Mixed-integer Nonlinear Problem Research Articles

Coordinated active-reactive power optimization considering photovoltaic abandon based on second order cone programming in active distribution networks

On the basis of predecessors’ coordination optimization of active and reactive power in distribution network, For the necessity of the optimal operation in the distribution network, part of power generated from photovoltaic (PV) cannot be sold to users, and cannot enjoy subsidies. Similarly, the network loss in the power transmission will also bring a certain economic loss. This paper comprehensively considers the economic loss caused by the network loss and PV abandon of the distribution system, and establishes a model to minimize the economic loss. To solve this problem efficiently, the method of DistFlow equation and mixed integer second order cone programming (MISOCP) is used to solve the problem, in this method, the original mixed integer nonlinear programming non-convex problem is transformed into a convex problem, which makes the optimization problem easy to solve. The modified IEEE 33 and IEEE 69 distribution networks are tested by the above method. The optimized results are able to meet the target and have very small relaxation gaps, and the voltage level is also optimized. This coordinated optimization approach helps to optimize the economic operation for active distribution networks with PVs.

Thermodynamic modeling and optimal short-term scheduling of a green H2-fueled combined heat and power generation system for industrial zones

This paper presents a novel green combined heat and power generation system for industrial applications. It composes of a hydrogen-fueled combined cycle power plant and a battery energy storage. Firstly, the hydrogen-air rich mixture enters the combustion chamber of the gas turbine cycle for generating electricity, while recovering the heating energy from the exhausted flue gases for driving a steam turbine cycle. The heating energy extracted from the condenser heat exchanger is also used to supply the heating demand of the end-user. Moreover, a comprehensive thermodynamic model and analysis of H2 combustion process is provided to estimate the adiabatic flame temperature based on enthalpies of reactants and products. The optimum operating point of the cogeneration system is found by solving a mixed-integer nonlinear problem using MATLAB and GAMS over a 24-h study horizon aiming to minimize its daily operation cost considering all technical constraints of system components and load-generation balance criterion. It is found that the energy efficiency of the hydrogen-fueled combined cycle changes from 46 to 58 % while generating 11.331–12.982 MW electricity and 4.436–4.984 MW heat. Two cases are studied without and with participation of battery in energy procurement strategy. It is demonstrated that the objective function of the optimization problem improves from 18 $ cost in case 1 to 29 $ revenue in case 2.

Design optimization of mobile vehicle-borne microgrids

Interest in isolated microgrids continues to increase as more applications are being explored, such as military bases located in isolated areas, supplying critical infrastructures during emergencies, etc. This paper considers the integration of packaging into the optimal design of a vehicle-borne microgrid suitable for such an application with space limitations. The advantages of this type of microgrid are mobility and the ability to operate while mobile or stationary. Various types of micro-sources are considered to meet multiple loads. To this end, a mixed-integer nonlinear problem is formulated to integrate multiple micro-source sizing and packaging options. The relationship between loads and capital investment is investigated through four different case studies. The case study results show that the proposed optimization framework is highly flexible and effective in finding a design solution for varying operational scenarios. Unlike existing approaches, the proposed method considers packaging constraints in the selection of micro sources ensuring microgrid mobility and rapid deployment, and also identifies a packaging solution for the selected micro sources. A comparative case study showed that the existing approach results in a 20 kW PV favoring renewable sources while the proposed method results in a 10 kW PV prioritizing the packaging and mobility.

Continuous Switch Model and Heuristics for Mixed-Integer Nonlinear Problems in Power Systems

Continuous Switch Model and Heuristics for Mixed-Integer Nonlinear Problems in Power Systems

A Bayesian optimization approach for data‐driven mixed‐integer nonlinear programming problems

AbstractThe optimization of process systems within the field of Chemical Engineering often confronts uncertainties that can exert significant influences on the performance and dependability of the obtained solutions. This research endeavors to investigate the application of Bayesian optimization in the realm of constrained mixed integer nonlinear problems. A comparative analysis was conducted, exploring different surrogate models, and evaluating diverse kernel functions and acquisition functions. Furthermore, a sampling strategy was devised to assess the enhancement achieved by the acquisition function. The findings of this article reveal the superior performance of sparse Gaussian processes in conjunction with computationally inexpensive acquisition functions, thereby highlighting their suitability for addressing mixed integer nonlinear programming problems characterized by noisy functions and stochastic behavior. Consequently, this article presents a computationally efficient approach to effectively tackle the challenges associated with data‐driven mixed integer nonlinear programming problems within the domain of Process System Engineering.

Mixed Integer Nonlinear Programming-Based Unit Commitment of Conventional Thermal Generators Using Hybrid Evolutionary Algorithms

Unit Commitment (UC) discusses the optimized generation resources (to turn on economical generators and turn off expensive generators),which are subjected to satisfy all the operational constraints. The operational constraints such as load balancing, security maximization, minimum up and down time, spinning reserve, and ramp up and down constraints are difficult to satisfy. Although, UC is a cost minimization problem that is realized by committing less expensive units while satisfying the corresponding constraints, and dispatching the committed units economically. The UC problem is an np-hard Mixed Integer Nonlinear Problem (MINLP). Therefore, in this paper, hybrid EA based on a Genetic Algorithm (GA) has been applied to find the optimal solution to the UC problem. Moreover, during the search process, it is very difficult to discard infeasible solutions in EAs. Hence, the Genetic Algorithm (GA) is integrated with the feasibility rule constraint handling technique to emphasize feasible solutions. IEEE RTS Eleven Thermal Generator Standard Test system is used to validate the performance of proposed methods. For the validation and the superiority of the proposed algorithm, simulation results are compared with the classical Lagrangian Relaxation (LR) methods. Results show that the proposed method can find the global optimal solution to the UC problem which is subjected to satisfy all the operational constraints.

Code and Data Repository for Computing Optimality Certificates for Convex Mixed-Integer Nonlinear Problems

The goal of this software is to compute (the size of) optimality certificates for convex mixed-integer nonlinear problems.

Optimal operation of pumped storage power plants with fixed- and variable-speed generators in multiple electricity markets considering overload operation

This work studies the optimal operation of pumped storage power plants with fixed- and variable-speed generators in different electricity markets. This paper extends the state of the art by systematically considering the detailed plant behavior for heterogeneous pumped storage power plants and the possible short-term electrical overload operation. The Day-Ahead, ancillary service, and Intraday markets are studied in the first part by developing a mixed integer nonlinear problem (MINLP). The results demonstrate that variable-speed units, especially if equipped with doubly-fed induction machines (DFIMs), yield the highest profit, particularly in the presence of automatic Frequency Restoration Reserve (aFRR). The proposed optimization of the Intraday market shows that the total profit of the Day-Ahead, Ancillary services, and Intraday markets are the highest in the case of variable-speed units with aFRR, where it might be a drawback offering Frequency Containment Reserve. Finally, a robust optimization-based bidding curve generation strategy is developed in the last step. The strategy allows the plant to operate with high profits under price prediction uncertainties and enables optimal reservoir management. The developed optimization tasks and the bidding curve generation strategy also exhibit shorter computation times than the state-of-the-art strategies.

Efficient resource allocation for 5G/6G cognitive radio networks using probabilistic interference models

The Cognitive Radio Network, incorporating Device-to-Device communication and a heterogeneous network, has garnered significant attention due to its ability to address spectrum shortage issues and optimize the efficient utilization of spectrum resources. However, resource allocation considering stochastic behavior has not been considered in existing studies. In this paper, our work aimed to maximize the throughput of the overall network considering multiple users under the umbrella of the Cognitive radio network assisted by amplify and forward relay. The constraints are treated as chance constraints with a probability of satisfaction in them, which leads to a non-convex mixed integer nonlinear problem which is an NP-Hard problem. To solve this problem an exhaustive search solution for optimal results is required. However, the computational burden always increases with the user equipment. Therefore, to obtain an optimal solution with having low computational burden, the Outer Approximation Algorithm is utilized in this research. To evaluate the desired results, extensive simulations have been carried out. The effectiveness of the proposed algorithm is verified by results in terms of throughput maximization under the impact of chance constraint formulation in the cognitive radio networks.

A distributed randomized method for the identification of switched ARX systems

SummaryThe identification of switched systems amounts to a mixed integer nonlinear optimization problem, where the continuous variables are associated to the model parameterizations of the different modes, and the discrete ones are related to the switching signal (each data sample is assigned to a mode, and switching occurs when the mode assignment changes over time). In the batch form of the identification problem, the combinatorial complexity increases exponentially with the size of the training set, which makes the precise identification of the switching signal the most challenging task in the identification problem. To tackle this complexity we propose a distributed optimization approach, based on the solution of multiple instances of a much simpler problem, where switching can occur only at specific time instants (different for each subproblem), and an information sharing mechanism that preserves likely switching times to improve the local solutions. We employ an adapted version of a previously developed randomized algorithm to solve the individual subproblems. Another important feature of the proposed method is an a posteriori heuristic correction method, that is applied to further refine the switching locations based on the estimated local models before the information sharing phase. The performance of the proposed algorithm is analyzed and compared with other methods on synthetic datasets.

A cooperative optimization method for the layout of shared bicycle parking areas and delivery quantity

With the popularity of shared bicycles in urban areas, more and more residents choose this fast and convenient mode of transportation for short-distance travel. By optimizing the layout of shared bicycle parking areas and delivery quantity, the investment cost of shared bicycle enterprises can be effectively reduced, and the convenience of residents' travel can be improved at the same time. In this paper, we develop a collaborative optimization model for the layout of the shared bicycle parking area and delivery quantity, aiming at minimizing the walking distance of residents and the investment cost of enterprises, while considering the constraints of the parking area's attractive range and the number of bicycles placed. Aiming at the characteristics of this mixed integer nonlinear problem, an improved genetic algorithm incorporating symmetric individual precision control mechanism is designed. Finally, taking the planned area between the Second Ring Road and the Third Ring Road in the northern part of Jin-niu District, Chengdu as the background, the proposed collaborative optimization model for the layout of shared bicycle parking areas and delivery quantity is applied to a real scene. The results show that after optimization, the number of parking areas is reduced by 2, and the total investment cost is reduced by about 12.2%.

Lua APIs for mathematical optimization

In this paper we present our Lua programming language libraries that enable modeling and solving mixed integer linear and nonlinear mathematical optimization problems. On one side, these libraries provide a framework for developing algorithms written in Lua that use certain well known solvers within more complex procedures. On the other side, they facilitate the transformation of both input and output data of a mathematical programming problem, in order to compute the standardized coefficients that have to be transmitted to the solvers or prepare solution of solved problems for further data processing. Both of these use cases, together with Lua programming language simplicity, versatility and performance, make Lua a suitable programming language for use in scientific and engineering researches.

Outer approximation for pseudo-convex mixed-integer nonlinear program problems

Outer approximation for pseudo-convex mixed-integer nonlinear program problems

Integrating Flight Scheduling, Fleet Assignment, and Aircraft Routing Problems with Codesharing Agreements under Stochastic Environment

Airlines face the imperative of resource management to curtail costs, necessitating the solution of several optimization problems such as flight planning, fleet assignment, aircraft routing, and crew scheduling. These problems present some challenges. The first pertains to the common practice of addressing these problems independently, potentially leading to locally optimal outcomes due to their interconnected nature. The second challenge lies in the inherent uncertainty associated with parameters like demand and non-cruise time. On the other hand, airlines can employ a strategy known as codesharing, wherein they operate shared flights, in order to minimize these challenges. In this study, we introduce a novel mathematical model designed to optimize flight planning, fleet assignment, and aircraft routing decisions concurrently, while accommodating for codesharing. This model is formulated as a three-stage non-linear mixed-integer problem, with stochastic parameters representing the demand and non-cruise time. For smaller-scale problems, optimization software can effectively solve the model. However, as the number of flights increases, conventional software becomes inadequate. Moreover, considering a wide array of scenarios for stochastic parameters leads to more robust results; however, it is not enabled because of the limitations of optimization software. In this work, we introduce two new simulation-based metaheuristic algorithms for solving large-dimensional problems, collectively called “simheuristic.” These algorithms integrate the Monte Carlo simulation technique into Simulated Annealing and Cuckoo Search. We have applied these simheuristic algorithms to various problem samples of different flight sizes and scenarios. The results demonstrate the efficacy of our proposed modeling and solution approaches in efficiently addressing flight scheduling, fleet assignment, and aircraft routing problems within acceptable timeframes.

Profit-based unit commitment models with price-responsive decision-dependent uncertainty

Highlighting the increasing importance of demand elasticity in electricity markets and its impact on the revenues of power generating companies, this paper proposes new profit-based unit commitment models that effectively capture the uncertainty in the willingness-to-pay the price set for the elastic demand. To develop a new revenue scheme for power generating companies, we use a coupling function to model the willingness-to-pay response of the elastic demand as a decision-dependent source of uncertainty. The coupling function reflects how power generating companies’ pricing decisions may influence the market appeal (i.e., the buyer’s willingness-to-pay) and how it affects their revenues. The optimization models are stochastic mixed-integer nonlinear problems with nonconvex continuous relaxations and are not amenable to a numerical solution in their original forms. We devise a convexification reformulation method and derive valid inequalities to strengthen the formulation. We propose a learning framework to parameterize the willingness-to-pay functions and the concept of the value of the decision-dependent solution to quantify the value of the uncertainty modeling approach. Numerical tests on power systems of various sizes, demand portfolios, and price elasticity levels show (i) how the valid inequalities speed up the solution process, (ii) the benefits of properly modeling decision-dependent uncertainty and demand elasticity, and (iii) how the incorporation of decision-dependent uncertainty in demand elasticity can change the power generating companies’ decisions and revenue estimation.

Risk-constrained probabilistic coordination in coupled transmission and distribution system

High penetration of renewable energy has instigated stochastic power injection at interconnection between transmission system (TS) and distribution system (DS). This paper delves into the intricate collaborative risk based stochastic dispatching challenges due to contingencies and the integration of renewable sources in the TS and DS. A framework of risk constrained probabilistic problem (RCPC) is presented, which is divided into Probabilistic coordination (PC) and risk-based stochastic security-constrained unit commitment (RSSCUC). The PC is a stochastic linear problem and RSSCUC is a stochastic mixed integer non-linear problem. Therefore, the probabilistic analytical target cascading along with polynomial chaos expansion (PCE) has been utilized for solving the PC problem for coupled TS and DS. Here, PCE has provided the proposed algorithm with the needed capability to present stochastic shared variables as coefficients for PC. Further, the benders decomposition algorithm has been utilized for solving RSSCUC, by dividing it into master problem and sub problem to generate feasibility cuts. The proposed technique reduces the computational burden on the system, as it requires single stochastic coordination problem for all scenarios as an alternative of each coordination problem for each scenario and polynomial coefficients instead of multiple scenarios for each shared variable between TS and DS. Different case studies have been performed utilizing the 6-bus system and IEEE 118-bus system as TSs, 7-bus, 9-bus, 85-bus and 69-bus systems as DSs. Results depict the efficacy of the proposed method.

A new continuous variables and convex relaxation based formulation for reconfiguration of unbalanced mutually coupled active distribution networks

With the integration of renewable energy-based sources and demand response initiatives, the distribution network has transformed into an active network with bidirectional flows. Network Reconfiguration (NR), i.e., changing network topology, is an alternative to minimize power loss in the distribution network with sectionalizing switches (normally closed) and tie-line switches (normally open). Due to the discrete nature of switches (on or off), the NR formulation is generally a mixed-integer NP-hard nonlinear problem. This paper proposes the first NR formulation for an unbalanced active distribution network with continuous variables to indicate switches’ statuses in NR while considering mutual coupling between line impedances. The obtained solution provides the optimal real power and voltage magnitude settings of dispatchable Distributed Generators (DGs) and network topology for the minimum active power loss in the network. The proposed formulation considers all practical aspects of the distribution network, i.e., mutual coupling, load unbalances, angular unbalance, and the absence of one or two phases in a line section, which, otherwise, have not been considered together in previous formulations. Further, a novel convex relaxation for bus voltage phase angles avoids explicit voltage recovery. Compared to prior formulations, numeric results for unbalanced radial distribution networks showcase the proposed formulation’s effectiveness.

Workload-Aware Scheduling of Multiple- Criticality Real-Time Applications in Vehicular Edge Computing System

In this article, we study the problem of designing an adaptive scheduling scheme for dynamic multiple-criticality real-time applications in vehicular edge computing systems. This scheduling problem is formulated as a mixed-integer nonlinear problem. We propose a workload-aware scheduling approach that not only guarantees the applicaitons' mixed-criticality schedulability but also adaptively manages their execution depending on their released frequencies at runtime. In particular, we first present the response time analysis for multiple-criticality applications in the edge computing system with different computing capability servers. Then, we derive a state-transition equation that makes the dynamic programming applicable to building an excellent schedule for one specific criticality-level mode. Such an approach is extended to the system's different criticality-level modes. For the purpose of increasing the quality-of-service toward low-critical applications, we leave low-critical applications to execute as much as possible at runtime, depending on their predicted frequencies. Extensive experimental results show the superiority of our proposed approaches in terms of improving the schedulability success rate and reducing the number of suspended applications online

Power system resilience against climatic faults: An optimized self-healing approach using conservative voltage reduction

The resilience of power systems is critical in mitigating faults caused by the impending effects of climate change. Typical operational methods, such as network reconfiguration, may be insufficient to mitigate faults in the event of a contingency. On the other hand, reducing system demand may help increase the number of restored loads. As a result, this paper proposes a novel self-healing optimization approach based on a power grid concept known as conservative voltage reduction (CVR), which results in system demand reduction. The proposed optimization model is formulated as a mixed integer non-linear (MINLP) problem to fulfill an objective of minimizing unserved loads within the system. Voltage, thermal capacity, system radiality, and several more constraints have been taken into consideration while formulating the proposed model to handle both grid-connected and isolated modes of operation. Both dispatchable and non-dispatchable distributed generators (DGs) are taken into consideration. Dispatchable DGs are assumed to be capable of switching back and forth between constant power (PQ) and droop controls for the purpose of grid following and grid forming in grid-connected and isolated modes of operation, respectively. The proposed optimization approach is coded and solved using the General Algebraic Modeling System (GAMS) software. The IEEE 69-bus power distribution test system is utilized to test the validity and superiority of the proposed model. The results show that the proposed model effectively increases the system resilience by reducing the unserved power/energy within the system following a contingency.

The drone latency location routing problem under uncertainty

This paper addresses a location routing problem arising in the last-mile drone delivery context, where drones are used to deliver small packages to a set of customers. Each drone is launched from a fulfillment center to serve multiple customers on a single trip. The goal is to find the optimal subset of fulfillment centers to use as drone launching and landing platforms and the optimal drone routes with the aim of minimizing the sum of customers’ waiting times. We study the problem under two realistic assumptions. First, the drone energy consumption is a nonlinear function of the drone load that varies along the route, as parcels are delivered. Second, the drone flight time is not deterministically known. To hedge against drone flight time uncertainty, we adopt a robust optimization approach. Due to the complex nature of the problem, which turns out to be a nonlinear mixed-integer problem, we design an exact method based on a tailored efficient Branch & Check algorithm that uses customized no-good cuts. The computational experiments show the validity of the proposed model and the promising performance of the exact method. Moreover, we present a case study on last-mile parcel delivery in Turin, Italy, providing insights into the advantages of a drone-based delivery system.