Mixed Integer Nonlinear Programming Research Articles

Integrating resilience and reliability in semiconductor supply chains during disruptions

The semiconductor industry, a cornerstone of modern technology, has been crucial in driving globalization and supporting various sectors, from consumer electronics to automotive industries. However, in recent years, the industry has faced substantial challenges threatening its ability to meet the surging demand for semiconductor chips. Disruptions at any point in the supply chain, from raw material sourcing to end-product delivery, can substantially influence the semiconductor ecosystem. The intricate nature of such SCs makes them highly vulnerable to various disruptions, emphasizing the critical need for building resilient and reliable supply chain strategies. This article presents comprehensive research aimed at addressing critical gaps in the understanding and management of resilience and reliability within the semiconductor supply chain (SSC). This study proposes a multi-objective mixed-integer non-linear programming (MO-MINLP) model to configure an SSC while considering reliability and resilience measures. It emphasizes and draws attention to the importance of resilience and reliability in managing SSC disruptions during a pandemic and potential future epidemic outbreak. Exploring the precise breakdown of batch transportation between two sites shows how disruption can affect product flow along the SC. The applicability of the proposed method is demonstrated through a numerical example of an SSC, solved using the LINGO solver. Finally, a sensitivity analysis is conducted on the model's parameters to assess the capability and effectiveness of the results from managerial viewpoints.

A modelling and solution approach for wind-affected drone-truck routing problem under uncertainty

In the field of logistics and transportation, drones and trucks effectively enhance each other’s capabilities by offering complementary benefits in terms of speed, cargo capacity, and charging frequency. Thus, efficient management of their collaboration is an important task. Although there is a vast literature addressing different aspects of drone-truck combined operations (DTCO), only a few studies incorporate the energy consumption of drones into the optimization model, and the existing ones have made simplified assumptions. This paper proposes an optimization model for DTCO by incorporating a comprehensive energy function affected by the drone speed, cargo weight, wind speed, and wind direction, paying attention to environmental viewpoints. Due to this energy function, the problem is formulated as a mixed-integer nonlinear programming (MINLP) model. To enhance tractability and efficiency, we provide a linear approximation for the MINLP model. Given the stochastic nature of wind conditions throughout the day, we extend the deterministic model as a scenario-based stochastic one. Incorporating uncertainty makes the model more complex and hence, we adopt a modified progressive hedging algorithm (PHA) to efficiently solve the model. Computational results over a variety of instances confirm the effectiveness of the proposed approach.

Energy expansion planning with a human evolutionary model

This study presents a novel method for planning the expansion of transmission lines and energy storage systems while considering the interconnectedness of electricity and gas networks. We developed a two-level stochastic planning model that addresses both the expansion of transmission and battery systems in the electrical grid and the behavior of the gas network. This research explores the challenges and effects of integrating high levels of renewable energy sources while ensuring security within both networks. Our model uses a stochastic mixed-integer non-linear programming approach. To solve this complex model, we applied the Human Evolutionary Model (HEM). We tested our approach on two case studies: a simple 6-node network and the more complex IEEE RTS 24-bus network for the electricity grid, combined with 5-node and 10-node gas networks, respectively. The results demonstrate the effectiveness of our model, particularly in scenarios where connections in the power and gas networks are disrupted, preventing load shedding even when integrated network connections are cut.

Energy storage comparison of chemical production decarbonization: Application of photovoltaic and solid oxide electrolysis cells

The fossil fuel driven chemical production leads to significant greenhouse emission, and the low-carbon emission technologies are necessary for carbon neutrality. The integration of solid oxide electrolysis cells (SOEC) and H2-O2 combustion can replace the fossil fuel and supply high-temperature heat for reactions. However, the energy demand keeps consistent but the renewable energy fluctuates with time. Therefore, energy storage is important for such a change. Clean fuel replacement and electrification are applied in a case study of ethylene plant, which requires 147 MW of clean fuel and 91.36 MW of grid power. Photovoltaic (PV) solar energy drives SOEC and liquefied H2, compressed H2, compressed air energy storage (CAES) are compared. A mixed integer nonlinear programming model is proposed to evaluate decarbonization effect and cost, which are balanced by multi-objective optimization. The results show that the liquefied H2 is superior to other choices because of the high efficiency. The hydrogen of 126.27 MW is the optimal point, which requires 415 MW SOEC and PV panels. Also, this study proposes that the power grid should communicate with energy consumers such as chemical plants to ensure the energy storage method, or supply renewable energy directly, which avoids energy loss and unreasonable energy transition.

Globally optimal sequencing of optimal reactive dispatch control adjustments to minimize operational losses in transmission systems by graph shortest path, parallel computing, and dynamic programming

Minimizing operational losses in transmission systems through the Optimal Reactive Dispatch (ORD), a non-convex mixed-integer nonlinear programming problem, is crucial for operational cost reduction, resource optimization, and greenhouse gas emission mitigation. Besides all intricacies associated with solving ORDs, transmission system operators encounter the challenge of determining sequences in which ORD control adjustments must be implemented before significant changes occur in generators scheduled power output and system loading. Sequencing ORD control adjustments, in spite of not being novel, remains modestly scrutinized in the literature. This paper introduces a two-phase framework that tackles the globally optimal sequencing of n ORD control adjustments over n! potential paths by solving the ORD to minimize operational losses in transmission systems in the first phase, and optimally sequencing ORD control adjustments employing fast power flow calculations, graph shortest path, parallel computing, and dynamic programming in the second phase. We discuss the framework’s second phase asymptotic time complexity, which is exponential over factorial for brute-force approaches, and its capability to guarantee globally optimal paths toward minimal operational losses determined in the framework’s first phase. ORD control adjustments for transmission systems with up to 27 controllable variables are benchmarked against two mixed-integer nonlinear programming solvers: BARON, a global non-convex solver, and Knitro, a local solver (assuming convexity around local optima). Globally optimal sequences of ORD control adjustments over n! potential paths (more than 1028 for sequencing 27 control adjustments) and average algorithm runtimes validate the straightforward application and, more importantly, effectiveness of such a comprehensive framework.

Game theoretic approach for the synthesis and optimization of economically optimal coalitions in integrated renewable energy and polygeneration networks

This study presents the generation of an integrated resource network that encompasses a bioenergy supply chain and a polygeneration hub. The resource network is designed using a superstructure that comprises 3 layers. The first layer is a supply chain network of seasonally available renewable and non-renewable energy sources and is connected to the second layer by a transport system comprised of rail, road, and pipeline. The second layer, which is the polygeneration hub, comprises a boiler to produce high-pressure steam, steam turbines for generating power, a multi-effect evaporation system for desalinating salt-water and an absorption refrigeration system to produce chilled water. The option of connecting the boiler to a solar-thermal and heat storage subnetwork for feedwater pre-heating is included in the second layer. Piping and electrical cables connect the polygeneration layer to the third layer, which comprises industrial heat demand, represented by heat exchanger network, and electrical power demand. The model is applied to a case study in which the subnetworks in the overall integrated superstructure layers are considered as individual players in an industrial symbioses network with the possibility to be in a cooperative game. The objective function of the model, which is represented as a mixed integer nonlinear programming model, involves the minimization of the summation of the players' marginal contribution, with equal weighting applied for each player, to the coalition's total annual cost. The result obtained involves preference for a coalition among participating subnetworks that include combined heat and power, multi-effect evaporation, and heat exchanger network.

The traveling purchaser problem for perishable foods

This paper addresses the well-known traveling purchaser problem (TPP) considering restrictions related to perishable food, which is called the traveling purchaser problem for perishable foods (TPP-PF). In addition to the main assumptions of the capacitated TPP, the TPP-PF takes into account the release times of perishable foods at markets. In this context, a product can only be purchased at a market after it becomes available for sale. The TPP-PF also considers that the quality of perishable products decreases due to waiting on the market shelves and during transportation, and it additionally takes the deterioration cost of the foods into account. The aim of the problem is to find the best procurement and route plan for the purchaser to minimize the total transportation cost of the temperature-controlled vehicle, the damage cost of perishable foods, and the purchasing cost. Since the deterioration cost of products based on the waiting time is determined through exponential functions, the problem is formulated as a mixed-integer non-linear programming model. To find efficient results for the problem, an adaptive large neighborhood search (ALNS) algorithm is introduced with new problem-specific destroy/repair operators. Furthermore, an additional mechanism is included in the ALNS to change the direction of the search when the algorithm cannot improve the best solution after a number of iterations. In order to analyze the performance of the proposed ALNS, a new benchmark problem set is generated using a well-known TPP benchmark set. The proposed ALNS is first performed for the TPP-PF instances and compared to GUROBI and a simulated annealing algorithm. Following the TPP-PF experiments, the ALNS is carried out for the TPP instances and compared to six state-of-the-art solution approaches. The computational results show that the proposed ALNS outperforms those approaches by finding better results for almost all instances.

A distributed economic model predictive control-based FPPT scheme for large-scale solar farm

Increasing solar-photovoltaic-power penetration necessitates the implementation of flexible power point tracking (FPPT) in solar farms. However, coordinating multiple solar photovoltaic (PV) power generation systems (SPVPGSs) poses a significant challenge due to their inherent intermittency and varying dynamic characteristics, complicating FPPT implementation. To overcome this challenge, this paper proposes a distributed economic model predictive control (DEMPC) scheme to achieve FPPT, while simultaneously enhancing overall economic performance in solar farms. By integrating solar farm control and local control into one optimal control framework, this scheme eliminates the need for power allocation, PV voltage reference calculation, and pulse width modulation. Leveraging the SPVPGS model and soft power constraint, DEMPC controllers are designed to achieve the economic targets of solar farms, which cooperate through a communication network to realize FPPT and economic optimization. Additionally, the strong nonlinearity of SPVPGS causes a non-convex mixed integer nonlinear programming (MINLP) problem, solved by a MINLP algorithm using finite converter switching states. Simulations under step-changed irradiance and power reference, as well as urgent maintenance conditions, demonstrate that the DEMPC-based FPPT scheme significantly outperforms the traditional hierarchical model predictive control-based FPPT scheme, presenting both superior dynamic response and enhanced economic performance in FPPT implementation.

Bi-Objective Mixed Integer Nonlinear Programming Model for Low Carbon Location-Inventory-Routing Problem with Time Windows and Customer Satisfaction

In order to support a low-carbon economy and manage market competition, location–inventory–routing logistics management must play a crucial role to minimize carbon emissions while maximizing customer satisfaction. This paper proposes a bi-objective mixed-integer nonlinear programming model with time window constraints that satisfies the normal distribution of stochastic customer demand. The proposed model aims to find Pareto optimal solutions for total cost minimization and customer satisfaction maximization. An improved non-dominated sorting genetic algorithm II (IMNSGA-II) with an elite strategy is developed to solve the model. The model considers cost factors, ensuring that out-of-stock inventory is not allowed. Factors such as a carbon trading mechanism and random variables to address customer needs are also included. An entropy weight method is used to derive the total cost, which is comprised of fixed costs, transportation costs, inventory costs, punishment costs, and the weight of carbon emissions costs. The IMNSGA-II produces the Pareto optimal solution set, and an entropy–TOPSIS method is used to generate an objective ranking of the solution set for decision-makers. Additionally, a sensitivity analysis is performed to evaluate the influence of carbon pricing on carbon emissions and customer satisfaction.

Synthesis of refinery hydrogen networks based on compressor performance models

Synthesis of refinery hydrogen network contributes to reductions in hydrogen consumption, production cost, and emissions. Hydrogen compressors are drivers for hydrogen distribution, which has a direct effect on the performance of hydrogen networks. The existing works focus on the hydrogen network synthesis and often use simple compressor models for easy modelling and solving, which may lead to overly ideal results. This work proposes a novel mathematical method for refinery hydrogen network synthesis considering compressor performances, incorporating both centrifugal and reciprocating compressors. The compression power vs. volumetric flowrate curves and the compression ratio vs. volumetric flowrate curves are considered for a centrifugal compressor, while the efficiency of a reciprocating compressor is correlated with the compression ratio. A mixed integer nonlinear programming model (MINLP) is formulated to minimize the total annualized cost. The developed MINLP model is examined based on two hydrogen network cases reported in literature. The results show that the minimum total annualized cost is a co-optimization of compressor type, operating points, compressor placement, and hydrogen network structure. In the two cases, compression efficiencies of centrifugal compressors range from 0.760 to 0.795 and that of reciprocating compressors are between 0.539 and 0.807. The consideration of centrifugal compressors rather than just reciprocating compressors not only improves the compression efficiencies but also simplify the hydrogen network structures. Moreover, it also brings reductions in the compression power by 2.23% and 1.97%, and decreases in the compressor investment by 7.12% and 6.87%.

Integrated optimization of worker assignment, batch splitting and scheduling for a hybrid assembly line-seru production system

This paper studies an integrated optimization problem of worker assignment, batch splitting and scheduling for a hybrid assembly line-seru production system, which includes multiple serus and a short assembly line. The worker assignment involves assigning each multi-skilled worker to a seru or the assembly line, and assigning the worker tasks to perform. The batch splitting determines the number of subbatches split for each batch, the size of each subbatch, and in which seru the production of each subbatch is performed. The batch scheduling aims to optimize the process sequences of batches in serus and on the assembly line. For the integrated optimization problem, we propose a mixed-integer nonlinear programming model that minimizes the makespan. To solve large-scale instances of the problem, we develop a tailored hybrid variable neighborhood search algorithm with a four-layer solution coding scheme and four novel neighborhood structures. We validate the effectiveness of our model and solution algorithm on two sets of instances. The experimental results indicate that the proposed hybrid metaheuristic achieves a significant reduction in makespan, with an improvement of up to 20.94% compared to the solutions obtained by the Gurobi optimization solver within one hour. In addition, we demonstrate the advantage of optimized batch splitting by comparing it with no batch splitting and equal-size batch splitting strategies in the literature.

Covert Communications in Active-RIS-Aided NOMA Systems: Element Grouping or Not?

This paper investigates the impacts of element grouping on the covert communication performance of an active reconfigurable intelligent surface (ARIS)-aided uplink non-orthogonal multiple access (NOMA) system. Through element grouping, each element of the ARIS works in either the reflecting mode to reflect the information signal or the jamming mode to generate a jamming signal. Optimizing the NOMA transmit power, ARIS beamforming, and receive beamforming jointly is necessary to maximize the covert communication rate. To tackle the unsolvable covert communication rate maximization problem, we decouple the original problem into three sub-problems of optimizing the NOMA transmit power, ARIS beamforming, and receive beamforming, respectively. To tackle the mixed-integer non-linear programming for the element grouping, we introduce the arithmetic- and geometric-mean-based penalty term and apply the Dinkelbach transform to reformulate the optimization problem. Next, we propose an alternating optimization algorithm to optimize the system parameters. The numerical results demonstrate the effectiveness of the element grouping in improving the covert communication rate. However, the element grouping scheme achieves a lower covert communication rate performance compared to the scheme without element grouping, indicating that using element grouping for covert communications in the ARIS-aided uplink NOMA system is not the preferred option.

Access strategies in mmWave cell-free network: A matching and auction theory based approach

The mmWave cell-free network is viewed as an energy-efficient and emerging architecture for beyond 5G systems. However, many practical issues should be solved for this system before the benefits are enjoyed, whereof feasible implementation of access strategy is one of the most vital. To this end, the access strategy including user scheduling and bandwidth allocation is investigated in this paper. Firstly, to maximize the defined utility function, the joint optimization problem of user scheduling and bandwidth allocation is formulated as a mixed integer nonlinear programming problem, which is intractable to search for an optimal solution in polynomial time. Secondly, a two-stage matching and sealed-auction-based access strategy is proposed to obtain a sub-optimal solution, where UEs with high-quality channel conditions are scheduled in the first-stage matching as much as possible, and the rest unmatched UEs are scheduled in the second-stage matching with the sealed-auction based bandwidth allocation. Thirdly, a simplified full-matching based access strategy with lower complexity is proposed for the high-dynamic scenario caused by the high-speed movement of UEs, and the complexities and convergence of the two proposed strategies are quantitatively analyzed. Finally, the performance of proposed strategies is evaluated through abundant simulations in different scenarios, and the superiorities of the proposed strategies are demonstrated through the comparison with reference strategies.

An Iterative Procurement Combinatorial Auction Mechanism for the Multi-Item, Multi-Sourcing Supplier-Selection and Order-Allocation Problem under a Flexible Bidding Language and Price-Sensitive Demand

This study addresses the multi-item, multi-sourcing supplier-selection and order-allocation problem. We propose an iterative procurement combinatorial auction mechanism that aims to reveal the suppliers’ minimum acceptable selling prices and assign orders optimally. Suppliers use a flexible bidding language to submit procurement bids. The buyer solves a Mixed Integer Non-linear Programming (MINLP) model to determine the winning bids for the current auction iteration. We introduce a buyer’s profit-improvement factor that constrains the suppliers to reduce their selling prices in subsequent bids. Moreover, this factor enables the buyer to strike a balance between computational effort and optimality gap. We develop a separate MINLP model for updating the suppliers’ bids while satisfying the buyer’s profit-improvement constraint. If none of the suppliers can find a feasible solution, the buyer reduces the profit-improvement factor until a pre-determined threshold is reached. A randomly generated numerical example is used to illustrate the proposed mechanism. In this example, the buyer’s profit improved by as much as 118% compared to a single-round auction. The experimental results show that the proposed mechanism is most effective in competitive environments with several suppliers and comparable costs. These results reinforce the importance of fostering competition and diversification in a supply chain.

Distributed reinforcement learning-based optimization of resource scheduling for telematics

As a reliable computational model in telematics, Mobile Edge Computing (MEC) is utilized to lighten the load on individual autonomous vehicles. It enables computationally expensive and latency-sensitive jobs to be offloaded from cars with limited processing power to servers at edge nodes. This paper presents the joint optimization problem as a mixed nonlinear integer programming problem. The scheduling of vehicle tasks and the distribution of communication resources are then rationalized using a resource allocation algorithm based on Deep Deterministic Policy Gradient (DDPG) reinforcement learning to arrive at a suboptimal solution based on the resource allocation policies of single-intelligent DDPG and multi-intelligent DDPG. The numerical simulation demonstrates the superior service experience of the proposed joint optimization strategy of distributed task offloading and resource allocation based on multi-intelligent DDPG over other association and channel selection strategies and joint resource allocation based on single-intelligent DDPG.

Two-Tier Efficient QoE Optimization for Partitioning and Resource Allocation in UAV-Assisted MEC.

Unmanned aerial vehicles (UAVs) have increasingly become integral to multi-access edge computing (MEC) due to their flexibility and cost-effectiveness, especially in the B5G and 6G eras. This paper aims to enhance the quality of experience (QoE) in large-scale UAV-MEC networks by minimizing the shrinkage ratio through optimal decision-making in computation mode selection for each user device (UD), UAV flight trajectory, bandwidth allocation, and computing resource allocation at edge servers. However, the interdependencies among UAV trajectory, binary task offloading mode, and computing/network resource allocation across numerous IoT nodes pose significant challenges. To address these challenges, we formulate the shrinkage ratio minimization problem as a mixed-integer nonlinear programming (MINLP) problem and propose a two-tier optimization strategy. To reduce the scale of the optimization problem, we first design a low-complexity UAV partition coverage algorithm based on the Welzl method and determine the UAV flight trajectory by solving a traveling salesman problem (TSP). Subsequently, we develop a coordinate descent (CD)-based method and an alternating direction method of multipliers (ADMM)-based method for network bandwidth and computing resource allocation in the MEC system. Extensive simulations demonstrate that the CD-based method is simple to implement and highly efficient in large-scale UAV-MEC networks, reducing the time complexity by three orders of magnitude compared to convex optimization methods. Meanwhile, the ADMM-based joint optimization method achieves approximately an 8% reduction in shrinkage ratio optimization compared to baseline methods.

Consequential versus attributional life cycle optimization of poultry manure management technologies in a food-energy-water-waste nexus

To model the environmental and economic tradeoffs of managing poultry manure wastes in a food-energy-water-waste nexus, this work builds a framework to conduct a combined life cycle and techno-economic optimization and a spatial analysis of poultry manure management technologies. To align with the United Nations Sustainable Development Goals 6: Clean Water and Sanitation and 13: Climate Action by mitigating the massive water and climate impacts induced by the common practice of fertilizer crops using direct land application of poultry manure, the framework minimizes freshwater eutrophication (FE) impact and climate change impact (GWP). To account for the circular economy, the net present value (NPV) is maximized to measure the economic feasibility of implementing alternative management pathways. A multi-objective mixed-integer non-linear programming framework accounts for the selection of direct land application, and waste to energy technologies, spatial variation in manure supply, facility sizing, and the products’ consumption and end-of-life. This optimization framework is evaluated for a case study in New York state. Under an attributional life cycle optimization, anaerobic digestion minimizes FE with an impact of 0.002 kg P-eq/ton manure, while using a consequential life cycle optimization, hydrothermal carbonization minimizes FE with an impact of −0.96 kg P-eq/ton manure. For both life cycle methodologies, pyrolysis with land application of biochar minimizes GWP. At the attributional life cycle assessment tradeoff point for GWP and NPV, minimum carbon credits of US$33/ton CO2-eq are necessary for a pyrolysis plant to have a positive NPV, implying that harnessing economies of scale or robust carbon accounting is necessary for the widespread adoption of pyrolysis as a poultry manure management technology.

Firefighting Vehicle Dispatch and Route Planning Model Based on Priority Passage Rights

<div>Efficient fire rescue operations in urban environments are critical for saving lives and reducing property damage. By utilizing connected vehicle systems (CVS) for firefighting vehicles planning, we can reduce the response time to fires while lowering the operational costs of fire stations. This research presents an innovative nonlinear mixed-integer programming model to enhance fire rescue operations in urban settings. The model focuses on expediting the movement of firefighting vehicles within intricate traffic networks, effectively tackling the complexities associated with collaborative dispatch decisions and optimal path planning for multiple response units. This method is validated using a small-scale traffic network, providing foundational insights into parameter impacts. A case study in Sioux Falls shows its superiority over traditional “nearest dispatch” methods, optimizing both cost and response time significantly. Sensitivity analyses involving clearance speed, clearance time, minimum rescue force, and fire loss parameters contribute to the enhancement of urban fire rescue operations and the refinement of practical decision support systems.</div>

Effect of prediction uncertainties on the performance of a white-box model predictive controller for district heating networks

The performance of a model predictive controller (MPC) depends on the accuracy of the controller model and predictions of system disturbances. This paper studies the effect of prediction uncertainties and/or an imperfect state observer on the performance of a white-box MPC applied to a small-scale district heating network by performing a co-simulation with a detailed emulator model. This effect is studied for both a non-linear program (NLP)-based MPC and a mixed-integer NLP (MINLP)-based MPC. The results show a limited impact of prediction uncertainties when using a perfect state observer, with electricity use and thermal discomfort changing by only ▪ to ▪ and ▪/day/building to 0.56 ▪/day/building. An MPC with perfect predictions and a simple state observer only impacts the MPC's trade-off between electricity use and thermal discomfort: the former increases by 2–▪ but the latter decreases by 0.01–▪/day/building. The combined effect of both simplifications has a significant impact with an increase in electricity use and thermal discomfort of 2–▪ and 0.35–▪/day/building, but MPC still outperforms a conventional rule-based controller. The MINLP-based MPC better predicts the actual system behaviour, but its performance is similar compared to the NLP-based MPC in terms of electrical energy use and thermal comfort.

A flexible combinatorial auction bidding language for supplier selection and order allocation in a supply chain with price sensitive demand

This study addresses the multi-item multi-sourcing supplier selection and order allocation problem in a Combinatorial Auction (CA) framework. First, we propose a new flexible procurement CA bidding language, then prove that it can convey the same information as existing bidding languages while allowing more efficient auction outcomes and reduced computational complexity. Suppliers submit combinatorial bids to a single manufacturer. Each bid carries information about the supplier’s cost structure and potential discounts. The manufacturer purchases the items and assembles one or more product types that experience price-sensitive demand rates by end consumers. We use the realistic logit function to represent the price-sensitive demand rates of finished products. A Mixed Integer Non-Linear Programming (MINLP) model is developed to help the manufacturer make optimal supplier selection, order allocation, and pricing decisions under the proposed bidding language. The MINLP model considers purchasing, transportation, ordering, administrative, holding, and manufacturing costs. These considerations make the results of this study realistic with the potential to be used in practical applications. Also, we derive a set of necessary conditions that must exist in at least one optimal solution to the problem. These conditions can be utilized to design efficient solution mechanisms for this difficult problem in the future. Finally, an extensive numerical analysis is performed to illustrate the bidding language and the key results.