Robust optimization for interactive multiobjective programming with imprecise information applied to R&D project portfolio selection

A multiobjective binary integer programming model for R&D project portfolio selection with competing objectives is developed when problem coefficients in both objective functions and constraints are uncertain. Robust optimization is used in dealing with uncertainty while an interactive procedure is used in making tradeoffs among the multiple objectives. Robust nondominated solutions are generated by solving the linearized counterpart of the robust augmented weighted Tchebycheff programs. A decision maker’s most preferred solution is identified in the interactive robust weighted Tchebycheff procedure by progressively eliciting and incorporating the decision maker’s preference information into the solution process. An example is presented to illustrate the solution approach and performance. The developed approach can also be applied to general multiobjective mixed integer programming problems

A critical review of the approaches to optimization problems under uncertainty

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Science of Bilkent University, 2001.Thesis (Master's) -- Bilkent University, 2001.Includes bibliographical references leaves 58-72.In this study, the issue of uncertainty in optimization problems is studied. First of all, the meaning and sources of uncertainty are explained and then possible ways of its representation are analyzed. About the modelling process, different approaches as sensitivity analysis, parametric programming, robust optimization, stochastic programming, fuzzy programming, multiobjective programming and imprecise optimization are presented with advantages and disadvantages from different perspectives. Some extensions of the concepts of imprecise optimization are also presented.Gürtuna, FilizM.S

A comprehensive approach to electricity investment planning for multiple objectives and uncertainty

Includes abstract.Includes bibliographical references.Appropriate Energy-Environment-Economic (E3) modelling provides key information for policy makers in the Electricity Supply Industry (ESI) faced with navigating a sustainable development path. Key challenges include engaging with stakeholder values and preferences, and exploring trade-offs between competing objectives in the face of underlying uncertainty. As such, a comprehensive framework is needed that integrates multiple objectives and uncertainty into a transparent methodology that policy makers and planners can use to analyse and plan for investment in the ESI, in a way which shapes decision outcomes, and enables confident choices to be made. This thesis is aimed at developing such a framework. As a case study the South African ESI was represented using a partial equilibrium (Energy-Economic-Environment) E3 modelling approach. This approach was extended to include multiple objectives under selected future uncertainties. This extension was achieved by assigning cost penalties (PGPs – Pareto Generation Parameters) to non-cost attributes to force the model’s least-cost objective function to better satisfy non-cost criteria. It was shown that using PGPs is an efficient method for extending the analysis to multiple objectives as the solutions generated are non-dominated and are generated from ranges of performances in the various criteria rather than from arbitrarily forcing the selection of particular technologies. Extensive sections of the non-dominated solution space can be generated and later screened to allow further, more detailed exploration of areas of the solution space. Aspects of flexibility to demand growth uncertainty were incorporated into each future expansion alternative (FEA) by introducing stochastic programming with recourse into the model. Technology lead times were taken into account by the inclusion of a decision node along the time horizon where aspects of real options theory were considered within the planning process by splitting power station investments into their Owner’s Development Cost (ODC) and Equipment and Procurement Cost (EPC) components. Hedging in the recourse programming was automatically translated from being purely financial, to include the other attributes that the cost penalties represented. The hedged solutions improved on the naïve solutions under the multiple criteria considered as well as better satisfying the non-cost objectives relative to the base case (least cost solution). From a retrospective analysis of the cost penalties, the correct market signals could be derived to meet policy goal, with due regard to demand uncertainty