Mixed Integer Nonlinear Programming Research Articles

Joint optimization of selective maintenance and repairpersons assignment problem for mission-oriented systems operating under [formula omitted]-dependent competing risks

Mission-oriented systems (MOS) are designed to operate a series of missions seceded by scheduled breaks of limited duration. For MOS, the most appropriate maintenance strategy is the selective maintenance (SM). Under limited maintenance resources, the SM problem (SMP) aims to identify the optimal set of components to maintain in order to meet the required minimum performance for the next missions. However, the majority of the existing SM models merely relies on stochastic independent (s-independent) components. To overcome this restrictive and unrealistic assumption, this work develops a novel SM approach for jointly optimizing SM and repairpersons assignment (RA) problem (RAP) in a MOS operating under s-dependent competing risks. The s-dependent competing risks between components are captured through copula functions whose unknown parameters are estimated by a two-stage maximum likelihood estimation (MLE) method. Furthermore, the MOS operate several missions and scheduled breaks, and multiple repair channels are available. The resulting joint SM and RAP (JSM-RAP) optimization model is formulated as a mixed-integer non-linear program (MINLP) where the objective is to minimize the total maintenance and labor costs for a SM plan that ensures a required minimum reliability threshold for each mission. A genetic algorithm (GA) is used as a solution method. Several numerical experiments are conducted on a ball screw system. The results obtained demonstrate the validity and the add value of the proposed approach, in addition to the robustness and efficiency of the solution method.

Distributed Multi-Agent Approach for Achieving Energy Efficiency and Computational Offloading in MECNs Using Asynchronous Advantage Actor-Critic

Mobile edge computing networks (MECNs) based on hierarchical cloud computing have the ability to provide abundant resources to support the next-generation internet of things (IoT) network, which relies on artificial intelligence (AI). To address the instantaneous service and computation demands of IoT entities, AI-based solutions, particularly the deep reinforcement learning (DRL) strategy, have been intensively studied in both the academic and industrial fields. However, there are still many open challenges, namely, the lengthening convergence phenomena of the agent, network dynamics, resource diversity, and mode selection, which need to be tackled. A mixed integer non-linear fractional programming (MINLFP) problem is formulated to maximize computing and radio resources while maintaining quality of service (QoS) for every user’s equipment. We adopt the advanced asynchronous advantage actor-critic (A3C) approach to take full advantage of distributed multi-agent-based solutions for achieving energy efficiency in MECNs. The proposed approach, which employs A3C for computing offloading and resource allocation, is shown through numerical results to significantly reduce energy consumption and improve energy efficiency. This method’s effectiveness is further shown by comparing it to other benchmarks.

Energy scheduling for microgrids with renewable energy sources considering an adjustable convex hull based uncertainty set

In this paper, a risk-based robust energy scheduling model for microgrids is proposed to address the uncertainty of renewable energy sources (RESs). The proposed model introduces a novel adjustable convex hull based uncertainty set (ACHUS), which is a subset of the maximum uncertainty set, to quantify the uncertainty of RESs. The operational risk of an ACHUS is evaluated by a historical data-based method. This method defines the operational risk as the expected penalty cost of all historical data when the operational safety of the microgrid is guaranteed in the ACHUS. Based on the evaluation of the operational risk, a day-ahead energy scheduling model with the ACHUS for microgrids is formulated as a mixed integer nonlinear programming. By introducing auxiliary variables and constraints, the mixed integer nonlinear programming is converted into a solvable mixed integer linear programming. The effectiveness of the proposed method is validated on the IEEE 6-bus and 118-bus systems. The simulation results show that the proposed method can effectively reduce the conservativeness of uncertainty quantification and the improve the economic efficiency of the microgrid.

An optimal flow rate allocation model of the oilfield treated oil pipeline network

Oilfield treated oil pipeline network is the link connecting the upstream oilfields and the downstream refineries. Due to the differences in operating costs and transportation fee between different pipelines and the fluctuation in the demand and sales prices of the treated oil, there is an optimal flow allocation plan for the pipeline network to make the oilfield company obtain the highest social and economic benefit. In this study, a mixed integer nonlinear programming (MINLP) model is developed to determine the optimal flow rate allocation plan of the large-scale and complex treated oil pipeline network, and both the social and economic benefits are considered simultaneously. The optimization objective is the multi-objective which includes the largest user satisfaction and the highest economic benefit. The model constraints include the oilfield production capacity, refinery demand, pipeline transmission capacity, flow, pressure, and temperature of the node and station, and the pipeline hydraulic and thermal calculations. Python 3.7 is utilized for the programming of the off-line calculation procedure and the MINLP model, and GUROBI 9.0.2 is served as the MINLP solver. Moreover, the model is applied to a real treated oil pipeline network located in China, and three optimization scenarios are analyzed. For social benefit, the values of the user satisfaction of each refinery and the total network are 1 before and after optimization for scenarios 1, 2, and 3. For economic benefit, the annual revenue can be increased by 0.227, 0.293, and 0.548 billion yuan after the optimization in scenario 1, 2, and 3, respectively.

Optimising fleet sizing and management of shared automated vehicle (SAV) services: A mixed-integer programming approach integrating endogenous demand, congestion effects, and accept/reject mechanism impacts

Shared automated vehicles (SAV) are expected to benefit the sustainable development of urban regions and alleviate the negative impacts brought by the increasing number of private cars. In this paper, we envision a future scenario where non-pooled SAVs replace private cars and provide public on-demand mobility services to satisfy the mobility needs of a city’s residents. To help service providers make profitable fleet sizing and management decisions, we develop a mixed-integer non-linear programming model that considers the congestion effects and the mode choice of urban travellers in different income classes, between SAVs and bicycles. Our model optimises both strategic decisions (fleet size, initial fleet distribution, and service quality level) and operational decisions (trip assignment, vehicle routing, parking, and relocation). Travellers’ preference for both transport modes is described through a binary logit model and congestion effects are described by dynamically varying travel times with respect to traffic flow in a non-linear fashion. In addition, we investigate two types of accept/reject mechanisms (mandatory vs. non-mandatory acceptance) which lead to an endogenously determined acceptance rate that can affect travellers’ willingness to use SAV services. The computational challenge posed by the non-linear and non-convex nature of the model is addressed through reformulation and the use of outer-inner approximation methods combined with a breakpoint generation algorithm. We demonstrate the effectiveness of our proposed method in a case study of the city of Delft in The Netherlands, as well as a scaling analysis on three toy networks with various sizes and demand profiles. A sensitivity analysis of key parameters is carried out to assess system performance. Computational results indicate that fleet sizing decisions are influenced not only by the population’s geographical distribution and land use patterns but also by the pricing strategy, unit operating costs of the SAV fleet, network congestion level, and traveller behaviour. When the price rate of using SAVs is low, the fleet sizing decisions can also be influenced by the trip accept/reject mechanism and the travellers’ sensitivity to the service quality level. In addition, a low price of SAV service will attract more users but may not necessarily bring a higher profit because of the increased traffic congestion.

Optimal Control of District Cooling Energy Plant With Reinforcement Learning and MPC

Abstract We consider the problem of optimal control of district cooling energy plants (DCEPs) consisting of multiple chillers, a cooling tower, and a thermal energy storage (TES), in the presence of time-varying electricity price. A straightforward application of model predictive control (MPC) requires solving a challenging mixed-integer nonlinear program (MINLP) because of the on/off of chillers and the complexity of the DCEP model. Reinforcement learning (RL) is an attractive alternative since its real-time control computation is much simpler. But designing an RL controller is challenging due to myriad design choices and computationally intensive training. In this paper, we propose an RL controller and an MPC controller for minimizing the electricity cost of a DCEP and compare them via simulations. The two controllers are designed to be comparable in terms of objective and information requirements. The RL controller uses a novel Q-learning algorithm that is based on least-squares policy iteration. We describe the design choices for the RL controller, including the choice of state space and basis functions, that are found to be effective. The proposed MPC controller does not need a mixed integer solver for implementation, but only a nonlinear program (NLP) solver. A rule-based baseline controller is also proposed to aid in comparison. Simulation results show that the proposed RL and MPC controllers achieve similar savings over the baseline controller, about 17%.

Deep reinforcement learning based trajectory design and resource allocation for task-aware multi-UAV enabled MEC networks

Computing tasks in the air is an important form of mobile edge computing (MEC) to improve the quality of service and enhance network coverage. In this paper, we investigate a multi-UAV cooperative computing model and massive devices access scenario in a service area without infrastructure. There are various types of ground devices with different tasks. Moreover, we consider that the UAV executing tasks of devices need to cache the content that task required. Therefore, we propose a multi-UAV enabled MEC network based on task awareness where each UAV caches some programs to execute tasks offloaded from devices. To minimize completion time, a joint UAV trajectory design, access decision and resource allocation problem is formulated. To address this intractable mixed integer non-linear programming problem, a multi-agent trajectory design and resource allocation (MATR) algorithm is proposed, where the multi-agent deep deterministic policy gradient (MADDPG) is applied. Considering the complexity of high-dimensional continuous action space, we introduce the particle swarm optimization (PSO) algorithm to jointly optimize access decisions, and computation resource allocation to reduce action space. In addition, we discuss the impact of the size of UAV cache space and the location of ground devices on the completion time. Simulation results show that the MATR algorithm can significantly reduce the completion time compared to the baselines.

Multiperiod optimization of cooling water system with flexible topology network

Cooling water systems (CWSs) are extensively utilized in various industries to eliminate the excess heat and converse energy. Studies on CWSs mainly concentrated on finding the optimal cooler network structure. In addition, some works also considered the optimal design under varied operation conditions. However, in these works, once the optimal design of the cooler's network is determined, its arrangement remains fixed and cannot be adapted to accommodate diverse operating conditions. In this work, a flexible topology network concept is proposed to make the adjustment of network structure possible under different operation conditions. The CWS with integrated air cooler and flexible topology network has better overall performance, represented by a mixed integer nonlinear programming (MINLP) model that require advanced tools such as GAMS software. Case studies revealed that the proposed methodology can realize better energy-saving performance, and improve the economic performance under varied operation conditions. The impact of critical flexible nodes on system configuration and economy is achieved by sensitivity analysis.

A Security-constrained Unit Commitment-based Optimal Battery Usage Pattern Model

This paper discusses multiple strategies of security-constrained unit commitment (SCUC)-based optimal battery usage pattern models to drive the charging and discharging of different batteries and help the operation cycles satisfy their preferences according to battery characteristics. Previous studies mainly focus on either battery storage integration as a controllable resource into the grid with high penetration of renewable energy, or battery degradation costs as additional terms in the objective function of SCUC. In comparison, this paper first considers whether battery operation cycles satisfy their preferences according to specific battery characteristics. It discusses a full charging/discharging strategy for Ni-Cd batteries, which have a memory effect and prefer deep cycles. Then, the paper explores a shallow cycle strategy for Lithium-ion, lead acid, and Ni-H batteries, which have no memory effect and prefer shallow cycles for long service life. Subsequently, it is extended to a hybrid strategy when batteries with/without memory effects are at the same node. The proposed model minimizes the total operation cost of SCUC while including the penalties for battery usage strategies. The original problem is a mixed integer non-linear programming (MINLP) one, and then it can be mathematically converted into a mixed integer linear programming (MILP) one. Consequently, the models with multiple strategies are tested through IEEE 6-node power system. Computational results show that, compared to the base case without any strategy, the proposed optimal battery usage pattern approaches have an advantage in driving Ni-Cd batteries toward deep cycles, guiding Lithium-ion batteries towards shallow cycles, and improving the flexibility of performance with hybrid applications.

Joint Task Offloading and Resource Allocation for Fog-Based Intelligent Transportation Systems: A UAV-Enabled Multi-Hop Collaboration Paradigm

Unmanned aerial vehicles (UAVs) have been widely used in Intelligent Transportation Systems (ITS) due to their rapid deployment and high mobility, which are considered as a promising solution to expand the scope of communication, especially in inaccessible areas. However, there is a lack of a universal and extensible multi-hop collaboration model in the existing research on UAV-involved ITS. In this paper, we innovatively introduce a novel UAV-enabled multi-hop collaborative fog computing (FC) system model, in which several moving UAVs with unpredictable locations provide effective and efficient communication and computation services for ground user equipments (UEs). With this model, we mathematically formulate a joint user association, UAV association, task offloading, transmission power, computation resource allocation, and UAV location optimization problem, which is a mixed integer nonlinear programming (MINLP) problem and challenging to deal with. To solve the non-convex problem, we propose a novel multi-hop collaborative algorithm to derive the optimal task offloading and resource allocation decisions for each UAV. Simulation results demonstrate the superiority of the UAV-enabled multi-hop collaborative FC system and validate the effectiveness of the proposed scheme.

IDESS: a toolbox for identification and automated design of stochastic gene circuits.

One of the main causes hampering predictability during the model identification and automated design of gene circuits in synthetic biology is the effect of molecular noise. Stochasticity may significantly impact the dynamics and function of gene circuits, specially in bacteria and yeast due to low mRNA copy numbers. Standard stochastic simulation methods are too computationally costly in realistic scenarios to be applied to optimization-based design or parameter estimation. In this work, we present IDESS (Identification and automated Design of Stochastic gene circuitS), a software toolbox for optimization-based design and model identification of gene regulatory circuits in the stochastic regime. This software incorporates an efficient approximation of the Chemical Master Equation as well as a stochastic simulation algorithm-both with GPU and CPU implementations-combined with global optimization algorithms capable of solving Mixed Integer Nonlinear Programming problems. The toolbox efficiently addresses two types of problems relevant in systems and synthetic biology: the automated design of stochastic synthetic gene circuits, and the parameter estimation for model identification of stochastic gene regulatory networks. IDESS runs under the MATLAB environment and it is available under GPLv3 license at https://doi.org/10.5281/zenodo.7788692.

Multi-IRS-Aided Millimeter-Wave Multi-User MISO Systems for Power Minimization Using Generalized Benders Decomposition

Difficulties in controlling IRSs to form the optimized passive beamforming have rarely been considered in intelligent reflecting surface (IRS)-aided systems, which are summarized as follows: 1) sending the optimized passive precoding vectors to the IRS controller incurs significant control overheads; 2) implementing the optimized passive precoding needs to set massive modes in the IRS control circuit. To address these issues, we investigate codebook-based passive beamforming for multi-IRS-aided millimeter-wave (mmWave) multi-user multiple-input single-output (MU-MISO) systems, where the control overheads are reduced to several scalars and the number of modes set in the IRS control circuit is reduced to that of codewords. Moreover, we formulate a joint passive and active precoding problem in the multi-IRS-aided mmWave MU-MISO system as a mixed-integer nonlinear programming (MINLP) problem, and then develop a generalized Benders decomposition (GBD)-based joint passive and active precoding algorithm. The proposed algorithm offers near-optimal performance (≥ 99.9%) with significantly-reduced computational complexity. Simulation results show that the proposed algorithm achieves energy savings of up to 50% and 95%, compared to the benchmark by the maximum ratio transmission and that without IRSs, respectively. In addition, the energy savings increase with the number of reflecting elements packed on each IRS as well as that of codewords.

Modeling and Optimization of Parallel Disassembly Line Balancing Problem With Parallel Workstations

To reasonably arrange disassembly facilities and plan enterprise space, we propose a parallel disassembly line balancing problem (PW-PDLBP) with parallel workstations. Additionally, a mixed-integer non-linear programming (MINLP) model that minimizes the line length, number of workstations, idle time balancing index, and energy consumption is established based on the problem characteristics and is solved using the GUROBI optimizer. Furthermore, a multi-objective enhanced differential evolution algorithm (MEDE) is developed to obtain high-quality disassembly schemes for PW-PDLBP. The correctness of encoding and decoding and the solving performance of MEDE are verified by comparing with the MINLP model and four existing algorithms. Then, an instance consisting of two different types of end-of-life TVs is optimized. Finally, the effectiveness of PW-PDLBP in improving enterprise space utilization is validated by comparing it with the parallel line layout without parallel workstations.

Coordinated Optimization of Emergency Response Resources in Transportation-Power Distribution Networks Under Extreme Events

The proliferation of electric vehicles (EVs) and the increasing interdependence across power distribution networks (DNs) and transportation networks (TNs) have increased the complexity and vulnerability of the two systems in extreme circumstances. As the interdependence of two infrastructures tightens over time, it is viewed as a dire necessity to strengthen the resilience of the coordinated transportation-power distribution networks (TDNs) against natural disasters. This paper constructs a coordinated optimization method of TN traffic link reversing, DN line switching, and fast charging pile management, to improve the TDN performance in the emergency response stage after disasters. A dynamic TN model and a multi-period DN model are integrated in TDN modeling to capture flow propagations and state variations among time intervals. The coordinated optimization for TDN emergency response is designed as a mixed-integer nonlinear programming (MINLP) problem with high-order objective functions and nonlinear constraints to minimize TN travel costs and DN active and reactive power shortages. An accuracy-aware adaptive piecewise linearization approach combined with Gray code-based encoding is utilized to improve the computational efficiency for solving the TDN optimization problem. Numerical simulations show that the TDN performance is enhanced by coordinating various DN and TN resources, as compared with those of separate and conventional topology controls. The proposed TDN solution method has significantly reduced the computation time for managing extreme conditions while guaranteeing the accuracy of the results as compared with those of the nonlinear model and the linearized model by uniform piecewise linearization.

Comparing perspective reformulations for piecewise-convex optimization

We aim at generalizing formulations for non-convex piecewise-linear problems to mathematical programs whose non-convexities are only expressed in terms of piecewise-convex univariate functions. This is motivated by solving Mixed-Integer Non-Linear Programming (MINLP) problems with separable non-convex functions via the Sequential Convex MINLP technique. We theoretically and computationally compare different formulations, showing that, unlike in the linear case, they are not equivalent when perspective reformulation is applied to strengthen the formulation of each single segment.

Height-Fixed UAV Enabled Energy-Efficient Data Collection in RIS-Aided Wireless Sensor Networks

Wireless sensor nodes (SNs) are usually energy-limited, a low energy efficiency of SN may be caused by the occlusion of transmission link in the unmanned aerial vehicle (UAV)-enabled data collection. Reconfigurable intelligent surfaces (RISs) provide potential communication opportunities by reflecting and enhancing the signal, thus increasing SNs’ energy efficiency. This paper investigates energy-efficient data collection aided by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> RIS elements, where a height-fixed and flight time-constrained UAV is considered as the collector, a tractable air-to-ground channel model is established considering the cascaded RIS channel and time-varying trajectory of UAV, and energy consumption of SNs is minimized. Specifically, coupling two intractable fourth-order moment variables, the air-to-ground channel model is processed into an easily computable expression through the Gamma function. Furthermore, based on the proposed two RIS deployment schemes, maximum energy consumption of SNs minimization problem is formulated as a non-convex mixed-integer nonlinear programming (NMNP) problem with optimization of UAV trajectory and SNs wake-up schedules. Additionally, through the slack technique and Taylor expansion, the NMNP problem is decoupled as linear programming and quadratically constrained quadratic programming, and an effective algorithm is designed to obtain the sub-optimal solution. Simulations prove the validity of our algorithm and RIS deployment insights are given for SNs energy saving.

Maximizing the Connectivity of Network Slicing Enabled Internet of Vehicle With Differentiated Services

The advent of 5G opens up hitherto unimagined opportunities for delivering the much-anticipated Internet of Vehicles (IoV). There are two typical types of services in IoV, i.e., safety service and non-safety service. However, the existing IoV framework cannot efficiently support the differentiated IoV services. In addition, maximizing the number of accessed vehicles/users is another critical issue in IoV, especially in the dense urban area. To address these problems, in this paper, we utilize the emerging network slicing technology to support different services and employ Non-Orthogonal Multiple Access technology (NOMA) to help increase the connectivity. In particular, for the safety service, we take advantage of the finite blocklength capacity to correctly record the delay. Our goal is to maximize the connectivity of users by jointly considering the user association and their beamforming vectors, under the restrictions of limited physical resource. The problem is formulated as a Mixed-Integer Nonlinear Programming problem (MINLP). To tackle the intractable MINLP, we propose a two-stage scheme. Firstly, we exploit efficient approaches to solve the beamforming problem, i.e., successive convex approximation, semidefinite relaxation and second-order cone programming. Secondly, we propose a low-complexity Greedy User Association (GUA) algorithm to solve the user association problem. Finally, comprehensive simulations verify that our proposed GUA algorithm is close to global optimal solution and outperforms the benchmark schemes.

Train rescheduling and platforming in large high-speed railway stations

To deal with train delays in large high-speed railway stations, a multi-objective mixed-integer nonlinear programming (MO-MINLP) optimization model was proposed. The model used the arrival time, departure time, track occupation, and route selection as the decision variables and fully considered the station infrastructure layout, train operational requirements, and time standards as limiting factors. The optimization objective was to minimize train delays and reduce track and route adjustments. To realize the large-scale and rapid solution of the MO-MINLP model, this study proposed a rolling horizon optimization algorithm that used “half an hour” as a time interval and solved the rescheduling and platforming problem of each time interval step-by-step. In numerical experiments, 227 train movements under delay circumstances in Hangzhoudong station were optimized by using the proposed model and solution algorithm. The results show that the proposed MO-MINLP model could resolve route conflicts, compress unnecessary dwell times, and reduce train delays; the solution algorithm could efficiently increase the computational speed. The maximum solution time for optimizing the 227 train movements is 15 min 24 s.

A two-stage optimization method for improving the load flexibility of existing district energy systems

Decarbonization of district energy systems is essential for China to meet its carbon neutrality goal by 2060. Most existing district energy systems are missing historical load data and have incomplete information, resulting in a lack of data support for the low-carbon transition. Moreover, demand-side load flexibility has not been fully exploited in the planning stage. In this paper, we developed a two-stage computational approach to optimize district loads. We first established an integrated Python framework, incorporating the TEASER simulation tool and AixLib model library, to efficiently calculate baseline loads through the bottom-up modeling and simulation of district buildings. Then, a price-based integrated demand response strategy was introduced. A mixed-integer nonlinear programming model was formulated to optimize the energy pricing strategy with the objective of minimum load fluctuations. Finally, a case study was employed to illustrate the feasibility of the calculation method, showing a normalized mean bias error of 7.17%. The results further demonstrated that the strategy could reduce the peak electric and heat loads by 3.55% and 9.57%, and increase load rates by 3.85% and 9.48%, respectively. The strategy could assist district energy service providers to optimize equipment capacity configuration and enhance the low-carbon planning potential of energy systems from the demand-side.

An optimization model for the layout of a branching water distribution system

This paper presents an optimization model for the layout of a branching water distribution system. The goal is to minimize construction costs while meeting the system's demands. The study utilizes the general algebraic modeling system (GAMS) to optimize a non-looping water distribution system. The methodology involves determining the existence and diameter of connections between demand nodes. The optimization problem is formulated as a mixed-integer non-linear programming (MINLP) problem. A simplified layout is used to illustrate the constraints and validate the model. The explicit model implemented in GAMS yields optimal solutions and demonstrates the effectiveness of the approach. The results highlight the decisions on connection existence, flow, and pipe diameter, contributing to cost minimization. The findings from this study provide insights for optimizing the design of branching water distribution systems and reducing construction costs.