Invited Session Wed.3.MA 549

Wednesday, 15:15 - 16:45 h, Room: MA 549

Cluster 18: Optimization in energy systems [...]

Stochastic programming in energy


Chair: Asgeir Tomasgard



Wednesday, 15:15 - 15:40 h, Room: MA 549, Talk 1

Gerardo Alfredo Perez Valdes
Parallel computational implementation of a branch and fix coordination algorithm

Coauthors: Laureano Escudero, Marte Fødstad, Adela Pages-Bernaus, Gloria Perez, Asgeir Tomasgard


Branch and fix coordination is an algorithm designed to solve large scale multi-stage stochastic mixed integer problems, based on the notion that the particular structure of such problems makes it so that they can be broken down into scenario groups with smaller subproblems, solvable almost independently.
With this in mind, it is possible to use parallel computing techniques to solve the subproblems created: each processor solves the subproblems pertaining to a particular cluster, and then the solutions are reported to a master routine.
To satisfy non-anticipativity in the master problem's binary variables, the values of the binary variables in the subproblem solutions are coordinated the entire process.
The treatment of the original problem this way not only makes it faster to solver, but also allows us to solve otherwise intractable instances, where the number of binary variables is too large to be efficiently computed in a single processor.
In this work, we present details and results about our computational implementation of the branch and fix coordination algorithm.



Wednesday, 15:45 - 16:10 h, Room: MA 549, Talk 2

Xiang Li
Stochastic nonconvex MINLP models and global optimization for natural gas production network design under uncertainty

Coauthors: Paul I. Barton, Asgeir Tomasgard


Scenario-based stochastic nonconvex MINLP models are developed to facilitate the design of natural gas production networks under uncertainty. Here the nonconvexity comes from bilinear, quadratic and power functions involved in the equations for tracking the gas qualities and pressures. As a gas network involves large investments, a small performance gain made in the design can translate into significant increase in profits, it is desirable to solve the nonconvex MINLPs to global optimality. An extension of generalized Benders decomposition (GBD), called nonconvex generalized Benders decomposition (NGBD), is developed for the global optimization of the stochastic MINLPs. As it takes advantage of the decomposable structure of the problem, NGBD has significant computational advantage over state-of-the-art global optimization solvers (such as BARON). The advantages of the proposed stochastic nonconvex MINLP models and NGBD are demonstrated through case studies of an industrial gas production system.



Wednesday, 16:15 - 16:40 h, Room: MA 549, Talk 3

Lars Hellemo
Stochastic programming with decision dependent probabilities

Coauthors: Paul I. Barton, Asgeir Tomasgard


We propose an investment problem modeled as a stochastic program with decision dependent probabilities. In addition to the available production technologies, we assume there is an activity or technology available that will alter the probabilities of the discrete scenarios occuring. By investing in such technology or activity, it is possible to increase the probability of some scenarios, while reducing the probability of the remaining scenarios, or vice versa.
We also demonstrate the use of a specialized decomposition algorithm for this class of problems, using generalized Benders decomposition and relaxation of algorithms/McCormick relaxations.
We illustrate the potential usefulness and the performance of the decomposition algorithm on this class of problems through an application from the Energy business


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