A hybrid algorithm for solving two-stage stochastic integer problems by combining evolutionary algorithms and mathematical programming methods

Till, Jochen; Sand, Guido; Engell, Sebastian; Emmerich, Michael; Schönemann, Lutz

doi:10.1016/s1570-7946(05)80153-1

Cited by 7 publications

(2 citation statements)

References 4 publications

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“…Other hybrid algorithms combine evolutionary and mathematical programming methods, cf. the heuristics by Till et al [51] for stochastic scheduling problems and by Borisovsky et al [6] for supply management problems.…”

Section: Metaheuristics Involving Exact Methodsmentioning

confidence: 99%

Polylithic modeling and solution approaches using algebraic modeling systems

Kallrath

2011

Optim Lett

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Based on the Greek term monolithos (stone consisting of one single block) Kallrath (Comput Chem Eng 33:1983-1993, 2009) introduced the term polylithic for modeling and solution approaches in which mixed integer or non-convex nonlinear optimization problems are solved by tailor-made methods involving several models and/or algorithmic components, in which the solution of one model is input to another one. This can be exploited to initialize certain variables, or to provide bounds on them (problem-specific preprocessing). Mathematical examples of polylithic approaches are decomposition techniques, or hybrid methods in which constructive heuristics and local search improvement methods are coupled with exact MIP algorithms. Tailormade polylithic solution approaches with thousands or millions of solve statements are challenges on algebraic modeling languages. Local objects and procedural structures are almost necessary. Warm-start and hot-start techniques can be essential. The effort of developing complex tailor-made polylithic solutions is awarded by enabling us to solve real-world problems far beyond the limits of monolithic approaches and general purpose solvers.

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Section: Metaheuristics Involving Exact Methodsmentioning

confidence: 99%

Polylithic modeling and solution approaches using algebraic modeling systems

Kallrath

2011

Optim Lett

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“…In this paper, the problem is solved by a stage decomposition based hybrid evolutionary approach which was published by Till et al (2005) for the first time. In the hybrid evolutionary approach, an evolutionary algorithm performs the search on the first-stage decision space while the decoupled second-stage scenario problems are solved by an efficient MILP solver.…”

Section: Introductionmentioning

confidence: 99%

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

Tometzki

Engell

2009

Evolutionary Computation

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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.

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Modeling Difficult Optimization Problems

Kallrath

2008

Encyclopedia of Optimization

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A hybrid algorithm for solving two-stage stochastic integer problems by combining evolutionary algorithms and mathematical programming methods

Cited by 7 publications

References 4 publications

Polylithic modeling and solution approaches using algebraic modeling systems

Polylithic modeling and solution approaches using algebraic modeling systems

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

Modeling Difficult Optimization Problems

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