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.

Computation of an Emptiable Minimal Siphon in a Subclass of Petri Nets Using Mixed-Integer Programming

Deadlock resolution strategies based on siphon control are widely investigated.Their computational efficiency largely depends on siphon computation.Mixed-integer programming(MIP)can be utilized for the computation of an emptiable siphon in a Petri net(PN).Based on it,deadlock resolution strategies can be designed without requiring complete siphon enumeration that has exponential complexity.Due to this reason,various MIP methods are proposed for various subclasses of PNs.This work proposes an innovative MIP method to compute an emptiable minimal siphon(EMS)for a subclass of PNs named S^(4)PR.In particular,many particular structural characteristics of EMS in S4 PR are formalized as constraints,which greatly reduces the solution space.Experimental results show that the proposed MIP method has higher computational efficiency.Furthermore,the proposed method allows one to determine the liveness of an ordinary S^(4)PR.

Continuity of the optimal value function and optimal solutions of parametric mixed-integer quadratic programs

To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints. The obtained results extend some existing results for continuous quadratic programs, and, more importantly, lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.

An Innovative Genetic Algorithms-Based Inexact Non-Linear Programming Problem Solving Method

In this paper, an innovative Genetic Algorithms (GA)-based inexact non-linear programming (GAINLP) problem solving approach has been proposed for solving non-linear programming optimization problems with inexact information (inexact non-linear operation programming). GAINLP was developed based on a GA-based inexact quadratic solving method. The Genetic Algorithm Solver of the Global Optimization Toolbox (GASGOT) developed by MATLABTM was adopted as the implementation environment of this study. GAINLP was applied to a municipality solid waste management case. The results from different scenarios indicated that the proposed GA-based heuristic optimization approach was able to generate a solution for a complicated nonlinear problem, which also involved uncertainty.

Unmanned Aerial Vehicle Inspection Routing and Scheduling for Engineering Management

Technological advancements in unmanned aerial vehicles(UAVs)have revolutionized various industries,enabling the widespread adoption of UAV-based solutions.In engineering management,UAV-based inspection has emerged as a highly efficient method for identifying hidden risks in high-risk construction environments,surpassing traditional inspection techniques.Building on this foundation,this paper delves into the optimization of UAV inspection routing and scheduling,addressing the complexity introduced by factors such as no-fly zones,monitoring-interval time windows,and multiple monitoring rounds.To tackle this challenging problem,we propose a mixed-integer linear programming(MILP)model that optimizes inspection task assignments,monitoring sequence schedules,and charging decisions.The comprehensive consideration of these factors differentiates our problem from conventional vehicle routing problem(VRP),leading to a mathematically intractable model for commercial solvers in the case of large-scale instances.To overcome this limitation,we design a tailored variable neighborhood search(VNS)metaheuristic,customizing the algorithm to efficiently solve our model.Extensive numerical experiments are conducted to validate the efficacy of our proposed algorithm,demonstrating its scalability for both large-scale and real-scale instances.Sensitivity experiments and a case study based on an actual engineering project are also conducted,providing valuable insights for engineering managers to enhance inspection work efficiency.

Optimal Micro-PMU Placement for Improving State Estimation Accuracy via Mixed-integer Semidefinite Programming

Micro-phasor measurement units(μPMUs)with a micro-second resolution and milli-degree accuracy capability are expected to play an important role in improving the state estimation accuracy in the distribution network with increasing penetration of distributed generations.Therefore,this paper investigates the problem of how to place a limited number ofμPMUs to improve the state estimation accuracy.Combined with pseudo-measurements and supervisory control and data acquisition(SCADA)measurements,an optimalμPMU placement model is proposed based on a two-step state estimation method.The E-optimal experimental criterion is utilized to measure the state estimation accuracy.The nonlinear optimization problem is transformed into a mixed-integer semidefinite programming(MISDP)problem,whose optimal solution can be obtained by using the improved Benders decomposition method.Simulations on several systems are carried out to evaluate the effective performance of the proposed model.

Characteristics of oxygen consumption of coal at programmed temperatures

Oxygen consumption is an important index of coal oxidation.In order to explore the coal-oxygen reaction,we developed an experimental system of coal spontaneous combustion and tested oxygen consumption of differently ranked coals at programmed temperatures.The size of coal samples ranged from 0.18~0.42 mm and the system heat-rate was 0.8℃/min.The results show that, for high ranked coals,oxygen consumption rises with coal temperature as a piecewise non-linear process.The critical coal temperature is about 50℃.Below this temperature,oxygen consumption decreases with rising coal temperatures and reached a minimum at 50℃,approximately.Subsequently,it begins to increase and the rate of growth clearly increased with temperature.For low ranked coals,this characteristic is inconspicuous or even non-existent.The difference in oxygen consumption at the same temperatures varies for differently ranked coals.The results show the difference in oxygen consumption of the coals tested in our study reached 78.6%at 100℃.Based on the theory of coal-oxygen reaction,these phenomena were analyzed from the point of view of physical and chemical characteristics,as well as the appearance of the coal-oxygen complex.From theoretical analyses and our experiments,we conclude that the oxygen consumption at programmed temperatures reflects the oxidation ability of coals perfectly.

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.

Non-Linear Localization Algorithm Based on Newton Iterations

In order to improve the performance of time difference of arrival(TDOA)localization,a nonlinear least squares algorithm is proposed in this paper.Firstly,based on the criterion of the minimized sum of square error of time difference of arrival,the location estimation is expressed as an optimal problem of a non-linear programming.Then,an initial point is obtained using the semi-definite programming.And finally,the location is extracted from the local optimal solution acquired by Newton iterations.Simulation results show that when the number of anchor nodes is large,the performance of the proposed algorithm will be significantly better than that of semi-definite programming approach with the increase of measurement noise.

An Evolutionary Firefly Algorithm, Goal Programming Optimization Approach for Setting the Osmotic Dehydration Parameters of Papaya

An evolutionary nature-inspired Firefly Algorithm (FA) is employed to set the optimal osmotic dehydration parameters in a case study of papaya. In the case, the functional form of the dehydration model is established via a response surface technique with the resulting optimization formulation being a non-linear goal programming model. For optimization, a computationally efficient, FA-driven method is employed and the resulting solution is shown to be superior to those from previous approaches for determining the osmotic process parameters. The final component of this study provides a computational experimentation performed on the FA to illustrate the relative sensitivity of this evolutionary metaheuristic approach over a range of the two key parameters that most influence its running time-the number of iterations and the number of fireflies. This sensitivity analysis revealed that for intermediate-to-high values of either of these two key parameters, the FA would always determine overall optimal solutions, while lower values of either parameter would generate greater variability in solution quality. Since the running time complexity of the FA is polynomial in the number of fireflies but linear in the number of iterations, this experimentation shows that it is more computationally practical to run the FA using a “reasonably small” number of fireflies together with a relatively larger number of iterations than the converse.

Green resource allocation for mobile edge computing

We investigate the green resource allocation to minimize the energy consumption of the users in mobile edge computing systems,where task offloading decisions,transmit power,and computation resource allocation are jointly optimized.The considered energy consumption minimization problem is a non-convex mixed-integer nonlinear programming problem,which is challenging to solve.Therefore,we develop a joint search and Successive Convex Approximation(SCA)scheme to optimize the non-integer variables and integer variables in the inner loop and outer loop,respectively.Specifically,in the inner loop,we solve the optimization problem with fixed task offloading decisions.Due to the non-convex objective function and constraints,this optimization problem is still non-convex,and thus we employ the SCA method to obtain a solution satisfying the Karush-Kuhn-Tucker conditions.In the outer loop,we optimize the offloading decisions through exhaustive search.However,the computational complexity of the exhaustive search method is greatly high.To reduce the complexity,a heuristic scheme is proposed to obtain a sub-optimal solution.Simulation results demonstrate the effectiveness of the developed schemes.

TACKLING INDUSTRIAL-SCALE SUPPLY CHAIN PROBLEMS BY MIXED-INTEGER PROGRAMMING

The modeling flexibility and the optimality guarantees provided by mixed-integer programming greatly aid the design of robust and future-proof decision support systems.The complexity of industrial-scale supply chain optimization,however,often poses limits to the application of general mixed-integer programming solvers.In this paper we describe algorithmic innovations that help to ensure that MIP solver performance matches the complexity of the large supply chain problems and tight time limits encountered in practice.Our computational evaluation is based on a diverse set,modeling real-world scenarios supplied by our industry partner SAP.

Energy Management of Networked Smart Railway Stations Considering Regenerative Braking, Energy Storage System, and Photovoltaic Units

The networking of microgrids has received significant attention in the form of a smart grid.In this paper,a set of smart railway stations,which is assumed as microgrids,is connected together.It has been tried to manage the energy exchanged between the networked microgrids to reduce received energy from the utility grid.Also,the operational costs of stations under various conditions decrease by applying the proposed method.The smart railway stations are studied in the presence of photovoltaic(PV)units,energy storage systems(ESSs),and regenerative braking strategies.Studying regenerative braking is one of the essential contributions.Moreover,the stochastic behaviors of the ESS’s initial state of energy and the uncertainty of PV power generation are taken into account through a scenario-based method.The networked microgrid scheme of railway stations(based on coordinated operation and scheduling)and independent operation of railway stations are studied.The proposed method is applied to realistic case studies,including three stations of Line 3 of Tehran Urban and Suburban Railway Operation Company(TUSROC).The rolling stock is simulated in the MATLAB environment.Thus,the coordinated operation of networked microgrids and independent operation of railway stations are optimized in the GAMS environment utilizing mixed-integer linear programming(MILP).

An efficient approach for solving mixed-integer programming problems under the monotonic condition

Many important integer and mixed-integer programming problems are difficult to solve.A representative example is unit commitment with combined cycle units and transmission capacity constraints.Complicated transitions within combined cycle units are difficult to follow,and system-wide coupling transmission capacity constraints are difficult to handle.Another example is the quadratic assignment problem.The presence of cross-products in the objective function leads to nonlinearity.In this study,building upon the novel integration of surrogate Lagrangian relaxation and branch-and-cut,such problems will be solved by relaxing selected coupling constraints.Monotonicity of the relaxed problem will be assumed and exploited and nonlinear terms will be dynamically linearised.The linearity of the resulting problem will be exploited using branch-and-cut.To achieve fast convergence,guidelines for selecting stepsizing parameters will be developed.The method opens up directions for solving nonlinear mixed-integer problems,and numerical results indicate that the new method is efficient.

Planning method of droplet fusion scheduling based on mixedinteger programming

The emergence of new display devices,such as organic light-emitting diodes,has brought about numerous advantages,including high material utilization,low cost,and high adaptability.These devices are manufactured using inkjet printing and possess the potential to become a key technology for display transformations.However,a challenge in achieving this is the display effect that reveals uneven brightness and darkness,which can be avoided by controlling the volume of ink solution in a pixel to within 5%.Currently,the volume difference among the nozzles of commercial printheads does not meet the requirements for volume uniformity,thus challenging the printing process.Therefore,designing a suitable printing method that allows for the fusion of different volumes of ink droplets,ultimately reducing the error of the post fusion process,is necessary.In this study,we propose a print display droplet fusion scheduling method comprising two main steps.First,we use a dichotomous trust domain algorithm to obtain a feasible range of printhead docking point spacings for different nozzle and pixel panel resolutions.Second,we model the printing process as a droplet fusion scheduling model based on mixed integer programming,with the optimization objective of achieving intra pixel volume uniformity via ensuring the volume uniformity of ink droplets within all pixels.We verified this method through numerical simulations and printing experiments using 394 pixels per inch(ppi)pixel panels and successfully reduced the volume uniformity error among pixels to within 5%.

GLOBAL CONVERGENCE RESULTS OF A THREE TERM MEMORY GRADIENT METHOD WITH A NON-MONOTONE LINE SEARCH TECHNIQUE

In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.

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.

A Novel MILP Model Based on the Topology of a Network Graph for Process Planning in an Intelligent Manufacturing System

Intelligent process planning(PP)is one of the most important components in an intelligent manufacturing system and acts as a bridge between product designing and practical manufacturing.PP is a nondeterministic polynomial-time(NP)-hard problem and,as existing mathematical models are not formulated in linear forms,they cannot be solved well to achieve exact solutions for PP problems.This paper proposes a novel mixed-integer linear programming(MILP)mathematical model by considering the network topology structure and the OR nodes that represent a type of OR logic inside the network.Precedence relationships between operations are discussed by raising three types of precedence relationship matrices.Furthermore,the proposed model can be programmed in commonly-used mathematical programming solvers,such as CPLEX,Gurobi,and so forth,to search for optimal solutions for most open problems.To verify the effectiveness and generality of the proposed model,five groups of numerical experiments are conducted on well-known benchmarks.The results show that the proposed model can solve PP problems effectively and can obtain better solutions than those obtained by the state-ofthe-art algorithms.

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.