Search results for "Robust optimization"
showing 10 items of 12 documents
LR-NIMBUS : an interactive algorithm for uncertain multiobjective optimization with lightly robust efficient solutions
2022
In this paper, we develop an interactive algorithm to support a decision maker to find a most preferred lightly robust efficient solution when solving uncertain multiobjective optimization problems. It extends the interactive NIMBUS method. The main idea underlying the designed algorithm, called LR-NIMBUS, is to ask the decision maker for a most acceptable (typical) scenario, find an efficient solution for this scenario satisfying the decision maker, and then apply the derived efficient solution to generate a lightly robust efficient solution. The preferences of the decision maker are incorporated through classifying the objective functions. A lightly robust efficient solution is generated …
EABOT – Energetic analysis as a basis for robust optimization of trigeneration systems by linear programming
2008
Abstract The optimization of synthesis, design and operation in trigeneration systems for building applications is a quite complex task, due to the high number of decision variables, the presence of irregular heat, cooling and electric load profiles and the variable electricity price. Consequently, computer-aided techniques are usually adopted to achieve the optimal solution, based either on iterative techniques, linear or non-linear programming or evolutionary search. Large efforts have been made in improving algorithm efficiency, which have resulted in an increasingly rapid convergence to the optimal solution and in reduced calculation time; robust algorithm have also been formulated, ass…
Robust Energy Scheduling in Vehicle-to-Grid Networks
2017
The uncertainties brought by intermittent renewable generation and uncoordinated charging behaviors of EVs pose great challenges to the reliable operation of power systems, which motivates us to explore the integration of robust optimization with energy scheduling in V2G networks. In this article, we first introduce V2G robust energy scheduling problems and review the stateof- the art contributions from the perspectives of renewable energy integration, ancillary service provision, and proactive demand-side participation in the electricity market. Second, for each category of V2G applications, the corresponding problem formulations, robust solution concepts, and design approaches are describ…
Robust optimality of linear saturated control in uncertain linear network flows
2008
We propose a novel approach that, given a linear saturated feedback control policy, asks for the objective function that makes robust optimal such a policy. The approach is specialized to a linear network flow system with unknown but bounded demand and politopic bounds on controlled flows. All results are derived via the Hamilton-Jacobi-Isaacs and viscosity theory.
Interactive Multiobjective Robust Optimization with NIMBUS
2018
In this paper, we introduce the MuRO-NIMBUS method for solving multiobjective optimization problems with uncertain parameters. The concept of set-based minmax robust Pareto optimality is utilized to tackle the uncertainty in the problems. We separate the solution process into two stages: the pre-decision making stage and the decision making stage. We consider the decision maker’s preferences in the nominal case, i.e., with the most typical or undisturbed values of the uncertain parameters. At the same time, the decision maker is informed about the objective function values in the worst case to support her/him to make an informed decision. To help the decision maker to understand the behavio…
Multi-scenario multi-objective robust optimization under deep uncertainty: A posteriori approach
2021
This paper proposes a novel optimization approach for multi-scenario multi-objective robust decision making, as well as an alternative way for scenario discovery and identifying vulnerable scenarios even before any solution generation. To demonstrate and test the novel approach, we use the classic shallow lake problem. We compare the results obtained with the novel approach to those obtained with previously used approaches. We show that the novel approach guarantees the feasibility and robust efficiency of the produced solutions under all selected scenarios, while decreasing computation cost, addresses the scenario-dependency issues, and enables the decision-makers to explore the trade-off …
The price of multiobjective robustness : Analyzing solution sets to uncertain multiobjective problems
2021
Defining and finding robust efficient solutions to uncertain multiobjective optimization problems has been an issue of growing interest recently. Different concepts have been published defining what a “robust efficient” solution is. Each of these concepts leads to a different set of solutions, but it is difficult to visualize and understand the differences between these sets. In this paper we develop an approach for comparing such sets of robust efficient solutions, namely we analyze their outcomes under the nominal scenario and in the worst case using the upper set-less order from set-valued optimization. Analyzing the set of nominal efficient solutions, the set of minmax robust efficient …
Optimization under Uncertainty and Linear Semi-Infinite Programming: A Survey
2001
This paper deals with the relationship between semi-infinite linear programming and decision making under uncertainty in imprecise environments. Actually, we have reviewed several set-inclusive constrained models and some fuzzy programming problems in order to see if they can be solved by means of a linear semi-infinite program. Finally, we present some numerical examples obtained by using a primal semi-infinite programming method.
Decision making in multiobjective optimization problems under uncertainty: balancing between robustness and quality
2018
As an emerging research field, multiobjective robust optimization employs minmax robustness as the most commonly used concept. Light robustness is a concept in which a parameter, tolerable degradations, can be used to control the loss in the objective function values in the most typical scenario for gaining in robustness. In this paper, we develop a lightly robust interactive multiobjective optimization method, LiRoMo, to support a decision maker to find a most preferred lightly robust efficient solution with a good balance between robustness and the objective function values in the most typical scenario. In LiRoMo, we formulate a lightly robust subproblem utilizing an achievement scalarizi…