Search results for "Robust optimization"

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…

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 …

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.

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…

Dynamic Portfolio Optimization with Stochastic Programming

2010

Constrained Robust MultiObjective Optimization for Reactive Design in Distribution Systems

2006

This paper presents a new formulation including robustness of solution of constrained multiobjective design or reactive power compensation. The algorithm used for optimization is the NSGA-II (Non dominated Sorting Genetic Algorithm II) with a special crowded comparison operator for constraints handling. The need for including the issue of robustness of solutions derives from the simple observation that loads are uncertain in distribution systems and their estimation is often affected by errors. In design problems it is desirable to consider the loads with a certain range of variation. In this paper the NSGA-II algorithm is applied to efficiently solve the issue and the solutions attained co…

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…

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.

A fuzzy programming method for optimization of autonomous logistics objects

2013

Recently several studies have explored the realization of autonomous control in production and logistic operations. In doing so, it has been tried to transmit the merit of decision-making from central controllers with offline decisions to decentralized controllers with local and real-time decision makings. However, this mission has still some drawbacks in practice. Lack of global optimization is one of them, i.e., the lost chain between the autonomous decentralized decisions at operational level and the centralized mathematical optimization with offline manner at tactical and strategic levels. This distinction can be reasonably solved by considering fuzzy parameters in mathematical programm…