Nonconvex Mixed-integer Nonlinear Programming Research Articles

Enhancing airline connectivity: An optimisation approach for flight scheduling in multi-hub networks with bank structures

While one salient characteristic of hub airports lies in connecting passengers, the full-service airlines in North America concentrate their networks spatially over a number of hubs. Having witnessed the emerging multi-hub network, this paper investigated the flight scheduling problem under a multi-hub configuration, taking a well-defined bank structure and airport operational restrictions into account. An integrated non-convex Mixed-Integer Nonlinear Programming (MINLP) approach was proposed to enhance airline connectivity, considering different combinations of traffic flow direction and connecting times. To verify the scalability and effectiveness of the proposed model, a comprehensive case study has been undertaken with real-world scheduling data from Air China, which was solved by a novel problem-specific Selective Simulated Annealing (SSA) algorithm. Substantial improvements were achieved without sacrificing the scheduling efficiency. Precisely, the programme adjusted the flights during a typical operational day in a timely manner. The post-optimisation outcomes have witnessed its effectiveness with a 17.97%, 17.06%, 22.41% and 53.86% increase in airline connectivity at its four major hub airports (Chengdu Shangliu, Beijing Capital, Shanghai Pudong and Hongqiao) in China, respectively. A clear pattern of the bank structure also confirms its positive impact on airline connectivity under the multi-hub network configuration. Lastly, a comparative analysis for the distribution of all feasible connections further highlights the critical challenge concerning the role of the hubs in a multi-hub network. More specifically, Air China’s multi-hub network systematically performs better on Domestic-International routes, due to flight schedule, frequencies, geographical placements and detours. Among the four hub airports, Beijing Capital International Airport stands out as a dominant one, which implies its potential to serve as a robust international hub airport.

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.

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.

A centralized EMPC scheme for PV-powered alkaline electrolyzer

Photovoltaic (PV)-powered alkaline electrolyzer system (PVPAES) is an advanced technique to convert the off-grid and intermittent PV-based solar energy into storable and transportable electrolyzer-based hydrogen energy with zero carbon emissions. However, it is difficult to realize the coordinated control of the off-grid PV module and the alkaline electrolyzer, due to the multiple timescale dynamics. To address this challenge, the PVPAES is decomposed into the slow part and fast part based on the dynamic time scale. Exploiting the decomposed subsystems, the slow one is assumed to be managed well by the auxiliary controller. For the fast one, a centralized economic model predictive control (CEMPC) scheme is constituted. This CEMPC integrates the energy management system and local feedback control into a single optimal control framework. A mathematical model of the PVPAES is established, on the basis of which the CEMPC directly adopts the economic indices as the cost function to realize the flexible power point tracking, power supply-demand balance, and dynamic economic optimization. Moreover, the inherent strong nonlinearity of PVPAES results in the nonconvex mixed-integer nonlinear programming optimization problem in the CEMPC. The exhaustive search algorithm utilizing finite converter switching states is adopted to achieve the global economic optimum. The effectiveness of the proposed CEMPC controller is illustrated through simulations under varying irradiance conditions.

Large-scale optimization of nonconvex MINLP refinery scheduling

Modeling and optimization of large-scale refinery scheduling problems is challenging because of their complexity and size. Herein, we propose a mathematical model to represent such problems more accurately and realistically, and a state-of-the-art optimization framework for its solution. The framework leverages the use of mathematical optimization and algorithmic methods by combining modeling approaches (process design, model decompositions), solving strategies (rescheduling, heuristics), and machine learning regression (surrogate models). An industrial-size refinery scheduling problem (2 blenders, 4 feed tanks, distillation network with 5 towers, processing network with FCC, hydrotreaters, debutanizers, superfractionator, catalytic reformer) is formulated as a hierarchical nonconvex mixed-integer nonlinear programming (MINLP) model and is successfully optimized, providing higher profitability and more efficient scheduling operations considering 12 feedstocks, 10 products and multiple scenarios for time horizon and step. Results highlight the importance of tuning scheduling parameters and employing an enhanced computer-aided framework to enable the solution of industrial refinery scheduling operations.

Smart landscaping design for sustainable net-zero energy smart cities: Modeling energy hub in digital twin

In our study, we introduce an innovative energy management system optimized for energy hubs in net-zero energy smart cities, emphasizing sustainability as a core objective. Our approach intricately integrates distributed generation systems and storage facilities within a digital twin framework, incorporating landscape considerations to promote environmental harmony. By prioritizing sustainability, our strategy aims to minimize operational costs while maximizing energy efficiency and reducing carbon emissions. We employ specialized energy flow algorithms for each grid, designing energy hubs that leverage renewable resources and mobile storage to enhance sustainability. To address complexity, our model utilizes a non-convex mixed-integer nonlinear programming structure and robust adaptive optimization techniques, combining the Gray Wolf and Krill Herd algorithms. Through simulations, we demonstrate significant improvements in power system efficiency, including notable reductions in power loss, peak voltage fluctuations, and temperature variations. Our research underscores the critical role of smart landscaping in advancing sustainable energy management for net-zero energy smart cities, facilitating seamless integration of energy hubs with the surrounding landscape within a digital twin paradigm.

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.

Online Joint Optimization of Virtual Network Function Deployment and Trajectory Planning for Virtualized Service Provision in Multiple-Unmanned-Aerial-Vehicle Mobile-Edge Networks

The multiple-unmanned-aerial-vehicle (multi-UAV) mobile edge network is a promising networking paradigm that uses multiple resource-limited and trajectory-planned unmanned aerial vehicles (UAVs) as edge servers, upon which on-demand virtual network functions (VNFs) are deployed to provide low-delay virtualized network services for the requests of ground users (GUs), who often move randomly and have difficulty accessing the Internet. However, VNF deployment and UAV trajectory planning are both typical NP-complete problems, and the two operations have a strong coupling effect: they affect each other. Achieving optimal virtualized service provision (i.e., maximizing the number of accepted GU requests under a given period T while minimizing the energy consumption and the cost of accepting the requests in all UAVs) is a challenging issue. In this paper, we propose an improved online deep reinforcement learning (DRL) scheme to tackle this issue. First, we formulate the joint optimization of the two operations as a nonconvex mixed-integer nonlinear programming problem, which can be viewed as a sequence of one-frame joint VNF deployment and UAV-trajectory-planning optimization subproblems. Second, we propose an online DRL based on jointly optimizing discrete (VNF deployment) and continuous (UAV trajectory planning) actions to solve each subproblem, whose key idea is establishing and achieving the coupled influence of discrete and continuous actions. Finally, we evaluate the proposed scheme through extensive simulations, and the results demonstrate its effectiveness.

Energy-efficient BS sleeping, user association, and resource allocation in full-duplex ultra-dense networks

Full-duplex ultra-dense network (FD-UDN) is a promising technology in 5G mobile networks for handling the increase in network capacity. However, interference management and energy efficiency are two of the most important challenges that must be addressed. With the small base stations (SBSs) densification, employing sleeping strategy coupled with resource management becomes an effective approach to manage interference and power consumption in FD-UDN. To the best of our knowledge, this aspect has not been addressed in previous work. To this end, we develop a framework to optimize the BS sleeping and resource management with the aim of maximizing energy efficiency and maintaining the quality of service (QoS) requirements of users. The problem is formulated as a non-convex mixed-integer non-linear programming problem, which is difficult to handle. Employing the Dinkelbach method, the objective function of the problem is converted to an equivalent parametric subtractive form. Then, the problem is decoupled into two sub-problems: user association and resource allocation, as well as BSs on/off switching. The former is solved using the iterative reweighted lq-norm minimization (IRM) method, and the latter is solved using the Lagrangian dual method and the constrained concave-convex procedure (CCCP). The simulation results demonstrate that the proposed method is more effective than traditional ones in simultaneously improving the EE, reducing power consumption, and keeping fewer SBSs active, especially in high network loads.

Global optimization of mixed-integer nonlinear programs with SCIP 8

AbstractFor over 10 years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version 8.0, these capabilities have been largely reworked and extended. This paper discusses the motivations for recent changes and provides an overview of features that are particular to MINLP solving in SCIP. Further, difficulties in benchmarking global MINLP solvers are discussed and a comparison with several state-of-the-art global MINLP solvers is provided.

Coalitional Game Based Resource Allocation in D2D-Enabled V2V Communication

The joint resource block (RB) allocation and power optimization problem is studied to maximize the sum-rate of the vehicle-to-vehicle (V2V) links in the device-to-device (D2D)-enabled V2V communication system, where one feasible cellular user (FCU) can share its RB with multiple V2V pairs. The problem is first formulated as a nonconvex mixed-integer nonlinear programming (MINLP) problem with constraint of the maximum interference power in the FCU links. Using the game theory, two coalition formation algorithms are proposed to accomplish V2V link partitioning and FCU selection, where the transferable utility functions are introduced to minimize the interference among the V2V links and the FCU links for the optimal RB allocation. The successive convex approximation (SCA) is used to transform the original problem into a convex one and the Lagrangian dual method is further applied to obtain the optimal transmit power of the V2V links. Finally, numerical results demonstrate the efficiency of the proposed resource allocation algorithm in terms of the system sum-rate.

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.

Optimization under uncertainty of a hybrid waste tire and natural gas feedstock flexible polygeneration system using a decomposition algorithm

Market uncertainties motivate the development of flexible polygeneration systems that are able to adjust operating conditions to favor production of the most profitable product portfolio. However, this operational flexibility comes at the cost of higher capital expenditure. A scenario-based two-stage stochastic nonconvex Mixed-Integer Nonlinear Programming (MINLP) approach lends itself naturally to optimizing these trade-offs. This work studies the optimal design and operation under uncertainty of a hybrid feedstock flexible polygeneration system producing electricity, methanol, dimethyl ether, olefins or liquefied (synthetic) natural gas. A recently developed C++ based software framework (named GOSSIP) is used for modeling the optimization problem as well as its efficient solution using the Nonconvex Generalized Benders Decomposition (NGBD) algorithm. Two different cases are studied: The first uses estimates of the means and variances of the uncertain parameters from historical data, whereas the second assesses the impact of increased uncertain parameter volatility. The value of implementing flexible designs characterized by the value of the stochastic solution (VSS) is in the range of 260–405 M$ for a scale of approximately 893 MW of thermal input. Increased price volatility around the same mean results in higher expected net present value and VSS as operational flexibility allows for asymmetric exploitation of price peaks.

Joint Task Offloading and Resource Allocation for Vehicular Edge Computing With Result Feedback Delay

In this paper, we study the problem of joint Task offloading and resource Allocation for vehicular edge computing with Result Feedback Delay (TARFD). Specifically, we consider a typical roadside unit (RSU) and vehicles within its coverage area, and optimize the task offloading decisions of vehicles as well as the uplink bandwidth allocation and the computation resources allocation on the RSU. The TARFD problem is formulated as a non-convex mixed integer nonlinear programming (MINLP) to minimize the average delay consisting of task offloading delay, task computation delay, and result feedback delay. We derive a lower bound of the optimum to the TARFD problem, based on which we propose an approximate algorithm of the TARFD problem, called A-TARFD. The A-TARFD algorithm can effectively deliver solutions for small-scale scenarios. To tackle large-scale scenarios, a low-complexity algorithm for the TARFD problem, called L-TARFD, is developed by constructing an iteratively updated sequence of locally tight approximate geometric programming (GP) problems. The L-TARFD algorithm can converge to a Karush-Kuhn-Tucker (KKT) point and forces the offloading decisions arbitrarily close to binary values. By comparison with the lower bound, simulation results show that the proposed two algorithms have near-optimal performance over a wide range of parameter settings.

Incentive Mechanism and Resource Allocation for Collaborative Task Offloading in Energy-Efficient Mobile Edge Computing

We investigate a mobile edge computing (MEC) system that supports collaborative task offloading, allowing busy users to offload their tasks to the server and idle users, or perform them locally. However, executing computing tasks consumes device energy, making idle users unwilling to perform other users' tasks due to limited battery capacity. Additionally, the components of the total energy expenditure of the MEC system supporting collaborative task offloading are complex, necessitating appropriate resource allocation and offloading strategies to minimize the system's total energy consumption. To address these challenges, we propose a computing resource sharing auction (CRSA) algorithm to motivate idle users to participate in task offloading. Then, we establish a non-convex mixed-integer nonlinear programming (MINLP) problem to minimize the total energy consumed by the system. By utilizing the McCormick and continuous relaxation (CR) approaches, we develop a low-complexity resource allocation algorithm. Finally, the numerical results demonstrate the effectiveness of the proposed mechanism and resource allocation algorithm.

Pump scheduling optimization in water distribution system based on mixed integer linear programming

The energy consumption in water distribution systems (WDSs) is significant. Improving the efficiency of pump operation can significantly reduce energy costs. However, optimal pump operation is a nonconvex mixed-integer nonlinear programming (MINLP) problem, which can be challenging to solve. A feasible approach is to linearize the problem and convert it into a mixed-integer linear programming (MILP) problem. However, this approach introduces many auxiliary variables, which can lead to inefficiency in finding the optimal solution due to the expanded search space. To address this issue, we propose a novel method for linearization of the original MINLP problem and a strategy that can adaptively adjust the number of piecewise linearization breakpoints. By reducing the number of auxiliary variables, our approach achieved competitive computing efficiency and the ability to save energy costs, as demonstrated in two benchmark instances. Furthermore, in a realistic large-scale WDS, our approach saved 9.83% more energy costs than the genetic algorithm and achieved a gap of only 7.36% from the lower bound.

Joint Terminal Pairing and Multi-Dimensional Resource Allocation for Cooperative Computation in a WP-MEC System

The combination of multi-access edge computing (MEC) and wireless power transfer (WPT) can potentially improve system performance and prolong terminals’ battery lifetime. In this paper, we study cooperative computation in a wireless powered multi-access edge computing (WP-MEC) system. In this system, there are an access point (AP) deployed with an MEC server and multiple cellular terminals that are powered by harvested energy from a power station. The computational task of each terminal is partially completed locally and partially offloaded to the AP and an nearby idle terminal. In order to minimize energy consumption in the system, we jointly optimize terminal pairing and multi-dimensional resource (i.e., computing power and communication resource) allocation. A non-convex mixed-integer non-linear programming (MINLP) problem is formulated in this paper. To solve this challenging problem, we propose a bilevel optimization approach, in which the multi-dimensional resource allocation scheme is designed under given terminal pairing relationships in the inner level, and then the pairing relationships between terminals are obtained in the outer level based on the obtained multi-dimensional resource allocation scheme. Extensive numerical results show that the proposed bilevel optimization scheme can reduce energy consumption considerably compared to some baseline schemes.

AI-Based Resource Allocation in End-to-End Network Slicing Under Demand and CSI Uncertainties

Network slicing (NwS) is one of the main technologies in the fifth-generation of mobile communication and beyond (5G+). One of the important challenges in the NwS is information uncertainty which mainly involves demand and channel state information (CSI). Demand uncertainty is divided into three types: number of users requests, amount of bandwidth, and requested virtual network functions workloads. Moreover, the CSI uncertainty is modeled by three methods: worst-case, probabilistic, and hybrid. In this paper, our goal is to maximize the utility of the infrastructure provider by exploiting deep reinforcement learning (DRL) algorithms in end-to-end NwS resource allocation under demand and CSI uncertainties. Enhanced mobile broadband (eMBB) requires high data rates. The uncertainties we argued above have a direct negative impact on the data rate and our objective function. Therefore, we focus primarily on eMBB. Additionally, we also consider ultra-reliable low latency communications (uRLLC) and massive machine-type communication (mMTC). The proposed formulation is a non-convex mixed-integer non-linear programming problem. To perform resource allocation in problems that involve uncertainty, we need a history of previous information. To this end, we use a recurrent deterministic policy gradient (RDPG) algorithm, a recurrent and memory-based approach in DRL. Then, we compare the RDPG method in different scenarios with soft actor-critic (SAC), deep deterministic policy gradient (DDPG), distributed, and greedy algorithms. The simulation results show that the SAC method is better than the DDPG, distributed, and greedy methods, respectively. Moreover, the RDPG method out performs the SAC approach on average by 70%.

Latency Minimization for Advanced RSMA-Enabled Wireless Caching Networks

The collaboration between wireless edge caching and rate splitting multiple access (RSMA) can significantly reduce the perceived latency of users. In this letter, an advanced RSMA transmission scheme is proposed with the consideration of users’ content requests. In traditional RSMA, multiple replicas of the same messages are transmitted when users request the same contents, which cause the redundant interference. The advanced RSMA is proposed to reduce such redundant interference. Based on the newly designed transmission paradigm, we investigate the joint cache placement and RSMA resource management problem, aiming to minimize the average latency of all users. The formulated problem is a non-convex mixed-integer nonlinear programming (MINLP) problem. By leveraging its structural features, we decompose the original minimization problem into two types of subproblems, i.e., the long-term caching decision problem and the short-term RSMA resource allocation problem. The caching decision problem is tackled by the dynamic programming approach. Whilst the RSMA resource allocation problem is solved by an alternating optimization method with one-dimensional search. Extensive simulation results validate the superiority of our proposed scheme compared to various benchmark strategies.

Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics

In this paper, we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. Cozad and Sahinidis propose a nonconvex mixed-integer nonlinear program (MINLP), in which binary variables are used to assign operators and nonlinear expressions are used to propagate data values through nonlinear operators, such as square, square root, and exponential. We extend this formulation by adding new cuts that improve the solution of this challenging MINLP. We also propose a heuristic that iteratively builds an expression tree by solving a restricted MINLP. We perform computational experiments and compare our approach with a mixed-integer program–based method and a neural network–based method from the literature. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods &amp; Analysis. Funding: This work was supported by the Applied Mathematics activity within the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research [Grant DE-AC02-06CH11357]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0050 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0050 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .