This paper introduces a framework for the quantitative analysis of collaborative service platforms. Stochastic programming solutions to supply chain management a dissertation submitted to the department of management science and engineering and the committee on graduate studies of stanford university in partial fulfillment of the requirements for the degree of doctor of philosophy in operations research rene c. A tutorial on stochastic programming alexandershapiro. Existence of solutions and sensitivity analyses we consider structural topology optimization problems including unilateral constraints arising from, for example, nonpenetration conditions in contact mechanics or noncompression conditions for elastic ropes. On the existence of solutions to stochastic mathematical. Among them are the natural gas cashout problem, the deregulated electricity market equilibrium problem, biofuel problems, a problem of designing coupled energy carrier networks, and so forth, if we mention only part of such. Necessary optimality conditions in pessimistic bilevel programming dempe et al. Whether interesting stability properties can be derived from an smpec model equipped with this relaxed joint upperlevel constraint is an interesting future research question. The paper presents theory dealing primarily with properties of the relevant functions that result in convex programming problems, and. Bilevel models to describe migration processes are also in the list of the most popular new themes of bilevel programming, as well as allocation, information protection, and cybersecurity problems. The structural design that responds the best, on average, to a given set of loads is obtained, where each load has its own probability of. The proposed project was aimed at exploring various theoretical and algorithmic issues at the intersection of three optimization areas, namely, parametric, stochastic and bilevel integer programming, as well as related applications. Dec 01, 20 read twostage stochastic bilevel programming over a transportation network, transportation research part b. By closing this message, you are consenting to our use of cookies.
This problem incorporates the classical truss topology optimization problem as well as the more. Computational optimization and applications covers a wide range of topics in optimization, including. Actually a stochastic programming extension of bilevel programming, whose underlying principles have been laid out by patriksson and wynter 1999, has been proposed by patriksson and wynter 1997 for addressing a structural optimization problem, and by christiansen et al. Convergence analysis of a smoothing saa method for a.
Discretecontinuous structural optimization with distributed evolution strategies. The first section describes a cutting hyperplane algorithm which is shown to be equivalent to a partial decomposition algorithm of the dual program. Stochastic programming offers a solution to this issue by eliminating uncertainty and characterizing it using probability distributions. A study on the existence, stability and computation of optimal solutions to stochastic mathematical programs with equilibrium constraints. A regularized sample average approximation method for.
Bilevel optimization is a special kind of optimization where one problem is embedded nested within another. Starshaped approximation approach for stochastic programming problems with probability function. Parameter inference of queueing models for it systems using endtoend measurements. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Then, the deterministic bilevel covariance programming problem is solved by backpropagation artificial neural network based on elite particle swam optimization algorithm bpannpso. In freight transportation, it is the norm to call a carrier the day.
This is the probabilistic or chance constraint of stochastic programming e. The present paper serves to introduce a new robust modelling technique and solution methodology for a class of problems in structural optimization, in which we calculate the structural design that responds the best on average to a given set of loads, each having its own probability of. A forerunner to the paper by patriksson and wynter 1999 was the conference presentation bilevel stochastic programming for network equilibrium problems at the international symposium on mathematical programming ismp97 by wynter 1997 see also wynter, 2002, in which the combination of stochastic programming and bilevel optimization. Monte carlo samplingbased methods for stochastic optimization tito homemdemello school of business universidad adolfo ibanez santiago, chile tito. It can be considered as a nontrivial extension of stochastic mathematical program with complementarity constraints, and could arise from a hardtohandle class of bilivel secondorder cone programming and inverse stochastic secondorder cone programming. Stochastic bilevel programming in structural optimization with s. The outer optimization task is commonly referred to as the upperlevel optimization task, and the inner optimization task is commonly referred to as the lowerlevel optimization task. Read on the applicability and solution of bilevel optimization models in transportation science. The present paper serves to introduce a new robust modelling technique and solution methodology for a class of problems in structural optimization, in which we calculate the structural design that responds the best on average to a given set of loads, each having its own probability of occurrence. Chapter 1 stochastic linear and nonlinear programming 1. The intended audience of the tutorial is optimization practitioners and researchers who wish to. Optimal design of truss structures by logicbased branch.
Approximating stationary points of stochastic mathematical. Behavioral pricing of energy swing options by stochastic bilevel optimization. For this problem, we prove the existence of solutions. The resulting stochastic bilevel optimization model finds a structural design that. Services built around platforms require the coordinated coll. Bilevel direct search method for leaderfollower equilibrium problems and applications dali zhang1 and guihua lin2 february 12, 2012 abstract in the paper, we propose a bilevel direct search method for the distributed computation of equilibria in leaderfollower problems. In stochastic programming terminology, we consider hereandnow models where decisions must be made before observing the uncertain parameter values and the responses of the network users. Structural and multidisciplinary optimization 21 5, 3671, 2001. For help with downloading a wikipedia page as a pdf, see help. On a stochastic bilevel programming problem request pdf. This is a wikipedia book, a collection of wikipedia articles that can be easily saved, imported by an external electronic rendering service, and ordered as a printed book. Solving planning and design problems in the process. In this article, a mixed integer bilevel problem having a probabilistic knapsack constraint in the first level is proposed.
Behavioral pricing of energy swing options by stochastic. Methodological on deepdyve, the largest online rental service for scholarly research with thousands of academic publications. December 2, 1999 abstract we consider the mathematical modelling and solution of robust and costoptimizing structural topology design problems. Stochastic programming stochastic programming certainty equivalent problem. We consider a twostage stochastic extension of the bilevel pricing model introduced by. The present paper serves to introduce a modelling technique and solution methodology for a robust and costoptimizing approach to structural optimization. Stochastic bilevel programming in structural optimization snorre christiansen. Existence and continuity of optimal solutions to some structural topology optimization problems including unilateral constraints and stochastic loads with joakim petersson zamm, 82 2002 435459. Examples of stochastic optimization problems in this chapter, we will give examples of three types of stochastic optimization problems, that is, optimal stopping, total expected discounted cost problem, and longrun average cost problem.
The other class of solution approaches employs statistical techniques such as sam. Twostage stochastic programming problems are not generally associated with bilevel programming. Optimization is a very lively area, hence standard textbooks become outdated very fast. Read twostage stochastic bilevel programming over a transportation network, transportation research part b. The setting is the optimal design of a linearelastic structure, for. Mathematical programs with optimization problems in the. Existence of solutions and sensitivity analyses we consider structural topology optimization problems including unilateral constraints arising from, for example, nonpenetration conditions in contact mechanics or noncompression. Introduction, history and overview, which allows the uncertainty in the values of the problem parameters to be expressed by a probability distribution on some or all of the variables of the model. Therefore only a very restricted and certainly subjective list of books is presented here, mainly extracted from the faqs initiated by gregory and presently maintained by r. A stochastic bilevel program sbp is a generalization of an ordinary bilevel program bp. Statistical average approximation stochastic approximation machine learning as stochastic optimization leading example. The problems in the constraints can be linear programs, nonlinear programs, or twosided optimization problems, including certain types of games. After introducing the general setting of stochastic bilevel programming and basic assumptions on the models section 2, the relevant risk functionals are discussed section 3.
Pdf we consider the mathematical modelling and solution of robust and cost optimizing structural topology design problems. The resulting stochastic bilevel optimization model. A heuristic and an exact algorithm for solving the program are presented, along with an effective parallelization strategy. Find materials for this course in the pages linked along the left. L 2 regularized linear prediction, as in svms connection to online learning break more careful look at stochastic gradient descent. Patriksson and wynter 3 considered an smpec model for a class of stochastic bilevel programming problem in structural optimization, xu 35 modeled a stochastic stackelberg. This type of problem will be described in detail in the following sections below.
We consider the mathematical modelling and solution of robust and cost optimizing structural topology design problems. This model is of special interest when a structural failure will lead to a reconstruction cost, rather than loss of life. A study on the existence, stability and computation of optimal solutions to stochastic mathematical programs with equilibrium constraints, transportation research part b. On the applicability and solution of bilevel optimization. The structure of the feasible set of bilevel optimization problems has been the. Robust bilevel optimization models in transportation.
Whereas deterministic optimization problems are formulated with known parameters, real world problems almost invariably include some unknown parameters. Dc programming and dca, which constitute the backbone of nonconvex programming and global optimization, were introduced in 1985 by pham dinh tao in the preliminary state, and have been extensively developed by le thi hoai an and pham dinh tao since 1994 to become now classic and increasingly popular. This paper considers simultaneous minimization of exp. Stochastic mathematical programs with equilibrium constraints, modeling and sample average. Siam journal on applied mathematics siam society for. The backpropagation artificial neural network based on elite.
The setup and solution of these problem will require the familiarity with probability theory. Monte carlo samplingbased methods for stochastic optimization. The structural design that responds the best, on average, to a given set of loads is obtained, where each load has its own probability of occurrence. Alternatively, you can download the file locally and open with. A very general stochastic model is presented, along with its mathematical properties, generalizing some recently published results. Methodological on deepdyve, the largest online rental service for scholarly research with thousands of academic. On the use of bilevel programming for solving a structural optimization problem with discrete variables. Stochastic bilevel programming in structural optimization core. Lecture slides dynamic programming and stochastic control. Stochastic bilevel programming in structural optimization. Based on elite particle swam optimization algorithm for stochastic linear bilevel programming problem. For a class of stochastic linear bilevel programming problem, we firstly transform it into a deterministic linear bilevel covariance programming problem. Pdf stochastic bilevel programming in structural optimization.
The backpropagation artificial neural network based on. We generalize stochastic mathematical programs with equilibrium constraints smpec introduced by patriksson and wynter ref. Because of our goal to solve problems of the form 1. The stochastic optimization setup and the two main approaches. Bradley and crane 19729 and kusy and zeimba 198610. The main objective is to optimize the leaders upper level stochastic programming problem, where the followers problem is assumed to be satisfied as part of the constraints. A stochastic mathematical program model with secondorder cone complementarity constraints ssocmpcc is introduced in this paper. Dec 01, 2008 read on the applicability and solution of bilevel optimization models in transportation science.
Optimal design of truss structures by logicbased branch and cut. Twostage stochastic bilevel programming over a transportation. Chapter 1 stochastic linear and nonlinear programming. Robust topology optimization has long been considered computationally intractable as it combines two highly expensive computational strategies. There exist a few minor alternatives, such as fuzzy sets based models and combinations of the approaches listed. This paper extends the approach to stochastic bilevel problems. This paper gives an algorithm for lshaped linear programs which arise naturally in optimal control problems with state constraints and stochastic linear programs which can be represented in this form with an infinite number of linear constraints.
The stochastic programming based models offer the richest modelling. Although this book mostly covers stochastic linear programming since that is the best developed topic, we also discuss stochastic nonlinear programming, integer programming and network. Stochastic programming models in financial optimization. We have stochastic and deterministic linear programming, deterministic and stochastic network. To learn about our use of cookies and how you can manage your cookie settings, please see our cookie policy. The most famous type of stochastic programming model is for recourse problems. The resulting stochastic bilevel optimization model finds a structural design that responds the best to the given probability distribution in the data. Researcharticle the backpropagation artificial neural network based on elite particle swam optimization algorithm for stochastic linear bilevel programming problem.
For the mathematical model, we provide results on the existence. In the field of mathematical optimization, stochastic programming is a framework for modeling optimization problems that involve uncertainty. Stochastic bilevel programming is a bilevel program having some form of randomness in the problem definition. Sensitivity analysis of separable traffic equilibrium equilibria with application to bilevel optimization in network design. Stochastic mathematical programs with equilibrium constraints. Bilevel optimization based on iterative approximation of. The problem formulation is mainly motivated by practical pricing and service provision problems as it can be interpreted as a model for the interaction between a service provider and customers.
A great amount of new applied problems in the area of energy networks has recently arisen that can be efficiently solved only as mixedinteger bilevel programs. Methodological on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Introduction operational models of problems in transportation and logistics o. Pdf we consider the mathematical modelling and solution of robust and costoptimizing structural topology design problems.