Search results for "Multiobjective optimization problem"
showing 10 items of 20 documents
SSPMO: A Scatter Tabu Search Procedure for Non-Linear Multiobjective Optimization
2007
We describe the development and testing of a metaheuristic procedure, based on the scatter-search methodology, for the problem of approximating the efficient frontier of nonlinear multiobjective optimization problems with continuous variables. Recent applications of scatter search have shown its merit as a global optimization technique for single-objective problems. However, the application of scatter search to multiobjective optimization problems has not been fully explored in the literature. We test the proposed procedure on a suite of problems that have been used extensively in multiobjective optimization. Additional tests are performed on instances that are an extension of those consid…
Optimistic NAUTILUS navigator for multiobjective optimization with costly function evaluations
2022
AbstractWe introduce novel concepts to solve multiobjective optimization problems involving (computationally) expensive function evaluations and propose a new interactive method called O-NAUTILUS. It combines ideas of trade-off free search and navigation (where a decision maker sees changes in objective function values in real time) and extends the NAUTILUS Navigator method to surrogate-assisted optimization. Importantly, it utilizes uncertainty quantification from surrogate models like Kriging or properties like Lipschitz continuity to approximate a so-called optimistic Pareto optimal set. This enables the decision maker to search in unexplored parts of the Pareto optimal set and requires …
Solving multiobjective optimization problems with decision uncertainty: an interactive approach
2018
We propose an interactive approach to support a decision maker to find a most preferred robust solution to multiobjective optimization problems with decision uncertainty. A new robustness measure that is understandable for the decision maker is incorporated as an additional objective in the problem formulation. The proposed interactive approach utilizes elements of the synchronous NIMBUS method and is aimed at supporting the decision maker to consider the objective function values and the robustness of a solution simultaneously. In the interactive approach, we offer different alternatives for the decision maker to express her/his preferences related to the robustness of a solution. To conso…
Assessing the Performance of Interactive Multiobjective Optimization Methods
2021
Interactive methods are useful decision-making tools for multiobjective optimization problems, because they allow a decision-maker to provide her/his preference information iteratively in a comfortable way at the same time as (s)he learns about all different aspects of the problem. A wide variety of interactive methods is nowadays available, and they differ from each other in both technical aspects and type of preference information employed. Therefore, assessing the performance of interactive methods can help users to choose the most appropriate one for a given problem. This is a challenging task, which has been tackled from different perspectives in the published literature. We present a …
Constructing a Pareto front approximation for decision making
2011
An approach to constructing a Pareto front approximation to computationally expensive multiobjective optimization problems is developed. The approximation is constructed as a sub-complex of a Delaunay triangulation of a finite set of Pareto optimal outcomes to the problem. The approach is based on the concept of inherent nondominance. Rules for checking the inherent nondominance of complexes are developed and applying the rules is demonstrated with examples. The quality of the approximation is quantified with error estimates. Due to its properties, the Pareto front approximation works as a surrogate to the original problem for decision making with interactive methods. Qc 20120127
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…
A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods
2015
Computationally expensive multiobjective optimization problems arise, e.g. in many engineering applications, where several conflicting objectives are to be optimized simultaneously while satisfying constraints. In many cases, the lack of explicit mathematical formulas of the objectives and constraints may necessitate conducting computationally expensive and time-consuming experiments and/or simulations. As another challenge, these problems may have either convex or nonconvex or even disconnected Pareto frontier consisting of Pareto optimal solutions. Because of the existence of many such solutions, typically, a decision maker is required to select the most preferred one. In order to deal wi…
No-Preference Methods
1998
In no-preference methods, where the opinions of the decision maker are not taken into consideration, the multiobjective optimization problem is solved using some relatively simple method and the solution obtained is presented to the decision maker. The decision maker may either accept or reject the solution. It seems quite unlikely that the solution best satisfying the decision maker could be found with these methods. That is why no-preference methods are suitable for situations where the decision maker does not have any special expectations of the solution and (s)he is satisfied simply with some optimal solution. The working order here is: 1) analyst, 2) none.
A Priori Methods
1998
In the case of a priori methods, the decision maker must specify her or his preferences, hopes and opinions before the solution process. The difficulty is that the decision maker does not necessarily know beforehand what it is possible to attain in the problem and how realistic her or his expectations are. The working order in these methods is: 1) decision maker, 2) analyst.
Interactive Method NIMBUS for Nondifferentiable Multiobjective Optimization Problems
1997
An interactive method, NIMBUS, for nondifferentiable multiobjective optimization problems is introduced. The method is capable of handling several nonconvex locally Lipschitzian objective functions subject to nonlinear (possibly nondifferentiable) constraints. The idea of NIMBUS is that the decision maker can easily indicate what kind of improvements are desired and what kind of impairments are tolerable at the point considered. The decision maker is asked to classify the objective functions into five different classes: those to be improved, those to be improved down to some aspiration level, those to be accepted as they are, those to be impaired till some upper bound, and those allowed to …