6,725 research outputs found
Algorithm Engineering in Robust Optimization
Robust optimization is a young and emerging field of research having received
a considerable increase of interest over the last decade. In this paper, we
argue that the the algorithm engineering methodology fits very well to the
field of robust optimization and yields a rewarding new perspective on both the
current state of research and open research directions.
To this end we go through the algorithm engineering cycle of design and
analysis of concepts, development and implementation of algorithms, and
theoretical and experimental evaluation. We show that many ideas of algorithm
engineering have already been applied in publications on robust optimization.
Most work on robust optimization is devoted to analysis of the concepts and the
development of algorithms, some papers deal with the evaluation of a particular
concept in case studies, and work on comparison of concepts just starts. What
is still a drawback in many papers on robustness is the missing link to include
the results of the experiments again in the design
Min-max regret versus gross margin maximization in arable sector modeling
"A sector model presented in this article, uses about 200 representative French cereal-oriented farms to estimate policy impacts by means of mathematical modeling. Usually, such models suppose that farmers intend to maximize expected gross margin. This rationality hypothesis however seems hardly justifiable, especially these days, when gross margin variability due to European Common Agricultural Policy changes may become significant. Increasing uncertainty introduces bounded rationality to the decision problem so that crop gross margins may be better approximated by interval rather than by expected (precise) values. The initial LP problem is specified as an “Interval Linear Programming (ILP)”. We assume that farmers tend to decide upon their surface allocation prudently in order to get through with minimum loss, which is precisely the rationale underlying the minimization of maximum regret decision criterion. Recent advances in operations research, namely Mausser and Laguna algorithms, are exploited to implement the min-max regret criterion to arable agriculture ILP. The validation against observed crop mix proved that as uncertainty increases about 40% of the farmers adopt the min-max regret decision rule instead of the gross margin maximization."Interval Linear Programming, Min-Max Regret, Common Agricultural Policy, Arable cropping, France
Hybrid linear programming to estimate CAP impacts of flatter rates and environmental top-ups
This paper examines evolutions of the Common Agricultural Policy (CAP) decoupling regime and their impacts on Greek arable agriculture. Policy analysis is performed by using mathematical programming tools. Taking into account increasing uncertainty, we assume that farmers perceive gross margin in intervals rather than as expected crisp values. A bottom-up hybrid model accommodates both profit maximizing and risk prudent attitudes in order to accurately assess farmers’ response. Marginal changes to crop plans are expected so that flatter single payment rates cause significant changes in incomes and subsidies. Nitrogen reduction incentives result in moderate changes putting their effectiveness in question.Interval Linear Programming, Min-Max Regret, Common Agricultural Policy, Arable cropping, Greece
Energy Crop Supply in France: A Min-Max Regret Approach
This paper attempts to estimate energy crop supply using an LP model comprising hundreds of representative farms of the arable cropping sector in France. In order to enhance the predictive ability of such a model and to provide an analytical tool useful to policy makers, interval linear programming (ILP) is used to formalise bounded rationality conditions. In the presence of uncertainty related to yields and prices it is assumed that the farmer minimises the distance from optimality once uncertainty resolves introducing an alternative criterion to the classic profit maximisation rationale. Model validation based on observed activity levels suggests that about 40% of the farms adopt the min-max regret criterion. Then energy crop supply curves, generated by the min-max regret model, are proved to be upward sloped alike classic LP supply curves.interval linear programming, min-max regret, energy crops, France, Crop Production/Industries, Resource /Energy Economics and Policy, C61, D81, Q18,
Minmax regret combinatorial optimization problems: an Algorithmic Perspective
Candia-Vejar, A (reprint author), Univ Talca, Modeling & Ind Management Dept, Curico, Chile.Uncertainty in optimization is not a new ingredient. Diverse models considering uncertainty have been developed over the last 40 years. In our paper we essentially discuss a particular uncertainty model associated with combinatorial optimization problems, developed in the 90's and broadly studied in the past years. This approach named minmax regret (in particular our emphasis is on the robust deviation criteria) is different from the classical approach for handling uncertainty, stochastic approach, where uncertainty is modeled by assumed probability distributions over the space of all possible scenarios and the objective is to find a solution with good probabilistic performance. In the minmax regret (MMR) approach, the set of all possible scenarios is described deterministically, and the search is for a solution that performs reasonably well for all scenarios, i.e., that has the best worst-case performance. In this paper we discuss the computational complexity of some classic combinatorial optimization problems using MMR. approach, analyze the design of several algorithms for these problems, suggest the study of some specific research problems in this attractive area, and also discuss some applications using this model
A decomposition approach to a stochastic model for supply-and-return network design
This paper presents a generic stochastic model for the design of networks comprising both supply and return channels, organized in a closed loop system. Such situations are typical for manufacturing/re-manufacturing type of systems in reverse logistics. The model accounts for a number of alternative scenarios, which may be constructed based on critical levels of design parameters such as demand or returns. We propose a decomposition approach for this model based on the branch and cut procedure known as the integer L-shaped method. Computational results show a consistent performance efficiency of the method for the addressed location problem. The stochastic solutions obtained in a numerical setting generate a significant improvement in terms of average performance over the individual scenario solutions. A solution methodology as presented here can contribute to overcoming notorious challenges of stochastic network design models, such as increased problem sizes and computational difficulty.Decomposition;Location;Remanufacturing;Integer L-shaped;Uncertainty
Adaptive Robust Optimization with Dynamic Uncertainty Sets for Multi-Period Economic Dispatch under Significant Wind
The exceptional benefits of wind power as an environmentally responsible
renewable energy resource have led to an increasing penetration of wind energy
in today's power systems. This trend has started to reshape the paradigms of
power system operations, as dealing with uncertainty caused by the highly
intermittent and uncertain wind power becomes a significant issue. Motivated by
this, we present a new framework using adaptive robust optimization for the
economic dispatch of power systems with high level of wind penetration. In
particular, we propose an adaptive robust optimization model for multi-period
economic dispatch, and introduce the concept of dynamic uncertainty sets and
methods to construct such sets to model temporal and spatial correlations of
uncertainty. We also develop a simulation platform which combines the proposed
robust economic dispatch model with statistical prediction tools in a rolling
horizon framework. We have conducted extensive computational experiments on
this platform using real wind data. The results are promising and demonstrate
the benefits of our approach in terms of cost and reliability over existing
robust optimization models as well as recent look-ahead dispatch models.Comment: Accepted for publication at IEEE Transactions on Power System
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