Exponential distribution-based genetic algorithm for solving mixed-integer bilevel programming problems

Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.

Nonlinear Model-Based Process Operation under UncertaintyUsing Exact Parametric Programming

In the present work, two new, （multi-）parametric programming （mp-P）-inspired algorithms for the solutionof mixed-integer nonlinear programming （MINLP） problems are developed, with their main focus being onprocess synthesis problems. The algorithms are developed for the special case in which the nonlinearitiesarise because of logarithmic terms, with the first one being developed for the deterministic case, and thesecond for the parametric case （p-MINLP）. The key idea is to formulate and solve the square system of thefirst-order Karush-Kuhn-Tucker （KKT） conditions in an analytical way, by treating the binary variables and/or uncertain parameters as symbolic parameters. To this effect, symbolic manipulation and solution tech-niques are employed. In order to demonstrate the applicability and validity of the proposed algorithms, twoprocess synthesis case studies are examined. The corresponding solutions are then validated using state-of-the-art numerical MINLP solvers. For p-MINLP, the solution is given by an optimal solution as an explicitfunction of the uncertain parameters.

SIMPLE NONLINEAR OPTIMIZATION-BASED SELECTION OF INSULATION MATERIAL AND WINDOW TYPE IN TURKEY:EFFECT OF HEATING AND COOLING BASE TEMPERATURES

The energy-savings of four hypothetical households in different climatic regions of Turkey were calculated via a nonlinear mixed integer optimization model.The ideal insulation material,its optimum thickness,and the ideal window type were determined.The standard degree days method was used with five different base temperatures for heating and five different base temperatures for cooling.The climatic conditions of the region,the properties of the insulation options,the unit price of fuel and electricity and the base temperature are used as model inputs,whereas the combination of selected insulation material with its optimum thickness and window type are given as model outputs.Stone Wool was found to be the ideal wall insulation material in all scenarios.The optimum window type was found to depend on the heating or cooling requirements of the house,as well as the lifetime of insulation.The region where the energy saving actions are deemed most feasible has been identified as Erzurum(Region 4),followed by Antalya(Region 1).Finally,the effect of changing the base temperature on energy savings was investigated and the results showed that an approximate average increase of$15/°C in annual savings is possible.Our model can be used by any prospective home-owner who would like to maximize their energy savings.

基于量子粒子群求解混合整数非线性规划

在经典微粒群算法的基础上提出一种有较高收敛性能的智能算法:量子粒子群(QPSO)算法。并用于求解混合整数非线性规划问题。实验室证明QPSO算法收敛性能好、速度快,为求解混合整数非线性规划开辟了新途径。

A two-stage optimization method for unmanned aerial vehicle inspection of an oil and gas pipeline network

Oil and gas pipeline networks are a key link in the coordinated development of oil and gas both upstream and downstream.To improve the reliability and safety of the oil and gas pipeline network, inspections are implemented to minimize the risk of leakage, spill and theft, as well as documenting actual incidents. In recent years, unmanned aerial vehicles have been recognized as a promising option for inspection due to their high efficiency. However, the integrated optimization of unmanned aerial vehicle inspection for oil and gas pipeline networks, including physical feasibility, the performance of mission, cooperation, real-time implementation and three-dimensional(3-D) space, is a strategic problem due to its large-scale,complexity as well as the need for efficiency. In this work, a novel mixed-integer nonlinear programming model is proposed that takes into account the constraints of the mission scenario and the safety performance of unmanned aerial vehicles. To minimize the total length of the inspection path, the model is solved by a two-stage solution method. Finally, a virtual pipeline network and a practical pipeline network are set as two examples to demonstrate the performance of the optimization schemes. Moreover, compared with the traditional genetic algorithm and simulated annealing algorithm, the self-adaptive genetic simulated annealing algorithm proposed in this paper provides strong stability.

A Method for Crude Oil Selection and Blending Optimization Based on Improved Cuckoo Search Algorithm

Refineries often need to find similar crude oil to replace the scarce crude oil for stabilizing the feedstock property. We introduced the method for calculation of crude blended properties firstly, and then created a crude oil selection and blending optimization model based on the data of crude oil property. The model is a mixed-integer nonlinear programming(MINLP) with constraints, and the target is to maximize the similarity between the blended crude oil and the objective crude oil. Furthermore, the model takes into account the selection of crude oils and their blending ratios simultaneously, and transforms the problem of looking for similar crude oil into the crude oil selection and blending optimization problem. We applied the Improved Cuckoo Search(ICS) algorithm to solving the model. Through the simulations, ICS was compared with the genetic algorithm, the particle swarm optimization algorithm and the CPLEX solver. The results show that ICS has very good optimization efficiency. The blending solution can provide a reference for refineries to find the similar crude oil. And the method proposed can also give some references to selection and blending optimization of other materials.

Connected Vehicle-Based Traffic Signal Coordination

This study presents a connected vehicles(CVs)-based traffic signal optimization framework for a coordinated arterial corridor.The signal optimization and coordination problem are first formulated in a centralized scheme as a mixed-integer nonlinear program(MINLP).The optimal phase durations and offsets are solved together by minimizing fuel consumption and travel time considering an individual vehicle’s trajectories.Due to the complexity of the model,we decompose the problem into two levels:an intersection level to optimize phase durations using dynamic programming(DP),and a corridor level to optimize the offsets of all intersections.In order to solve the two-level model,a prediction-based solution technique is developed.The proposed models are tested using traffic simulation under various scenarios.Compared with the traditional actuated signal timing and coordination plan,the signal timing plans generated by solving the MINLP and the two-level model can reasonably improve the signal control performance.When considering varies vehicle types under high demand levels,the proposed two-level model reduced the total system cost by 3.8%comparing to baseline actuated plan.MINLP reduced the system cost by 5.9%.It also suggested that coordination scheme was beneficial to corridors with relatively high demand levels.For intersections with major and minor street,coordination conducted for major street had little impacts on the vehicles at the minor street.

A Framework for the Systematic Design of Hybrid Separation Processe

The design of optimal separation flow sheets for multi-component mixtures is still not a solved problem This is especially the case when non-ideal or azeotropic mixtures or hybrid separation processes are considered. We review recent developments in this field and present a systematic framework for the design of separation flow sheets. This framework proposes a three-step approach. In the first step different flow sheets are generated. In the second step these alternative flow sheet structures are evaluated with shortcut methods. In the third step a rigorous mixed-integer nonlinear programming （MINLP） optimization of the entire flow sheet is executed to determine the best alternative. Since a number of alternative flow sheets have already been eliminated, only a few optimization runs are necessary in this final step. The whole framework thus allows the systematic generation and evaluation of separation processes and is illustrated with the case study of the separation of ethanol and water.

Multi-objective optimization of biomass to biomethane system

The superstructure optimization of biomass to biomethane system through digestion is conducted in this work. The system encompasses biofeedstock collection and transportation, anaerobic digestion, biogas upgrading, and digestate recycling. We propose a multicriteria mixed integer nonlinear programming(MINLP) model that seeks to minimize the energy consumption and maximize the green degree and the biomethane production constrained by technology selection, mass balance, energy balance, and environmental impact. A multi-objective MINLP model is proposed and solved with a fast nondominated sorting genetic algorithm Ⅱ(NSGA-Ⅱ). The resulting Pareto-optimal surface reveals the trade-off among the conflicting objectives. The optimal results indicate quantitatively that higher green degree and biomethane production objectives can be obtained at the expense of destroying the performance of the energy consumption objective.

Multi-area Frequency-constrained Unit Commitment for Power Systems with High Penetration of Renewable Energy Sources and Induction Machine Load

The increasing penetration of renewable energy sources(RESs)brings great challenges to the frequency security of power systems.The traditional frequency-constrained unit commitment(FCUC)analyzes frequency by simplifying the average system frequency and ignoring numerous induction machines(IMs)in load,which may underestimate the risk and increase the operational cost.In this paper,we consider a multiarea frequency response(MAFR)model to capture the frequency dynamics in the unit scheduling problem,in which regional frequency security and the inertia of IM load are modeled with high-dimension differential algebraic equations.A multi-area FCUC(MFCUC)is formulated as mixed-integer nonlinear programming(MINLP)on the basis of the MAFR model.Then,we develop a multi-direction decomposition algorithm to solve the MFCUC efficiently.The original MINLP is decomposed into a master problem and subproblems.The subproblems check the nonlinear frequency dynamics and generate linear optimization cuts for the master problem to improve the frequency security in its optimal solution.Case studies on the modified IEEE 39-bus system and IEEE 118-bus system show a great reduction in operational costs.Moreover,simulation results verify the ability of the proposed MAFR model to reflect regional frequency security and the available inertia of IMs in unit scheduling.

An Embedded Consensus ADMM Distribution Algorithm Based on Outer Approximation for Improved Robust State Estimation of Networked Microgrids

Networked microgrids(NMGs)are critical in theaccommodation of distributed renewable energy.However,theexisting centralized state estimation(SE)cannot meet the demandsof NMGs in distributed energy management.The currentestimator is also not robust against bad data.This study introducesthe concepts of relative error to construct an improvedrobust SE(IRSE)optimization model with mixed-integer nonlinearprogramming(MINLP)that overcomes the disadvantage ofinaccurate results derived from different measurements whenthe same tolerance range is considered in the robust SE(RSE).To improve the computation efficiency of the IRSE optimizationmodel,the number of binary variables is reduced based on theprojection statistics and normalized residual methods,which effectivelyavoid the problem of slow convergence or divergenceof the algorithm caused by too many integer variables.Finally,an embedded consensus alternating direction of multiplier method(ADMM)distribution algorithm based on outer approximation(OA)is proposed to solve the IRSE optimization model.This algorithm can accurately detect bad data and obtain SE resultsthat communicate only the boundary coupling informationwith neighbors.Numerical tests show that the proposed algorithmeffectively detects bad data,obtains more accurate SE results,and ensures the protection of private information in all microgrids.

Real-time microgrid economic dispatch based on model predictive control strategy

To deal with uncertainties of renewable energy,demand and price signals in real-time microgrid operation,this paper proposes a model predictive control strategy for microgrid economic dispatch, where hourly schedule is constantly optimized according to the current system state and latest forecast information. Moreover, implicit network topology of the microgrid and corresponding power flow constraints are considered, which leads to a mixed integer nonlinear optimal power flow problem. Given the non-convexity feature of the original problem, the technique of conic programming is applied to efficiently crack the nut. Simulation results from a reconstructed IEEE-33 bus system and comparisons with the routine day-ahead microgrid schedule sufficiently substantiate the effectiveness of the proposed MPC strategy and the conic programming method.

Whole-lifetime Coordinated Service Strategy for Battery Energy Storage System Considering Multi-stage Battery Aging Characteristics

One battery energy storage system(BESS)can be used to provide different services,such as energy arbitrage(EA)and frequency regulation(FR)support,etc.,which have different revenues and lead to different battery degradation profiles.This paper proposes a whole-lifetime coordinated service strategy to maximize the total operation profit of BESS.A multi-stage battery aging model is developed to characterize the battery aging rates during the whole lifetime.Considering the uncertainty of electricity price in EA service and frequency deviation in FR service,the whole problem is formulated as a twostage stochastic programming problem.At the first stage,the optimal service switching scheme between the EA and FR services are formulated to maximize the expected value of the whole-lifetime operation profit.At the second stage,the output power of BESS in EA service is optimized according to the electricity price in the hourly timescale,whereas the output power of BESS in FR service is directly determined according to the frequency deviation in the second timescale.The above optimization problem is then converted as a deterministic mixed-integer nonlinear programming(MINLP)model with bilinear items.Mc Cormick envelopes and a bound tightening algorithm are used to solve it.Numerical simulation is carried out to validate the effectiveness and advantages of the proposed strategy.

Solving Multi-period Interdiction via Generalized Bender's Decomposition

This paper considers a novel formulation of the multi-period network interdiction problem. In this model, delivery of the maximum flow as well as the act of interdiction happens over several periods, while the budget of resource for interdiction is limit. It is assumed that when an edge is interdicted in a period, the evader considers a rate of risk of detection at consequent periods. Application of the generalized Benders decomposition algorithm considers solving the resulting mixed-integer nonlinear programming problem. Computational experiences denote reasonable consistency with expectations.

A Polynomial-Time Algorithm with Tight Error Bounds for Single-Period Unit Commitment Problem

This paper proposes a Lagrangian dual-based polynomial-time approximation algorithm for solving the single-period unit commitment problem,which can be formulated as a mixed-integer quadratic programming problem and proven to be NP-hard.Tight theoretical bounds for the absolute errors and relative errors of the approximate solutions generated by the proposed algorithm are provided.Computational results support the effectiveness and efficiency of the proposed algorithm for solving large-scale problems.