Due to the increased number and intensity of wildfires, the need for solutions that minimize the impact of fire are needed. Fuel treatment is one of the methods used to mitigate the effects of fire at a certain area. ...
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Due to the increased number and intensity of wildfires, the need for solutions that minimize the impact of fire are needed. Fuel treatment is one of the methods used to mitigate the effects of fire at a certain area. In this thesis, a two-stage stochastic programming model for fuel treatment management is constructed. The model optimizes the selection of areas for fuel treatment under budget and man- hour constraints. The process makes use of simulation tools like PHYGROW, which mimics the growth of vegetation after treatment, and FARSITE, which simulates the behavior of fire. The model minimizes the costs of fuel treatment as well as the potential losses when fire occurs. Texas Wildfire Risk Assessment Model (TWRA) used by Texas Forest Service (TFS) is used to quantify risk at each area. The model is applied at TX 12, which is a fire planning unit under the administration of TFS. Results show that the total of the expenditures on fuel treatment and the expected impact justify the efforts of fuel treatment.
To enhance the hitting accuracy of tank with moving firing, an uncertain optimization method based on stochastic programming is adopted to reduce the initial disturbance of projectile. Firstly, the firing dynamics mod...
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To enhance the hitting accuracy of tank with moving firing, an uncertain optimization method based on stochastic programming is adopted to reduce the initial disturbance of projectile. Firstly, the firing dynamics model of moving tank is modeled to simulate the initial disturbance of projectile. Secondly, the controllable interior ballistic parameters such as projectile structure parameters and propellant parameters are treated as random design variables. The surrogate model for the firing dynamics model of moving tank is constructed by using the neural network based on deep learning. The uncertain optimization problem is transformed into a deterministic optimization problem by stochastic programming method. Then multi-objective genetic algorithm is adopted to settle optimization model, and reasonable design interval of random design variables is obtained. Finally, a six-degree-of-freedom rigid external ballistics model is used to establish a hitting accuracy evaluation model of moving tank based on interval uncertainty analysis. Through this model, the effectiveness of the optimization method is demonstrated.
stochastic dominance relations are well studied in statistics, decision theory and economics. Recently, there has been significant interest in introducing dominance relations into stochastic optimization problems as c...
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stochastic dominance relations are well studied in statistics, decision theory and economics. Recently, there has been significant interest in introducing dominance relations into stochastic optimization problems as constraints. In the discrete case, stochastic optimization models involving second order stochastic dominance constraints can be solved by linear programming. However, problems involving first order stochastic dominance constraints are potentially hard due to the non-convexity of the associated feasible regions. In this paper we consider a mixed 0-1 linear programming formulation of a discrete first order constrained optimization model and present a relaxation based on second order constraints. We derive some valid inequalities and restrictions by employing the probabilistic structure of the problem. We also generate cuts that are valid inequalities for the disjunctive relaxations arising from the underlying combinatorial structure of the problem by applying the lift-and-project procedure. We describe three heuristic algorithms to construct feasible solutions, based on conditional second order constraints, variable fixing, and conditional value at risk. Finally, we present numerical results for several instances of a real world portfolio optimization problem.
In this paper, we generalize the well-known Nesterov's accelerated gradient (AG) method, originally designed for convex smooth optimization, to solve nonconvex and possibly stochastic optimization problems. We dem...
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In this paper, we generalize the well-known Nesterov's accelerated gradient (AG) method, originally designed for convex smooth optimization, to solve nonconvex and possibly stochastic optimization problems. We demonstrate that by properly specifying the stepsize policy, the AG method exhibits the best known rate of convergence for solving general nonconvex smooth optimization problems by using first-order information, similarly to the gradient descent method. We then consider an important class of composite optimization problems and show that the AG method can solve them uniformly, i.e., by using the same aggressive stepsize policy as in the convex case, even if the problem turns out to be nonconvex. We demonstrate that the AG method exhibits an optimal rate of convergence if the composite problem is convex, and improves the best known rate of convergence if the problem is nonconvex. Based on the AG method, we also present new nonconvex stochastic approximation methods and show that they can improve a few existing rates of convergence for nonconvex stochastic optimization. To the best of our knowledge, this is the first time that the convergence of the AG method has been established for solving nonconvex nonlinear programming in the literature.
We study a stochastic outpatient appointment scheduling problem (SOASP) in which we need to design a schedule and an adaptive rescheduling (i.e., resequencing or declining) policy for a set of patients. Each patient h...
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We study a stochastic outpatient appointment scheduling problem (SOASP) in which we need to design a schedule and an adaptive rescheduling (i.e., resequencing or declining) policy for a set of patients. Each patient has a known type and associated probability distributions of random service duration and random arrival time. Finding a provably optimal solution to this problem requires solving a multistage stochastic mixed-integer program (MSMIP) with a schedule optimization problem solved at each stage, determining the optimal rescheduling policy over the various random service durations and arrival times. In recognition that this MSMIP is intractable, we first consider a two-stage model (TSM) that relaxes the nonanticipativity constraints of MSMIP and so yields a lower bound. Second, we derive a set of valid inequalities to strengthen and improve the solvability of the TSM formulation. Third, we obtain an upper bound for the MSMIP by solving the TSM under the feasible (and easily implementable)appointment order(AO)policy, which requires that patients are served in the order of their scheduled appointments, independent of their actual arrival times. Fourth, we propose a Monte Carlo approach to evaluate the relative gap between the MSMIP upper and lower bounds. Finally, in a series of numerical experiments, we show that these two bounds are very close in a wide range of SOASP instances, demonstrating the near-optimality of the AO policy. We also identify parameter settings that result in a large gap in between these two bounds. Accordingly, we propose an alternative policy based on neighbor-swapping. We demonstrate that this alternative policy leads to a much tighter upper bound and significantly shrinks the gap.
The multiresponse surface problem is modelled as a multiobjective stochastic optimisation, and diverse solutions are proposed. There are several crucial differences highlighted between this approach and the other prop...
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The multiresponse surface problem is modelled as a multiobjective stochastic optimisation, and diverse solutions are proposed. There are several crucial differences highlighted between this approach and the other proposed solutions. Finally, some particular solutions are applied and described in detail in a numerical example. (C) 2013 Elsevier Inc. All rights reserved.
Given its complexity and relevance in healthcare, the well-known Nurse Scheduling Problem (NSP) has been the subject of several researches and different approaches have been used for its solution. The importance of th...
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Given its complexity and relevance in healthcare, the well-known Nurse Scheduling Problem (NSP) has been the subject of several researches and different approaches have been used for its solution. The importance of this problem comes from its critical role in healthcare processes as NSP assigns nurses to daily shifts while respecting both the preferences of the nurses and the objectives of hospital. Most models in NSP literature have dealt with this problem in a deterministic environment, while in the real-world applications of NSP, the vagueness of information about management objectives and nurse preferences are sources of uncertainties that need to be managed so as to provide a qualified schedule. In this study, we propose a stochastic optimization model for the Department of Heart Surgery in Razavi Hospital, which accounts for uncertainties in the demand and stay period of patients over time. Sample Average Approximation (SAA) method is used to obtain an optimal schedule for minimizing the regular and overtime assignment costs, with the numerical experiments demonstrating the convergence of statistical bounds and moderate sample size for a given numerical experiment. The results confirm the validity of the model. (C) 2016 Elsevier Ltd. All rights reserved.
stochastic (or probabilistic) programming (SP) is an optimization technique in which the constraints and/or the objective function of an optimization problem contain random variables. The mathematical models of these ...
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stochastic (or probabilistic) programming (SP) is an optimization technique in which the constraints and/or the objective function of an optimization problem contain random variables. The mathematical models of these problems may follow any particular probability distribution for model coefficients. The objective here is to determine the proper values for model parameters influenced by random events. In this study, two modified differential evolution (DE) algorithms namely, LDE1 and LDE2 are used for solving SP problems. Two models of SP problems are considered;stochastic Fractional programming Problems and Multiobjective stochastic Linear programming Problems. The numerical results obtained by the LDE algorithms are compared with the results of basic DE, basic particle swarm optimization (PSO) and the available results from where it is observed that the LDE algorithms significantly improve the quality of solution of the considered problem in comparison with the quoted results in the literature.
An algebraic modelling language (AML) is a domain-specific computer programming language for describing and solving mathematical programming models. We propose extending AMLs so that solution algorithms that are based...
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An algebraic modelling language (AML) is a domain-specific computer programming language for describing and solving mathematical programming models. We propose extending AMLs so that solution algorithms that are based on iteratively manipulating, modifying and solving a model are supported at a high abstraction level. We specifically focus on stochastic programming models with random parameters formulated as discrete scenarios and mathematical decomposition algorithms, which are commonly applied to solve such models. We identify the necessary language constructs and develop a design based on the open-source modelling software APLEpy. The proposed design, although specifically addressing decomposition algorithms, proves useful for implementing heuristic solution algorithms as well. The object-oriented nature of the design enables the algorithms that are coded with the proposed extensions to work with any other model that satisfies the assumptions of the initial model. This flexible and robust design helps inexperienced modellers to easily apply an advanced solution algorithm, and experienced modellers to build sophisticated algorithms quickly within the same development environment that is used to describe the model under consideration.
Abstract-This article presents a stochastic methodology for volt/VAR/total harmonic distortion control to reduce power losses while satisfying the main recommended power quality standards and optimizing dispatch sched...
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Abstract-This article presents a stochastic methodology for volt/VAR/total harmonic distortion control to reduce power losses while satisfying the main recommended power quality standards and optimizing dispatch schedules for the switchable shunt capacitor and on-load tap-changer in distribution networks. The main aim is to find proper dispatch schedules for on-load tap-changer tap positions, substation capacitors, and along feeder capacitors. For this purpose, distribution network uncertainties, including load demand and wind power generation, are considered to provide a robust control scheme. A new scenario reduction method based on the highest potential cluster center is used to decrease the huge number of probable states. A new scenario-based probabilistic time-interval division framework, over a 24-hr period on both load curve and wind power output, is introduced to reduce effects of forecast plan uncertainty and switching operations in the on-load tap-changer. A genetic algorithm solution method is applied to find the best solution corresponding to various scenarios. To improve search ability, a method guaranteeing the suppression of maximum allowable daily substation capacitors switching and effectively correcting the convergence process is utilized. The proposed stochastic approach is tested on an IEEE 123-bus distribution network containing a number of non-linear loads and wind energy generation systems.
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