SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning

Abstract

Abstract. We consider interstage dependent stochastic linear programs where both the random right-hand side and the model of the underlying stochastic process have a special structure. Namely, for equality constraints (resp. inequality constraints) the right-hand side is an affine function (resp. a given function bt) of the process value for the current time step t. As for m-th component of the process at time step t, it depends on previous values of the process through a function htm.For this type of problem, to obtain an approximate policy under some assumptions for functions bt and htm, we detail a stochastic dual dynamic programming algorithm. Our analysis includes some enhancements of this algorithm such as the definition of a state vector of minimal size, the computation of feasibility cuts without the assumption of relatively complete recourse, as well as efficient formulas for sharing optimality and feasibility cuts between nodes of the same stage. The algorithm is given for both a non-risk-averse and a risk-averse model. We finally provide preliminary results comparing the performances of the recourse functions corresponding to these two models for a real-life application.

Multistage Stochastic Programs with a Random Number of Stages: Dynamic Programming Equations, Solution Methods, and Application to Portfolio Selection

“…Assumptions. Consider optimization problem (16) where ξ t does not depend on (ξ [t−1] , D t ) and D t only depends on D t−1 . We assume that the distributions of T and ξ t are discrete: the support of T is {2, .…”

“…, M t . In this context, equations (19), (20), (21), (22) are the dynamic programming equations for (16). We can now apply Stochastic Dual Dynamic Programming (SDDP, [34]), to solve these dynamic programming equations as long as recourse functions Q t (·, 1) are convex.…”

A parallel Branch-and-Fix Coordination based matheuristic algorithm for solving large sized multistage stochastic mixed 0–1 problems

“…Some works in the literature allow to consider Markovian multistage stochastic problems, where the uncertainty in each node of a given stage depends on the history of its ancestor nodes, see [6,30,75]. The treatment of the Conditional Value-at-Risk (CVaR) risk averse measure in SDP was introduced in [36,42,68]. Recently, some works consider mixed-integer problems, see [3,16] and, even time-consistent and time-inconsistent stochastic dominance risk averse measures, see [31,32].…”

Large-scale Unit Commitment under uncertainty

“…We mention in passing that similar techniques can also be applied to longer-term problems, such as the management of an hydro reservoirs, that although not strictly pertinent to this paper are clearly strongly related. For a recent instance, a specialized Stochastic Dual DP algorithm is proposed in Guigues (2013).…”