Hard uncertainties in multiobjective layout optimization of photovoltaic power plants

Abstract This paper describes how to treat hard uncertainties defined by so-called uncertainty maps in multiobjective optimization problems. For the uncertainty map being set-valued, a Taylor formula is shown under appropriate assumptions. The hard uncertainties are modeled using parametric set optimization problems for which a scalarization result is given. The presented new approach for the solution of multiobjective optimization problems with hard uncertainties is then applied to the layout optimization of photovoltaic power plants. Since good weather forecasts are difficult to obtain for future years, weather data are really hard uncertainties arising in the planning process. Numerical results are presented for a real-world problem on the Galapagos island Isabela.

[1]  Elisabeth Anna Sophia Köbis.  On robust optimization - a unified approach to robustness using a nonlinear scalarizing functional and relations to set optimization , 2014 .

[2]  Johannes Jahn,et al.  New Order Relations in Set Optimization , 2011, J. Optim. Theory Appl..

[3]  Johannes Jahn.  DIRECTIONAL DERIVATIVES IN SET OPTIMIZATION WITH THE SET LESS ORDER RELATION , 2015 .

[4]  Norman Neukel.  Order relations of sets and its application in socio-economics , 2013 .

[5]  A. Schöbel,et al.  The relationship between multi-objective robustness concepts and set-valued optimization , 2014 .

[6]  Matthias Ehrgott,et al.  Minmax robustness for multi-objective optimization problems , 2014, Eur. J. Oper. Res..

[7]  J. Jahn.  Introduction to the Theory of Nonlinear Optimization , 1994 .

[8]  S. Gagliano,et al.  Probability Analysis of Weather Data for Energy Assessment of Hybrid Solar/Wind Power System , 2008 .

[9]  Hendrik Ewe,et al.  Multi-objective Planning of Large-Scale Photovoltaic Power Plants , 2012, OR.

[10]  Elisabeth Köbis,et al.  Concepts of efficiency for uncertain multi-objective optimization problems based on set order relations , 2014, Math. Methods Oper. Res..

[11]  Johannes Jahn.  Vectorization in Set Optimization , 2015, J. Optim. Theory Appl..

[12]  Kai Plociennik,et al.  A Software-Based Planning Approach for Photovoltaic Power Plant Layouts , 2014 .

[13]  Constantin Zalinescu,et al.  Set-valued Optimization - An Introduction with Applications , 2014, Vector Optimization.

[14]  A. M. Rubinov,et al.  Difference of compact sets in the sense of demyanov and its application to non-smooth analysis , 1992 .