Integer Nonlinear Programming Research Articles

Autonomous Mission Planning for Spacecraft On-orbit Service Based on Hybrid Variant Particle Swarm Optimization

For the complex on-orbit service (OOS) mission planning problem, an improved hybrid variant particle swarm optimization (PSO) method was proposed to improve the fuel utilization efficiency of spacecraft. Firstly, considering the time and fuel constraints, a model for OOS mission planning under the scenario of multiple target spacecrafts is established. The Lambert orbit maneuver method is used and the problem is transformed into a large-scale hybrid nonlinear integer programming problem. Next, an improved hybrid variant PSO algorithm is designed to optimize the fuel performance cost, and its simple structure and lightweight operation facilitate autonomous planning, considering the limited computing power of the onboard computer. The hybrid algorithm is composed of discrete particle swarm optimization (DPSO) and PSO, so it has a strong ability to search for the optimal service sequence and orbit maneuver time simultaneously. Moreover, the adaptive and variant operators are used to improve the searching ability and avoid falling into local optimal solutions. Finally, simulation experiments show that the proposed method can quickly give optimal results, reducing fuel consumption effectively in the OOS mission and improving the OOS capability of the spacecraft.

Network-level pavement maintenance and rehabilitation planning considering uncertainties using chance-constrained programming

ABSTRACT In practice, given limited funds, to consider multiple strategic goals/objectives that different stakeholders concern, pavement network-level maintenance and rehabilitation (M&R) planning becomes a multi-objective optimisation (MOO) based project selection and budget allocation problem. In an attempt to solve this problem, most agencies established MOO models under the deterministic situation without appropriate consideration of uncertainties. However, ignoring performance uncertainties often leads to unreasonable decisions. To provide more convincing and reliable pavement M&R decisions, this paper proposes a Chance-Constrained Programming (CCP) based MOO method to incorporate performance uncertainties in network-level single period pavement M&R planning. First, a general deterministic MOO model with budget and network performance constraints is established. Then, three commonly-used statistical forms of network-level performance measures are introduced. To incorporate uncertainties, the probability distribution of each form of performance measure is derived. Based on the CCP method, the MOO model is transformed to an equivalent deterministic formulation as a mixed non-linear integer programming (MNLIP) problem. To demonstrate the proposed method, a case study using real data is conducted. The results show that the proposed method can effectively help decision-makers to appropriately incorporate performance uncertainties in conducting network-level pavement M&R planning.

A Multi-Agent RL Algorithm for Dynamic Task Offloading in D2D-MEC Network with Energy Harvesting.

Delay-sensitive task offloading in a device-to-device assisted mobile edge computing (D2D-MEC) system with energy harvesting devices is a critical challenge due to the dynamic load level at edge nodes and the variability in harvested energy. In this paper, we propose a joint dynamic task offloading and CPU frequency control scheme for delay-sensitive tasks in a D2D-MEC system, taking into account the intricacies of multi-slot tasks, characterized by diverse processing speeds and data transmission rates. Our methodology involves meticulous modeling of task arrival and service processes using queuing systems, coupled with the strategic utilization of D2D communication to alleviate edge server load and prevent network congestion effectively. Central to our solution is the formulation of average task delay optimization as a challenging nonlinear integer programming problem, requiring intelligent decision making regarding task offloading for each generated task at active mobile devices and CPU frequency adjustments at discrete time slots. To navigate the intricate landscape of the extensive discrete action space, we design an efficient multi-agent DRL learning algorithm named MAOC, which is based on MAPPO, to minimize the average task delay by dynamically determining task-offloading decisions and CPU frequencies. MAOC operates within a centralized training with decentralized execution (CTDE) framework, empowering individual mobile devices to make decisions autonomously based on their unique system states. Experimental results demonstrate its swift convergence and operational efficiency, and it outperforms other baseline algorithms.

Design and operation of modular biorefinery supply chain under uncertainty using generalized Benders decomposition

AbstractBiomass supply chain performance is heavily affected by uncertainties stemming from supply, demand, or unexpected disruptions. Unlike petrochemical plants that use crude oil, biorefineries often have to deal with the uneven spatial‐temporal distribution of feedstock supply. The modular production strategy provides more flexibility in chemical manufacturing by allowing fast capacity expansion and unit movement. However, modeling and optimizing modular biomass supply chain under uncertainties becomes challenging due to high dimensionality and the existence of discrete decisions. This work optimizes the multiperiod biomass supply chain using the rolling horizon planning and two‐stage stochastic programming framework. We then applied generalized Benders decomposition to reduce the computational complexity of the stochastic mixed integer nonlinear programming supply chain optimization. Furthermore, the solution of the stochastic programming could be used to quantitatively describe the life‐cycle assessment uncertainties of the biomass supply chain performance, demonstrating seasonality and random variability.

SMITS: Social and Mobility aware Intelligent Task Scheduling in Vehicular Fog Computing — A Federated DRL Approach

Vehicular fog computing (VFC) has become an enticing research hot spot to provide resources for the Internet of Vehicles (IoV) application requests. Moreover, with the massive expansion of services in vehicular fog networks such as augmented reality, 3-D gaming, and autonomous driving, the allocation of fog computing resources to IoV applications constraining the deadline and energy consumption of the vehicles is becoming challenging. In this paper, we investigate a task scheduling problem in vehicular fog networks to jointly optimize the success rate of vehicular tasks and energy consumption of vehicles by considering the moving paths of the vehicles and the social relationships among the vehicles. In this problem, we model the social relationship among the vehicles based on their communication patterns and social characteristics to improve the success rate of the tasks. We also incorporate the mobility of vehicles using the Markov renewal process (MRP) technique. Initially, we formulate a mixed integer nonlinear programming (MINLP) problem for the proposed problem and further prove it to be an NP-hard problem. To solve the proposed problem, we design a federated deep reinforcement learning (FDRL) mechanism by converting the problem into a Markov decision process (MDP) problem. We compare our proposed algorithm with existing scheduling approaches, and simulation results show that the proposed algorithm performs efficiently for task scheduling problems. The proposed algorithm achieved a substantial improvement of 12% in the maximization of the success rate and 36% in the minimization of the energy consumption compared to the existing algorithms.

Multi-period fourth-party logistics network design from the viability perspective: a collaborative hyper-heuristic embedded with double-layer Q-learning algorithm

In the ‘new normal’ setting of a mega-crisis, the viability becomes the driving force for the fourth party logistics (4PL) network design. In this paper, the viability is characterised in terms of agility, resilience and survival sustainability as the response to changes in demand, disruption and survivability. The fortification and recovery strategies are considered in possible disruptions at transfer centres and third-party logistics providers. A novel mixed integer non-linear programming model is proposed to obtain the multi-period 4PL network solution with minimum total cost under viability constraints. Considering the NP-hard characteristic of problem and the non-convex of proposed model, the hyper-heuristic algorithm is designed. To take advantage of both global optimality seeking and local search ability, a collaborative hyper-heuristic embedded with double-layer Q-learning (CHHDLQL) algorithm is proposed. The effectiveness and efficiency of the proposed algorithm is demonstrated by the promising numerical results. By stress-testing the existing network, appropriate adjustments to fortification and recovery strategies can effectively cope with changes in demand and disruption. Furthermore, the impact of 4PL strategy, fortification and recovery strategies, and viability constraints are investigated. The demand satisfaction, network resilience and capacity can be improved by adjusting agility, resilience and survival sustainability to influence different component network costs. Highlights A novel multi-period 4PL network model under viability constraints is presented. The CHHDLQL algorithm for construction and perturbation coevolution is proposed. The stress tests apply to the 4PL network, including demand, disruption and 3PL. 4PL improves demand satisfaction, resilience and capacity by adjusting viability.

Simultaneous Optimization of Work and Heat Exchange Networks

This paper introduces a simultaneous optimization approach to synthesizing work and heat exchange networks (WHENs). The proposed work and heat integration (WHI) superstructure enables different thermodynamic paths of pressure and temperature-changing streams. The superstructure is connected to a heat exchanger network (HEN) superstructure, enabling the heat integration of hot and cold streams identified within the WHI superstructure. A two-step solution strategy is proposed, consisting of initialization and design steps. In the first step, a thermodynamic path model based on the WHI superstructure is combined with a model for simultaneous optimization and heat integration. This nonlinear programming (NLP) model aims to minimize operating expenditures and provide an initial solution for the second optimization step. In addition, hot and cold streams are identified, enabling additional model reduction. In the second step of the proposed solution approach, a thermodynamic path model is combined with the modified HEN model to minimize the network’s total annualized cost (TAC). The proposed mixed integer nonlinear programming (MINLP) model is validated by several examples, exploring the impact of the equipment costing and annualization factor on the optimal network design. The results from these case studies clearly indicate that the new synthesis approach proposed in this paper produces solutions that are consistently similar to or better than the designs presented in the literature using other methodologies.

신에너지 자동차배터리 산업 공급망 네트워크의 최적화

In this study, an optimization of supply chain network for New Energy Vehicle Power Batteries (NEVPB) from the perspective of resource circulation is proposed. The model consists of seven stages in terms of collection center (CC), repairing center (RC), distribution center (DC), recycling center (RY), part supplier (PS), material supplier (MS), and disposal center (DP). The model is formulated as a nonlinear integer programming model and a comparison of LINGO and genetic algorithm (GA접근법) are conducted respectively. In numerical experiment, it has found a way to repair and recycle NEVPB. Retrieving as many NEVPBs in use demonstrates sustainable power generation benefits by maximizing the use of recovery through resource recycling and searching for recovery classification of batteries as well as shortening lifespan that occur during the process of producing initial parts and modules from raw materials.

Multi-User Computation Offloading and Resource Allocation Algorithm in a Vehicular Edge Network.

In Vehicular Edge Computing Network (VECN) scenarios, the mobility of vehicles causes the uncertainty of channel state information, which makes it difficult to guarantee the Quality of Service (QoS) in the process of computation offloading and the resource allocation of a Vehicular Edge Computing Server (VECS). A multi-user computation offloading and resource allocation optimization model and a computation offloading and resource allocation algorithm based on the Deep Deterministic Policy Gradient (DDPG) are proposed to address this problem. Firstly, the problem is modeled as a Mixed Integer Nonlinear Programming (MINLP) problem according to the optimization objective of minimizing the total system delay. Then, in response to the large state space and the coexistence of discrete and continuous variables in the action space, a reinforcement learning algorithm based on DDPG is proposed. Finally, the proposed method is used to solve the problem and compared with the other three benchmark schemes. Compared with the baseline algorithms, the proposed scheme can effectively select the task offloading mode and reasonably allocate VECS computing resources, ensure the QoS of task execution, and have a certain stability and scalability. Simulation results show that the total completion time of the proposed scheme can be reduced by 24-29% compared with the existing state-of-the-art techniques.

Fairness‐aware eMBB/URLLC spectrum resource multiplexing to ensure reliability in vehicular networks

AbstractSpectrum resource multiplexing of enhanced Mobile BroadBand (eMBB) and Ultra‐Reliable and Low Latency Communications (URLLC) via puncturing in vehicular networks has become an important research direction. The main issue in this direction is how to minimize the adverse impact of preemptive puncturing on eMBB traffic. However, the available eMBB/URLLC coexisting schemes lack considerations on the quality of service of a single eMBB user and fairness between users. In view of this, we formulate the eMBB/URLLC multiplexing problem to maximize eMBB reliability and fairness under the premise of meeting the requirements of URLLC as a nonlinear integer programming (NIP) in this article. To balance the performance and computational complexity, we decompose this NIP into two subproblems that be solved efficiently. For the eMBB spectrum resource allocation subproblem of maximizing the reliability and fairness under resource constraints, we prove that this problem is NP‐hard, and design a Deep Q‐Network (DQN)‐based spectrum resource allocation algorithm and a two‐stage heuristic spectrum resource allocation algorithm, respectively. For the URLLC preemption subproblem, we further propose bandwidth‐sensitive URLLC spectrum resource preemption algorithm and time‐sensitive URLLC spectrum resource preemption algorithm, respectively. Simulation results show that the proposed scheme can guarantee better fairness and reliability for eMBB users compared with the comparison schemes. Besides, for the eMBB resource allocation problem, the proposed scheme can achieve near‐optimal performance with low complexity.

An Effective Two-Stage Algorithm for the Bid Generation Problem in the Transportation Service Market

This study designs a two-stage algorithm to address the bid generation problem of carriers when adding new vehicle routes in the presence of the existing vehicle routes to provide transportation service. To obtain the best auction combination and bid price of the carrier, a hybrid integer nonlinear programming model is introduced. According to the characteristics of the problem, a set of two-stage hybrid algorithms is proposed, innovatively integrating block coding within a genetic algorithm framework with a depth-first search approach. This integration effectively manages routing constraints, enhancing the algorithm’s efficiency. The block coding and each route serve as decision variables in the set partition formula, enabling a comprehensive exploration of potential solutions. After a simulation-based analysis, the algorithm has been comprehensively validated analytically and empirically. The improvement of this research lies in the effectiveness of the proposed algorithm, i.e., the ability to handle a broader range of problem scales with less time in addressing complex operator bid generation in combinatorial auctions.

Optimal Sustainable Manufacturing for Product Family Architecture in Intelligent Manufacturing: A Hierarchical Joint Optimization Approach

As consumers and governments prioritize cost-effectiveness and ecological sustainability, the limitations of traditional manufacturing paradigms become apparent in the context of constrained resources. The adverse effects of these paradigms on the environment and society hinder the achievement of a sustainable product life cycle. Intelligent manufacturing processes offer a solution by efficiently gathering meaningful data, such as usage and product recycling information, from previous product generations to enhance product design and subsequent sustainable manufacturing processes (SMPs). Modular product family architecture (PFA) design holds promise in promoting product sustainability and addressing diverse consumer needs. PFA design and SMPs are inherently interconnected within intelligent manufacturing frameworks. This paper aims to integrate the decision-making processes underlying PFA with SMPs. We model integrated PFA and SMP decisions as a Stackelberg game, which involves hierarchical joint optimization (HJO) for assessing product modularity and sustainable manufacturing fulfillment. We develop a bilevel 0–1 integer nonlinear programming model to represent the HJO decision-making process and propose a nested genetic algorithm (NGA) to solve the HJO problem. A case study with a laptop is conducted to validate the feasibility and potential of the proposed HJO model for joint optimization problems in PFA design and SMPs.

Decision-Making for Land Conservation: A Derivative-Free Optimization Framework with Nonlinear Inputs

Protected areas (PAs) are designated spaces where human activities are restricted to preserve critical habitats. Decision-makers are challenged with balancing a trade-off of financial feasibility with ecological benefit when establishing PAs. Given the long-term ramifications of these decisions and the constantly shifting environment, it is crucial that PAs are carefully selected with long-term viability in mind. Using AI tools like simulation and optimization is common for designating PAs, but current decision models are primarily linear. In this paper, we propose a derivative-free optimization framework paired with a nonlinear component, population viability analysis (PVA). Formulated as a mixed integer nonlinear programming (MINLP) problem, our model allows for linear and nonlinear inputs. Connectivity, competition, crowding, and other similar concerns are handled by the PVA software, rather than expressed as constraints of the optimization model. In addition, we present numerical results that serve as a proof of concept, showing our models yield PAs with similar expected risk to that of preserving every parcel in a habitat, but at a significantly lower cost. The overall goal is to promote interdisciplinary work by providing a new mathematical programming tool for conservationists that allows for nonlinear inputs and can be paired with existing ecological software. The code and data are available at https://github.com/cassiebuhler/conservation-dfo.

Agile earth observation satellite constellations scheduling for large area target imaging using heuristic search

Demand for imaging of large area targets by space-based assets such as constellations of Earth Observation Satellites (EOS) is on the rise for different applications. The area targets coverage cannot be achieved by a single satellite in a single observation opportunity, as the region for imaging spreads wider than the coverage swaths of imaging sensors. Hence, the imaging satellites are scheduled in a cooperative way to achieve maximum coverage of the area in a given planning time horizon. The scheduling algorithms also aim to maximize or minimize some specific objectives of interest while simultaneously complying with all resource constraints for an efficient use of precious space resources. As the current generation satellites are highly agile, there are many ways of choosing an imaging location in the target area for each single observation opportunity of a satellite. Even though the possible imaging region in continuous space is discretized into a finite number of strips for each observation, the huge combinatorial search space formed with all satellites’ imaging opportunities makes the problem intractable. Thus, the area target imaging scheduling is a complex combinatorial NP-hard optimization problem. Many exact and heuristic methods were evolved to provide a solution to this scheduling problem. Even though the exact methods solve the problem to optimality, they are limited to smaller problem instances because of the high computational complexities involved in those methods. More focus is seen in the literature on heuristic approaches as they guarantee scheduling performance with feasible solutions within an acceptable computational complexity. This paper presents our efficient heuristic approach proposed for the scheduling problem for imaging a large area target using a constellation of multiple satellites. Our approach is an extension of a widely used greedy approach in combination with insights from dynamic programming. In this paper, first we addressed the scheduling problem by describing it in detail and formulating it into a non-linear integer programming problem, considering the multi-objectives of achieving maximum coverage and minimum imaging resolution. The solution to the problem comprises two phases, namely the area decomposition phase and the scheduling phase. In the area decomposition phase, the area target is divided into strips dynamically for each observation opportunity of a satellite. Then exact observation period of each strip is computed using a simplified semi-analytical computational method. In the scheduling phase, we applied our heuristic search strategy, namely Forward and Backward Heuristic Search (FBHS) to obtain a near optimal solution within an acceptable computational time. Through the extensive simulations conducted under various scenarios, the effectiveness of the proposed method is verified in comparison with the baseline greedy approach.

Integrated operation models with quay crane maintenance in a container terminal

This paper investigates an integrated optimization problem concerning berth allocation, quay crane assignment, and truck deployment in container terminals, with a specific focus on incorporating quay crane maintenance into the integrated models. A nonlinear integer programming model is proposed, and then a number of equivalent or relaxed models are developed to ease the model. To solve the model on large-scale instances, a SWO-GA is developed to provide a solution. Finally, a set of test instances are randomly generated to access the applicability of the proposed models and the efficiency of the algorithm. The results show that the SWO-GA can obtain a good solution with a small gap within a much shorter computation time than that of CPLEX. Quay crane maintenance significantly affects the operation plans and increases costs. The maintenance time step and the number of berths required for quay crane have a proportional impact on the total cost. It is also found that quay crane maintenance is of great concern for large-sized container terminals. The model and algorithm proposed in this paper provide important insights for operation managers.

Optimizing City-Scale Demolition Waste Supply Chain Under Different Carbon Policies.

In order to establish a green, low-carbon circular development economic system, imperative goals include achieving carbon peaking and carbon neutrality. This research delves into the resource utilization of city-scale demolition waste (C&DW), aligning with environmental protection needs and sustainable development principles. The paper introduces a unique closed-loop supply chain (CLSC) model tailored for C&DW and employs a distinctive mixed integer nonlinear programming (MINLP) model for optimization. Guangzhou serves as a case study for thorough analysis, verification, and practical application of the proposed model, especially under diverse scenarios of carbon price (CP) and carbon trading (CT) policies. The key conclusions drawn from this study include the following: (1) The cost of carbon emissions is intricately influenced by both carbon emissions and carbon price, with the latter effectively regulating the carbon emissions during C&DW recycling. (2) The implementation of a CT policy, with a fixed carbon price, contributes to a further reduction in the cost of C&DW recycling treatment. (3) Under equivalent conditions, the CT policy demonstrates the potential to decrease costs and enhance the economic benefits within the building environmental protection product market. The research outcomes not only contribute to the advancement of management theory in the C&DW recycling supply chain (SC) but also provide a robust theoretical foundation for governmental initiatives aimed at introducing effective C&DW recycling management policies.

Period-dependent pricing methods of multi-type vehicles for BOT highway projects with pavement rehabilitation effects

In the planning stage of a BOT highway project, the future traffic demand plays a pivotal role on designing contract factors. Considering that the traffic demand generally has variations with time, the constant toll during the concession period obviously is not a good choice. And the different toll charges classified by vehicles types definitely affect the traffic composition and maintenance cost. To address this practical issue, this study proposes the mixed integer nonlinear programming models to select the period-dependent toll charges for multi-type vehicles and highway capacity, by considering both the objectives of the government and private firms. Then two solution algorithms are provided to solve our proposed models. Finally, numerical experiments are conducted to assess the applicability and efficiency of our models and algorithms.

Fleet management for earthmoving operation in the phase of detail estimation using mixed integer nonlinear programming

ABSTRACT Earthmoving operations generally account for about a quarter of the construction budget in high-way constructions. Feasible planning is thus required for delivering the successful performance of such projects. Selecting the best fleet for the operation is one of the crucial factors affecting both duration and cost. However, owing to changing operating circumstances and the uncertainty of construction projects, this task is yet conducted based on the experience of site managers. The existing literature has witnessed that discrete event simulation (DES) and references such as the construction standard production rate (CSPR) are used to assist the decision-making. Those methods have shown limitations for practical application due to the need for expert knowledge of simulation modeling and time-consuming efforts for data collection. Accordingly, this study proposes a more efficient method of using mixed integer nonlinear programming (MINLP) in multi-objective problems, enabling optimal fleet information derivation based on given circumstances. The proposed method uses the CSPR-based mathematical equations for the consideration of productivity generated by the types and sizes of equipment. A comparative study of the proposed method and a DES approach was given for further discussions.

Matheuristics vs. metaheuristics for joint lot-sizing and dynamic pricing problem with nonlinear demands

This paper considers a joint dynamic pricing and production planning decisions problem for a profit-maximizing firm that produces and sells multiple products. The objective is to develop a coordinated decision approach for multi-product pricing and lot sizing decisions for a manufacturer considering a limited production capacity. The demand for each product is assumed to be iso-elastic and integrates the complementarity and the substitution effects between the products. First, the problem is formulated as a non-convex mixed integer nonlinear programming model (MINLP) incorporating capacity constraints, setup costs, and nonlinear demand functions. Then, since the model is nonlinear and non-convex, a set of approximate approaches based on the Genetic algorithm, Late Acceptance Hill Climbing and Simulated Annealing methods are designed to solve this problem. Based on this study, the performances of two variants of approximate methods: matheuristics and metaheuristics are discussed and analyzed. The extensive experimental study, performed on real-world inspired instances, shows that matheuristic methods with setup-variables encoding scheme outperform the rest of the methods. The research outcomes show that coordinating a decision-making process by optimizing both prices and production plans simultaneously can result in significant profit for a company. However, one must consider the joint effect of the parameters of the demand function as well as the impact of the production capacity. This comprehensive understanding enables the company to avoid excessive investments in less lucrative products with lower sales potential, thereby ensuring resource allocation aligns with profitability and market demand.

A Two-Phase Approach for Reliability-Redundancy Optimization of a Communication Satellite

The development and launch of communication satellite projects pose significant challenges and costs. The expenses can range from several hundred million dollars, contingent on factors such as mission objectives, satellite system size and complexity including the launch vehicle, and ground infrastructure. Satellites must be designed to withstand harsh conditions in space, such as the extreme temperatures, radiation, and other hazards, while delivering reliable communication services to its users. However, once a satellite is launched, physical maintenance interventions become infeasible in the event of technical problems. Thus, reliability is a critical aspect for these expensive systems. This study aims to minimize the cost of a high-tech communication satellite by addressing design considerations that meet customer reliability requirements without exceeding power and redundant equipment limits. To achieve this goal, we propose an integer non-linear programming model in this research. To solve the satellite design problem, we adopt a two-stage solution approach. Conventional industrial practices in satellite design often involve iterative attempts to determine the redundancy level of onboard units based on customer reliability requirements. These processes rely heavily on the experience of design engineers who evaluate a limited number of alternatives to determine the number of redundant units, resulting in sub-optimal outcomes. In contrast, our proposed approach systematically handles the problem and yields optimal results. Our findings demonstrate that the proposed two-phase approach can achieve optimal redundancy levels within seconds.