Vikas Goel

A Class of stochastic programs with decision dependent uncertainty

We address a class of problems where decisions have to be optimized over a time horizon given that the future is uncertain and that the optimization decisions influence the time of information discovery for a subset of the uncertain parameters. The standard approach to formulate stochastic programs is based on the assumption that the stochastic process is independent of the optimization decisions, which is not true for the class of problems under consideration. We present a hybrid mixed-integer disjunctive programming formulation for the stochastic program corresponding to this class of problems and hence extend the stochastic programming framework. A set of theoretical properties that lead to reduction in the size of the model is identified. A Lagrangean duality based branch and bound algorithm is also presented.

A stochastic programming approach to planning of offshore gas field developments under uncertainty in reserves

Abstract In this work we consider the optimal investment and operational planning of gas field developments under uncertainty in gas reserves. The resolution of uncertainty in gas reserves, and hence the shape of the scenario tree associated with the problem depends on the investment decisions. A novel stochastic programming model that incorporates the decision-dependence of the scenario tree is presented. A decomposition based approximation algorithm for the solution of this model is also proposed. We show that the proposed approach yields solutions with significantly higher expected net present value (ENPV) than that of solutions obtained using a deterministic approach. For a small sized example, the proposed approximation algorithm is shown to yield the optimal solution with more than one order of magnitude reduction in solution time, as compared to the full space method. “Good” solutions to larger problems, that require up to 165,000 binary variables in full space, are obtained in a few hours using the proposed approach.

A novel branch and bound algorithm for optimal development of gas fields under uncertainty in reserves

We consider the problem of optimal investment and operational planning for development of gas fields under uncertainty in gas reserves. Assuming uncertainties in the size and initial deliverabilities of the gas fields, the problem has been formulated as a multistage stochastic program by Goel and Grossmann (2004). In this paper, we present a set of theoretical properties satisfied by any feasible solution of this model. We also present a Lagrangean duality based branch and bound algorithm that is guaranteed to give the optimal solution of this model. It is shown that the properties presented here achieve significant reduction in the size of the model. In addition, the proposed algorithm generates significantly superior solutions than the deterministic approach and the heuristic proposed by Goel and Grossmann (2004). The optimality gaps are also much tighter.

Constraint Programming for LNG Ship Scheduling and Inventory Management

We propose a constraint programming approach for the optimization of inventory routing in the liquefied natural gas industry. We present two constraint programming models that rely on a disjunctive scheduling representation of the problem. We also propose an iterative search heuristic to generate good feasible solutions for these models. Computational results on a set of large-scale test instances demonstrate that our approach can find better solutions than existing approaches based on mixed integer programming, while being 4–10 times faster on average.

Computational strategies for non-convex multistage MINLP models with decision-dependent uncertainty and gradual uncertainty resolution

In many planning problems under uncertainty the uncertainties are decision-dependent and resolve gradually depending on the decisions made. In this paper, we address a generic non-convex MINLP model for such planning problems where the uncertain parameters are assumed to follow discrete distributions and the decisions are made on a discrete time horizon. In order to account for the decision-dependent uncertainties and gradual uncertainty resolution, we propose a multistage stochastic programming model in which the non-anticipativity constraints in the model are not prespecified but change as a function of the decisions made. Furthermore, planning problems consist of several scenario subproblems where each subproblem is modeled as a nonconvex mixed-integer nonlinear program. We propose a solution strategy that combines global optimization and outer-approximation in order to optimize the planning decisions. We apply this generic problem structure and the proposed solution algorithm to several planning problems to illustrate the efficiency of the proposed method with respect to the method that uses only global optimization.

Using diversification, communication and parallelism to solve mixed-integer linear programs

Performance variability of modern mixed-integer programming solvers and possible ways of exploiting this phenomenon present an interesting opportunity in the development of algorithms to solve mixed-integer linear programs (MILPs). We propose a framework using multiple branch-and-bound trees to solve MILPs while allowing them to share information in a parallel execution. We present computational results on instances from MIPLIB 2010 illustrating the benefits of this framework.

A lagrangean duality based branch and bound for solving linear stochastic programs with decision dependent uncertainty

Abstract We address a class of planning problems where the optimization decisions influence the time of information discovery for a subset of the uncertain parameters. The standard stochastic programming approach cannot be used for these problems. We present a hybrid mixed-integer disjunctive programming formulation and a Lagrangean duality based branch and bound algorithm for these problems and illustrate the advantages of this approach using examples for a manufacturing problem.

A parallel local search framework for the Fixed-Charge Multicommodity Network Flow problem

We present a parallel local search approach for obtaining high quality solutions to the Fixed Charge Multicommodity Network Flow problem (FCMNF). The approach proceeds by improving a given feasible solution by solving restricted instances of the problem where flows of certain commodities are fixed to those in the solution while the other commodities are locally optimized. We derive multiple independent local search neighborhoods from an arc-based mixed integer programming (MIP) formulation of the problem which are explored in parallel. Our scalable parallel implementation takes advantage of the hybrid memory architecture in modern platforms and the effectiveness of MIP solvers in solving small problems instances. Computational experiments on FCMNF instances from the literature demonstrate the competitiveness of our approach against state of the art MIP solvers and other heuristic methods. HighlightsNew parallel LNS algorithm for finding quality solutions to FCMNF instances.Solution improvements are found by the concurrent optimization of LNS.A novel parallel method allows to combine the improvements found concurrently.Parallel efficiency and scalability allow the optimization of large-scale instances.Extensive sets of experiments show the competitiveness of our approach.