Mixed-integer Nonlinear Optimization Problem Research Articles

PowerModelsRestoration.jl: An open-source framework for exploring power network restoration algorithms

With the escalating frequency of extreme grid disturbances, such as natural disasters, comes an increasing need for efficient recovery plans. Algorithms for optimal power restoration play an important role in developing such plans, but also give rise to challenging mixed-integer nonlinear optimization problems, where tractable solution methods are not yet available. To assist in research on such solution methods, this work proposes PowerModelsRestoration, a flexible, open-source software framework for rapidly designing and testing power restoration algorithms. PowerModelsRestoration constructs a mathematical modeling layer for formalizing core restoration tasks that can be combined to develop complex workflows and high performance heuristics. The efficacy of the proposed framework is demonstrated by proof-of-concept studies on three established cases from the literature, focusing on single-phase positive sequence network models. The results demonstrate that PowerModelsRestoration reproduces the established literature, and for the first time provide an analysis of restoration with nonlinear power flow models, which have not been previously considered.

Design Optimization of Tapered Steel Wind Turbine Towers by QPSO Algorithm

Wind energy has become one of the most widely used alternative energy sources in recent years due to its clean and renewable character. In the context of increasing demand for new facilities, the cost of a wind turbine is a key factor for the success of new wind farms. The reduction of the amount of material used to build the wind turbine tower is one way to reduce the project cost. This work presents a methodology for the minimization of the weight of the tubular steel towers of wind turbines using a metaheuristic optimization algorithm. The diameters of the cross-section at the base and the top of the conical tower are considered as continuous design variables. Due to constructional aspects, the tower is manufactured in many segments, which wall thicknesses are taken as discrete design variables. Besides the dead load, the design considers the action of wind load, which is taken as an equivalent static force determined using the Brazilian standard NBR6123. The design constraints considered in this work are the maximum admissible displacements at the top of the tower under service condition, the tower's lowest natural frequency and the safety criteria for steel structures defined by the Brazilian standard NBR8800. The mixed-integer nonlinear optimization problem formulated for the structural design in this work is solved using the quantum particle swarm optimization algorithm (QPSO). On average, the QPSO solution was 12% lighter than designs based on other well-established algorithms in a comparative study. Nonetheless, no significant improvement was observed concerning the standard particle swarm optimization.

Protection system planning for distribution networks: A probabilistic approach

This paper presents a multi-objective optimization approach to perform the allocation, sizing and coordination of control and protective devices in distribution networks with different types of distributed generation. The model consists of three objective functions that consider investment costs, the system’s non-supplied energy, and average interruption duration index. We use a probabilistic short-circuit routine to evaluate the currents values, taking into account the uncertainties of renewable power generation and the system’s loading, as well as the fault’s parameters randomness. The probabilistic approach allows the correct planning of the protection system and enables the user to admit some risk of not coordinated operation, aiming to reduce the solutions’ costs. This multi-objective mixed-integer non-linear optimization problem considers the possibility of load transfers from neighboring feeders and intentional islanding. In this paper, we use the Non-dominated Sorting Genetic Algorithm to solve this optimization problem. The algorithm is tested for a 135-bus feeder.

Hypergraph-based resource allocation for Device-to-Device underlay H-CRAN network

In the hybrid communication scenario of the Heterogeneous Cloud Radio Access Network and Device-to-Device in 5G, spectrum efficiency promotion and the interference controlling caused by spectrum reuse are still challenges. In this article, a novel resource management method, consisting of power and channel allocation, is proposed to solve this problem. An optimization model to maximum the system throughput and spectrum efficiency of the system, which is constrained by Signal to Interference plus Noise Ratio requirements of all users in diverse layers, is established. To solve the non-convex mixed integer nonlinear optimization problem, the optimization model is decomposed into two sub-problems, which are all solvable quasi-convex power allocation and non-convex channel allocation. The first step is to solve a power allocation problem based on solid geometric programming with the vertex search method. Then, a channel allocation constructed by three-dimensional hypergraph matching is established, and the best result of this problem is obtained by a heuristic greed algorithm based on the bipartite conflict graph and µ-claw search. Finally, the simulation results show that the proposed scheme improves the throughput performance at least 6% over other algorithms.

Inversion of convection–diffusion equation with discrete sources

We present a convection–diffusion inverse problem that aims to identify an unknown number of sources and their locations. We model the sources using a binary function, and we show that the inverse problem can be formulated as a large-scale mixed-integer nonlinear optimization problem. We show empirically that current state-of-the-art mixed-integer solvers cannot solve this problem and that applying simple rounding heuristics to solutions of the relaxed problem can fail to identify the correct number and location of the sources. We develop two new rounding heuristics that exploit the value and a physical interpretation of the continuous relaxation solution, and we apply a steepest-descent improvement heuristic to obtain satisfactory solutions to both two- and three-dimensional inverse problems. We also provide the code used in our numerical experiments in open-source format.

Solving Unit Commitment Problem in Deregulated Power Systems Environment. (Dept. E. )

With the fast-paced changing technologies in the power industry, new power references addressing new technologies are coming to the market. So there is an urgent need to keep track of international experiences and activities taking place in the field of modern unit-commitment (UC) problem. UC is a nonlinear mixed integer optimization problem to schedule the operation of the generating units at minimum operating cost while satisfying the demand and other equality and inequality constrains. The UC problem has to determine the on/off state of the generating units at each hour of the planning period and optimally dispatch the load among the committed units. UC is the most significant optimization task in the operation of the power systems. Solving the UC problem for large power systems is computationally expensive. The complexity of the UC problems grows exponentially with the number of generating units especially by applying the deregulated rules in power system. Where in this environment the objective function is maximizing the profit while satisfying the regular unit commitment constrains in addition to new constrains such as bilateral and multilateral contracts. So in this paper, an exact mathematical optimization procedure called “dynamic programming.” is presented to solve of the UC problem in the deregulated environment. The proposed algorithm is implemented in MATLAB environment.

Resilience‐based tri‐level framework for simultaneous transmission and substation expansion planning considering extreme weather‐related events

In this study, a new resilience-based framework is presented for multi-period simultaneous transmission and substation expansion planning (ST&SEP) considering extreme weather-related events (EWEs). The formation of the proposed planning framework falls into a tri-level optimisation problem with the aim of strengthening power network resilience in response to the EWEs. In the lower-level problem, short-term remedial corrective strategies of the independent system operator (ISO) after the EWEs are determined by applying network reconfiguration and generation redispatch. In the intermediate-level problem, an enhanced scenario-building approach is developed to model and analyse the EWEs, as non-random uncertain events, and their subsequent detrimental effects using the notion of the fragility curves corresponding to power network components. In the upper-level problem, however, long-term remedial preventive strategies of the ISO, as network planner, after the EWEs are obtained through integrated decisions between multi-period ST&SEP and transmission switching equipment planning. The newly proposed planning framework is formulated as a large-scale mixed-integer non-linear tri-level optimisation problem and is solved by a powerful symphony orchestra search algorithm in order to obtain the final optimal solution. The proposed planning framework is examined on the real-world large-scale Iranian 400-kV power transmission network and its profitableness is assured by thorough simulation studies.

Network Slicing Enabled Resource Management for Service-Oriented Ultra-Reliable and Low-Latency Vehicular Networks

Network slicing has been considered as a promising candidate to provide customized services for vehicular applications that have extremely high requirements of latency and reliability. However, the high mobility of vehicles poses significant challenges to resource management in such a stochastic vehicular environment with time-varying service demands. In this paper, we develop an online network slicing scheduling strategy for joint resource block (RB) allocation and power control in vehicular networks. The long-term time-averaged total system capacity is maximized while guaranteeing strict ultra-reliable and low-latency requirements of vehicle communication links, subject to stability constraints of task queues. The formulated problem is a mixed integer nonlinear stochastic optimization problem, which is decoupled into three subproblems by leveraging Lyapunov optimization. In order to tackle this problem, we propose an online algorithm, namely JRPSV, to obtain the optimal RB allocation and power control at each time slot according to the current network state. Furthermore, rigorous theoretical analysis is conducted for the proposed JRPSV algorithm, indicating that the system capacity and the system average latency obey a $[ {{\mathcal O}({1/V}),{\mathcal O}(V)} ]$ trade-off with the control parameter $V$ . Extensive simulation results are provided to validate the theoretical analysis and demonstrate the effectiveness of JRPSV as well as the impacts of various parameters.

User-Edge Collaborative Resource Allocation and Offloading Strategy in Edge Computing

The foundation of urban computing and smart technology is edge computing. Edge computing provides a new solution for large-scale computing and saves more energy while bringing a small amount of latency compared to local computing on mobile devices. To investigate the relationship between the cost of computing tasks and the consumption of time and energy, we propose a computation offloading scheme that achieves lower execution costs by cooperatively allocating computing resources by mobile devices and the edge server. For the mixed-integer nonlinear optimization problem of computing resource allocation and offloading strategy, we segment the problem and propose an iterative optimization algorithm to find the approximate optimal solution. The numerical results of the simulation experiment show that the algorithm can obtain a lower total cost than the baseline algorithm in most cases.

Stimulating sustainable energy at maritime ports by hybrid economic incentives: A bilevel optimization approach

Over the past few decades, maritime ports have faced ever-increasing critiques regarding their significant production of air emissions resulting from their energy activities. To promote sustainability at ports, regulatory authorities have introduced the concept of regulations and economic incentives. In this paper, we analyze the process in which a regulatory authority defines regulations, incentives, and tax policies to motivate one or more ports in the region to initiate energy sustainability and emission-reduction efforts. We model the behaviors of both the regulatory authority and the participating ports in the form of a multi-objective mixed-integer nonlinear bilevel optimization problem to capture the hierarchy of the policy-making process and the existing competitions among the ports. The proposed model finds the optimal incentive and tax policies for the policy-maker in the upper-level and provides the ports in the region with the optimal choice of sustainable energy solutions and service prices in the lower-level. Simulation results show that the proposed approach can effectively reduce the region-wide emission from the port activities while ensuring port entities’ welfare, competitiveness, and sustainable growth as regional energy hubs.

Joint Sampling Time and Resource Allocation for Power Efficiency in Industrial Cyber–Physical Systems

Cyber-physical systems (CPSs) form from convergence of computation, networking, and control of physical processes. In this article, the focus is on an industrial CPS consisting of many control plants and rate constrained (RC) users communicating over a single-cell orthogonal frequency-division multiple access network. We formulate a multiobjective mixed integer nonlinear optimization problem that seeks to determine the next maximum acceptable sampling moment of control plants and to minimize the energy usage in the uplinks and downlinks while taking into account the dynamics and intended performance of control plants, the quality of service of RC users, and power and subcarrier constraints. To address this problem, a decoupling approach is taken, leading to a Pareto solution. Our simulations show that the proposed scheme decreases the total power consumption in the CPS to a significant degree.

Optimizing the Learning Performance in Mobile Augmented Reality Systems With CNN

It is an essential goal for future wireless networks to provide better artificial intelligent services. In this paper, we investigate the joint communication and computation resource optimization in the mobile edge learning system to support augmented reality applications, where the convolutional neural networks (CNNs) are deployed at the edge server. For such a system, we first develop a delay model to characterize the relation between the computation latency and the input image size of general CNN models. Then, we formulate a mixed integer nonlinear optimization problem to maximize the system computation capacity under the constraints of learning accuracy, end-to-end latency, and energy consumption. To solve this problem, we first investigate maximizing the system learning accuracy under the communication and computation resource constraints. The optimal resource allocation policy can be achieved by a low-complexity search algorithm. We further prove that the original problem is NP-hard and propose an efficient heuristic algorithm with a newly-developed offloading priority function. An upper bound for the proposed algorithm is also derived. Finally, test results validate the applicability of the delay model and demonstrate the performance improvement of the proposed algorithm as compared with the existing algorithms.

Bounds on the Objective Value of Feasible Roundings

For mixed-integer linear and nonlinear optimization problems we study the objective value of feasible points which are constructed by the feasible rounding approaches from Neumann et al. (Comput. Optim. Appl. 72, 309–337, 2019; J. Optim. Theory Appl. 184, 433–465, 2020). We provide a-priori bounds on the deviation of such objective values from the optimal value and apply them to explain and quantify the positive effect of finer grids of integer feasible points on the performance of the feasible rounding approaches. Computational results for large scale knapsack problems illustrate our theoretical findings.

Optimal reactive power dispatch for real power loss minimization and voltage stability enhancement using Artificial Bee Colony Algorithm

Reactive Power Dispatch (RPD) plays important role in power system reliability and security. This paper proposes the Optimal Reactive Power Dispatch (ORPD) for real power loss minimization, voltage deviation minimization and voltage stability enhancement using Artificial Bee Colony (ABC) Algorithm. ORPD is a mixed integer nonlinear optimization problem which includes both continuous and discrete control variables. The ABC algorithm is used to find the setting of control variables such as generator voltage magnitude, tap position of tap changing transformer and reactive power output of the compensation devices. The proposed algorithm is tested on IEEE 30 and 57 bus systems, Simulation results show that the proposed approach converges to better solutions and much faster than the earlier reported approaches in the literature. The optimization strategy is general and can be used to solve other power system optimization problems.

Evaluation of Solvent Recovery Options for Economic Feasibility through a Superstructure-Based Optimization Framework

As the chemical market continues to expand, environmental concerns have increased due to excessive disposal of organic solvents. To date, there is no comprehensive mitigation plan to completely handle such a volume of solvent waste generated annually by the chemicals sector. These organic solvents can account for up to 90% of the process by mass and are often discarded after a single use. Incineration, the most widely used process for solvent disposal, is not a green method because of the release of harmful pollutants and greenhouse gases to the environment. A systematic framework for solvent recovery has been developed to overcome the drawbacks of the existing disposal methods. This framework uses a superstructure-based approach that considers the simultaneous comparison of multiple separation technologies for solvent recovery. The viability of this framework was tested using two representative case studies of varying complexities. These case studies were analyzed and formulated as mixed-integer nonlinear programming optimization problems. In both cases, solvent recovery is an economically favorable choice to conventional incineration. Herein, we demonstrate the capability of our solvent recovery framework to obtain economically viable solvent recovery pathways.

Joint C-OMA and C-NOMA Wireless Backhaul Scheduling in Heterogeneous Ultra Dense Networks

Heterogeneous ultra dense network (UDN) emerges as one of the potential techniques to tackle the $1000\times $ data challenge in 5G network. However, by cell densification, backhaul becomes one of the key issues in 5G heterogeneous UDN. In this paper, the cooperative wireless backhaul scheduling is concerned. First, a novel two-layers hierarchical model is proposed for the cooperative wireless backhaul, based on which energy efficiencies (EEs) of the cooperative orthogonal multiple access (C-OMA) and the cooperative non-orthogonal multiple access (C-NOMA) schemes are derived and analyzed. Moreover, based on the proposed model, a cooperative wireless backhaul optimization which maximizes EE is formulated. To solve this mixed integer non-linear optimization problem, the greedy algorithm-based C-OMA, C-NOMA and joint C-OMA and C-NOMA (JCC) schemes for cooperative wireless backhaul are proposed. Due to the benefits of both the C-OMA and C-NOMA, the proposed JCC scheme shows its superiority over C-OMA, C-NOMA and the traditional OMA schemes, which is validated by the simulation results.

Spectrum-Efficient QoS-Aware Resource Assignment for FFR-Based D2D-Enabled Heterogeneous Networks

Small cells and Device-to-Device (D2D) communication can improve the coverage and capacity of cellular systems, thereby enabling an enriched customer experience. To optimize that experience, this paper considers a problem of uplink weighted sum rate maximization for a single cell heterogeneous network containing macro cellular users, D2D users and femto-cell users. In particular, in order to control the co-tier and cross-tier interferences, a new Fractional Frequency Reuse (FFR) architecture is developed in which we seek to maximize a weighted sum rate, subject to minimum rate requirements and transmission power constraints. In order to tackle the resulting mixed integer nonlinear optimization problem, we develop a decomposition-based strategy. The proposed strategy solves the admission control, power control, and matching subproblems optimally, and allocates the remaining free sub-channels by using a heuristic suboptimal algorithm. Numerical results demonstrate that the proposed scheme, on average, achieves around 96% of the system sum rate of the optimal Branch and Bound method with much lower computational cost.

A Hybrid Optimization Method Combining Network Expansion Planning and Switching State Optimization

Combining switching state optimization (SSO) and network expansion planning (NEP) in AC systems results in a mixed-integer non-linear optimization problem. Two methodically different solution approaches are mathematical programming and heuristic methods. In this paper, we develop a hybrid optimization method combining both methods to solve the combined optimization of SSO and NEP. The presented hybrid method applies a DC programming model as an initialization strategy to reduce the search space of the heuristic. A greedy heuristic ensures that the obtained solutions are AC feasible. We compare the hybrid method with other heuristic methods and three mathematical programming models on the same set of planning problems. We show optimization results for four realistic sized power system study cases. Evaluation criteria are convergence, solution cost, and run time. Results show that the hybrid method is able to find a higher number of valid AC-solutions in comparisons to the mathematical programming methods. Furthermore, the obtained solutions have lower expansions costs and are obtained in a shorter run-time compared to the remaining methods for the analyzed study cases. As an addition to this paper, the hybrid implementation and the defined benchmark cases are available as open-source software.

Reconciling periodic rhythms of large-scale biological networks by optimal control.

Periodic rhythms are ubiquitous phenomena that illuminate the underlying mechanism of cyclic activities in biological systems, which can be represented by cyclic attractors of the related biological network. Disorders of periodic rhythms are detrimental to the natural behaviours of living organisms. Previous studies have shown that the state transition from one to another attractor can be accomplished by regulating external signals. However, most of these studies until now have mainly focused on point attractors while ignoring cyclic ones. The aim of this study is to investigate an approach for reconciling abnormal periodic rhythms, such as diminished circadian amplitude and phase delay, to the regular rhythms of complex biological networks. For this purpose, we formulate and solve a mixed-integer nonlinear dynamic optimization problem simultaneously to identify regulation variables and to determine optimal control strategies for state transition and adjustment of periodic rhythms. Numerical experiments are implemented in three examples including a chaotic system, a mammalian circadian rhythm system and a gastric cancer gene regulatory network. The results show that regulating a small number of biochemical molecules in the network is sufficient to successfully drive the system to the target cyclic attractor by implementing an optimal control strategy.

Collaborative Computation Offloading and Resource Allocation in Cache-Aided Hierarchical Edge-Cloud Systems

The hierarchical edge-cloud enabled paradigm has recently been proposed to provide abundant resources for 5G wireless networks. However, the computation and communication capabilities are heterogeneous which makes the potential advantages difficult to be fully explored. Besides, previous works on mobile edge computing (MEC) focused on server caching and offloading, ignoring the computational and caching gains brought by the proximity of user equipments (UEs). In this paper, we investigate the computation offloading in a three-tier cache-assisted hierarchical edge-cloud system. In this system, UEs cache tasks and can offload their workloads to edge servers or adjoining UEs by device-to-device (D2D) for collaborative processing. A cost minimization problem is proposed by the tradeoff between service delay and energy consumption. In this problem, the offloading decision, the computational resources and the offloading ratio are jointly optimized in each offloading mode. Then, we formulate this problem as a mixed-integer nonlinear optimization problem (MINLP) which is non-convex. To solve it, we propose a joint computation offloading and resource allocation optimization (JORA) scheme. Primarily, in this scheme, we decompose the original problem into three independent subproblems and analyze their convexity. After that, we transform them into solvable forms (e.g., convex optimization problem or linear optimization problem). Then, an iteration-based algorithm with the Lagrange multiplier method and a distributed joint optimization algorithm with the adoption of game theory are proposed to solve these problems. Finally, the simulation results show the performance of our proposed scheme compared with other existing benchmark schemes.