Hybrid Evolutionary Optimization of Two-Stage Stochastic Integer Programming Problems: An Empirical Investigation

Abstract

In this contribution, we consider decision problems on a moving horizon with significant uncertainties in parameters. The information and decision structure on moving horizons enables recourse actions which correct the here-and-now decisions whenever the horizon is moved a step forward. This situation is reflected by a mixed-integer recourse model with a finite number of uncertainty scenarios in the form of a two-stage stochastic integer program. A stage decomposition-based hybrid evolutionary algorithm for two-stage stochastic integer programs is proposed that employs an evolutionary algorithm to determine the here-and-now decisions and a standard mathematical programming method to optimize the recourse decisions. An empirical investigation of the scale-up behavior of the algorithms with respect to the number of scenarios exhibits that the new hybrid algorithm generates good feasible solutions more quickly than a state of the art exact algorithm for problem instances with a high number of scenarios.

Two‐stage stochastic demand response in smart grid considering random appliance usage patterns

“…L-shaped method [33] has been widely used to solve two-stage stochastic programming problems. However, for large-size problems, the study in [34] indicates that the evolutionary algorithm such as a genetic algorithm performs better in finding the optimal solutions than the L-shaped method. Besides, the genetic algorithm, as a common mature algorithm in evolutionary computing, has been widely used in DR problems [9].…”

Evolutionary framework for two-stage stochastic resource allocation problems

“…However, for practical resource allocation problems, the deterministic equivalent forms are usually too large to tackle, even with a state-of-the-art MIP solver. Moreover, Tometzki & Engell (2009) points out that MILP solvers still do not exploit the staircase structure of these deterministic formulations.…”