Integer Linear Programming Models and Greedy Heuristic for the Minimum Weighted Independent Dominating Set Problem

This paper explores the Minimum Weighted Independent Dominating Set Problem and proposes novel approaches to tackle it. Namely, two integer linear programming formulations and a fast greedy heuristic as an alternative approach are proposed. Extensive computational experiments are conducted to evaluate the performance of these approaches on the established set of benchmark instances for the problem. The obtained results demonstrate that the introduced integer linear programming models are able to achieve optimal solutions on all instances with 100 nodes and significantly outperform existing exact methods on numerous other instances. Additionally, the greedy heuristic exhibits superior performance compared to competing greedy heuristics, particularly on random graphs. These findings suggest promising directions for future research, including the integration of these methods into hybrid algorithms or metaheuristic frameworks.

A logistics provider’s profit maximization facility location problem with random utility maximizing followers

We introduce a strategic decision-making problem faced by logistics providers (LPs) seeking facility location decisions that lead to profitable operations. The profitability depends on the revenue generated through agreements with shippers, and the costs arising when satisfying these agreements. The latter depends, in turn, on the service levels and characteristics of the shippers’ customers. However, at a strategic level, the LP has imperfect information thereof.We propose a stochastic bilevel formulation where a given LP (leader) anticipates the decisions of shippers (followers) arising from a random utility maximization model. Using a sample average approximation and properties of the associated optimal solutions, we propose a heuristic that can compute high-quality solutions. It is based on a reduced single-level mixed integer linear programming formulation that can be solved by a general-purpose solver after a preprocessing phase. We can quickly identify situations that lead to zero expected profit for the LP. Experimental results show that expected profit highly depends on shippers’ price sensitivities. Underestimating price sensitivities can lead to an overestimation of the expected profit.

On the [formula omitted]-gain of 2D positive Roesser systems with bounded time-varying delays

The focus of this article is on ℓ∞-gain analysis and the observer design, which are applicable to linear two-dimensional (2D) positive systems (PSs) featuring bounded time-varying delays. Firstly, a computation method for the exact ℓ∞-gain value of linear 2D PSs with no delay and constant delays is presented. Secondly, by constructing the comparison results with the constant delayed systems, it is found that the ℓ∞-gain of the addressed system is exactly that of a constant delayed system where the constant delay is the upper bound of the time-varying delays. To maintain the asymptotic stability and optimal ℓ∞-gain performance, necessary and sufficient conditions in the form of Linear Programming (LP) are created. Thirdly, a positive observer is further designed to ensure that the residual system remains asymptotically stable and has the optimal ℓ∞-gain performance, but only an algorithm for obtaining a sufficient solution is given. Finally, two examples are given to show that the above findings are correct.

The Continuous Time-Resource Trade-off Scheduling Problem with Time Windows

We introduce a variant of the cumulative scheduling problem (CuSP) characterized by continuous modes, time windows, and a criterion that involves safety margin maximization. The study of this variant is motivated by the Geospatial based Environment for Optimisation Systems Addressing Fire Emergencies Horizon 2020 Project, which is devoted to the design of evacuation plans in the face of natural disasters and more specifically, wildfire. People and goods have to be transferred from endangered places to safe places, and evacuation planning consists of scheduling evacuee moves along precomputed paths under arc capacities and deadlines. The resulting model is relevant in other contexts, such as project or industrial process scheduling. We consider here several formulations of the continuous time-resource trade-off scheduling problem (CTRTP-TW) with a safety maximization objective. We establish a complete complexity characterization distinguishing polynomial and NP-hard special cases depending on key parameters. We show that the problem with fixed sequencing (i.e., with predetermined overlap or precedence relations between activities) is convex. We then show that the preemptive variant is polynomial, and we propose lower and upper bounds based on this relaxation. A flow-based mixed-integer linear programming formulation is presented, from which a branch-and-cut exact method and an insertion heuristic are derived. An exact dedicated branch-and-bound algorithm is also designed. Extensive computational experiments are carried out to compare the different approaches on evacuation planning instances and on general CTRTP-TW instances. The experiments also show the interest of the continuous model compared with a previously proposed discrete approximation. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This work was funded by the Horizon 2020 Marie Skłodowska-Curie Research and Innovation Staff Exchange European Project 691161 GEO-SAFE (Geospatial based Environment for Optimisation Systems Addressing Fire Emergencie). This work has also been supported by ANITI, the Artificial and Natural Intelligence Toulouse Institute. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0142 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0142 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Optimizing service networks to support freight rail decarbonization: Flow selection, facility location, and energy sourcing

We present a framework to support decarbonization of energy intensive transportation systems offering periodic service on expansive networks (e.g., freight rail, trucking, and intercity bus services). The framework consists of two optimization problems that respectivelyaddress (i) flow selection and facility location, and (ii) energy sourcing/procurement at the service facilities to enable the selected flows. The framework generalizes mixed integer linear programming formulations for flow refueling facility location and flow-based set cover models appearing in the literature to situations where it is of interest to account for repositioning of assets along cyclical trajectories to allow for periodic service, and to account for intermediate flow capture (i.e., trip chaining). The framework also consists of a minimum cost network flow model to determine optimal energy sourcing and distribution strategies, which dictate capacity requirements at the service facilities. The energy demands are obtained from the solution to the flow selection and facility location model. To illustrate the framework, we analyze the deployment of charging stations to support battery-electric locomotive service on a subset of the US freight rail network (i.e., an aggregate network of 3 Class I Railroads). The results show that the deployment of 30 charging stations can support battery-electric locomotives (with 1600-km ranges) to serve 86% of distance-weighted flows (ton-km) and reduce emissions by approximately 50%.

Near-Optimal Scheduling for IC Packaging Operations Considering Processing-Time Variations and Factory Practices

Due to the short life cycles of electronic products, trial run lots of new products are crucial in IC packaging for production verification and engineering adjustments. The processing time of trial run lots may differ significantly from production lots due to engineering adjustments and is difficult to predict without sufficient historical data. The purpose of this paper is to develop a framework for near-optimal scheduling of IC packaging considering processing time variations and factory practices. Using an orthogonal greedy algorithm and recurrent neural network, this framework extracts key features and predicts the processing times of trial run lots and production lots for each operation using these algorithms. After formulating the scheduling problem in an integer linear programming form, an ordinal optimization method is embedded within the decomposition and coordination framework to obtain dynamic and near-optimal schedules in a computationally efficient manner. This approach can improve the efficiency of IC packaging and potentially other operations by optimizing lot scheduling, reducing production tardiness, and increasing productivity in the factory, paving the way for self-optimizing factories in the future.

A Bi-Objective Home Health Care Routing and Scheduling Problem under Uncertainty.

Home health care companies provide health care services to patients in their homes. Due to increasing demand, the provision of home health care services requires effective management of operational costs while satisfying both patients and caregivers. In practice, uncertain service times might lead to considerable delays that adversely affect service quality. To this end, this paper proposes a new bi-objective optimization problem to model the routing and scheduling problems under uncertainty in home health care, considering the qualification and workload of caregivers. A mixed-integer linear programming formulation is developed. Motivated by the challenge of computational time, we propose the Adaptive Large Neighborhood Search embedded in an Enhanced Multi-Directional Local Search framework (ALNS-EMDLS). A stochastic ALNS-EMDLS is introduced to handle uncertain service times for patients. Three kinds of metrics for evaluating the Pareto fronts highlight the efficiency of our proposed method. The sensitivity analysis validates the robustness of the proposed model and method. Finally, we apply the method to a real-life case and provide managerial recommendations.

Intelligent Resource Orchestration for 5G Edge Infrastructures

The adoption of edge infrastructure in 5G environments stands out as a transformative technology aimed at meeting the increasing demands of latency-sensitive and data-intensive applications. This research paper presents a comprehensive study on the intelligent orchestration of 5G edge computing infrastructures. The proposed Smart 5G Edge-Cloud Management Architecture, built upon an OpenNebula foundation, incorporates a ONEedge5G experimental component, which offers intelligent workload forecasting and infrastructure orchestration and automation capabilities, for optimal allocation of virtual resources across diverse edge locations. The research evaluated different forecasting models, based both on traditional statistical techniques and machine learning techniques, comparing their accuracy in CPU usage prediction for a dataset of virtual machines (VMs). Additionally, an integer linear programming formulation was proposed to solve the optimization problem of mapping VMs to physical servers in distributed edge infrastructure. Different optimization criteria such as minimizing server usage, load balancing, and reducing latency violations were considered, along with mapping constraints. Comprehensive tests and experiments were conducted to evaluate the efficacy of the proposed architecture.

Optimal scheduling of an integrated energy system considering carbon trading mechanism and multi-energy supply uncertainties in a real-time price environment

This research presents an optimized scheduling model for Integrated Energy Systems (IES) that harmonizes economic efficiency with low carbon emissions in a Real-Time Price (RTP) environment. Integrating a ladder-type carbon tax approach, this model adeptly addresses the unpredictability of renewable energy generation and IES load demands. It introduces a carbon trading mechanism for efficient emission control, complemented by an RTP model that manages interactions between the IES and the main power grid through piecewise linear functions. The model also proposes an adaptable operation strategy for thermoelectric and electric cooling ratios, enhancing the IES’s economic and operational flexibility. The objective function, crafted on a deviation preference optimization basis, reflects the diverse goals of decision-makers, and the model is skillfully translated into a mixed-integer linear programming format through a series of mathematical transformations. Simulation results demonstrate the model’s efficacy in achieving an optimal balance between cost-effectiveness and reliability, particularly by setting a strategic confidence level for spinning reserves. Additionally, incorporating a ladder-type carbon tax and Electric Vehicle (EV) charging within the IES underscores its significant environmental benefits, marking a stride towards a low-carbon future.

Coordinating scheduling and rejection decisions in a two-machine flow shop scheduling problem

We study a two-machine flow shop scheduling problem where any operation can be rejected at a certain cost. A solution for such a problem requires two sets of decisions. The first involves the partition of the set of operations into two subsets: the set of operations that are accepted for scheduling in the shop, and the set of rejected operations. The second decision involves scheduling the set of accepted operations in the shop. The objective is to find a solution that minimizes the sum of the makespan and the total rejection cost. We prove that the problem is NP-hard even if all processing operations have identical processing times and identical rejection costs on either one of the two machines. We show, however, that the problem is fixed parameterized tractable with respect to a parameter that combine the number of different processing times on both machines with the number of different rejection costs on one out of the two machines. We also provide a pseudo-polynomial time algorithm for the problem, which we then convert into a fully polynomial time approximation scheme. This is achieved by dividing the problem into a set of subproblems and deriving a fully polynomial time approximation scheme for each one of them, separately. Finally, we present an integer linear programming formulation of the problem and two simple 2-approximation algorithms.

Performance Optimization Across the Edge-Cloud Continuum: A Multi-agent Rollout Approach for Cloud-Native Application Workload Placement

The advancements in virtualization technologies and distributed computing infrastructures have sparked the development of cloud-native applications. This is grounded in the breakdown of a monolithic application into smaller, loosely connected components, often referred to as microservices, enabling enhancements in the application’s performance, flexibility, and resilience, along with better resource utilization. When optimizing the performance of cloud-native applications, specific demands arise in terms of application latency and communication delays between microservices that are not taken into consideration by generic orchestration algorithms. In this work, we propose mechanisms for automating the allocation of computing resources to optimize the service delivery of cloud-native applications over the edge-cloud continuum. We initially introduce the problem’s Mixed Integer Linear Programming (MILP) formulation. Given the potentially overwhelming execution time for real-sized problems, we propose a greedy algorithm, which allocates resources sequentially in a best-fit manner. To further improve the performance, we introduce a multi-agent rollout mechanism that evaluates the immediate effect of decisions but also leverages the underlying greedy heuristic to simulate the decisions anticipated from other agents, encapsulating this in a Reinforcement Learning framework. This approach allows us to effectively manage the performance–execution time trade-off and enhance performance by controlling the exploration of the Rollout mechanism. This flexibility ensures that the system remains adaptive to varied scenarios, making the most of the available computational resources while still ensuring high-quality decisions.

Solving the Set Covering Problem with Conflicts on Sets: A new parallel GRASP

In this paper, we analyze a new variant of the well-known NP-hard Set Covering Problem, characterized by pairwise conflicts among subsets of items. Two subsets in conflict can belong to a solution provided that a positive penalty is paid. The problem looks for the optimal collection of subsets representing a cover and minimizing the sum of covering and penalty costs. We introduce two integer linear programming formulations and a quadratic one for the problem and provide a parallel GRASP (Greedy Randomized Adaptive Search Procedure) that, during parallel executions of the same basic procedure, shares information among threads. We tailor such a parallel processing to address the specific problem in an innovative way that allows us to prevent redundant computations in different threads, ultimately saving time. To evaluate the performance of our algorithm, we conduct extensive experiments on a large set of new instances obtained by adapting existing instances for the Set Covering Problem. Computational results show that the proposed approach is extremely effective and efficient providing better results than Gurobi (tackling three alternative mathematical formulations of the problem) in less than 1/6 of the computational time.

Dissipative PID control for uncertain positive Roesser system under the try-once-discard protocol

This paper addresses the problem of dissipative proportional–integral–derivative (PID) control for the delayed positive Roesser system with interval uncertainties under the try-once-discard (TOD) protocol. To alleviate the undesired data congestion phenomenon in the shared communication network, the TOD protocol is introduced to regulate which sensor node could release its measurement at each transmission instant. An output-feedback-based PID controller is designed for the two-dimensional (2-D) system with TOD protocol. Based on the co-positive Lyapunov–Krasovskii function method, sufficient criteria in the linear programming form are attained to ensure the positivity, 2-D (ζ,η)-γ-dissipativity and robust asymptotic stability of the closed-loop system. Finally, an illustrative example is given to show effectiveness of the PID control scheme designed.