Search results for "Pareto"

PAINT–SiCon: constructing consistent parametric representations of Pareto sets in nonconvex multiobjective optimization

2014

We introduce a novel approximation method for multiobjective optimization problems called PAINT–SiCon. The method can construct consistent parametric representations of Pareto sets, especially for nonconvex problems, by interpolating between nondominated solutions of a given sampling both in the decision and objective space. The proposed method is especially advantageous in computationally expensive cases, since the parametric representation of the Pareto set can be used as an inexpensive surrogate for the original problem during the decision making process. peerReviewed

A new preference handling technique for interactive multiobjective optimization without trading-off

2015

Because the purpose of multiobjective optimization methods is to optimize conflicting objectives simultaneously, they mainly focus on Pareto optimal solutions, where improvement with respect to some objective is only possible by allowing some other objective(s) to impair. Bringing this idea into practice requires the decision maker to think in terms of trading-off, which may limit the ability of effective problem solving. We outline some drawbacks of this and exploit another idea emphasizing the possibility of simultaneous improvement of all objectives. Based on this idea, we propose a technique for handling decision maker’s preferences, which eliminates the necessity to think in terms of t…

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…

Applying the approximation method PAINT and the interactive method NIMBUS to the multiobjective optimization of operating a wastewater treatment plant

2014

Using an interactive multiobjective optimization method called NIMBUS and an approximation method called PAINT, preferable solutions to a five-objective problem of operating a wastewater treatment plant are found. The decision maker giving preference information is an expert in wastewater treatment plant design at the engineering company Pöyry Finland Ltd. The wastewater treatment problem is computationally expensive and requires running a simulator to evaluate the values of the objective functions. This often leads to problems with interactive methods as the decision maker may get frustrated while waiting for new solutions to be computed. Thus, a newly developed PAINT method is used to spe…

A NEW PROGRESSIVE DESIGN METHODOLOGY FOR COMPLEX SHEET METAL STAMPING OPERATIONS: COUPLING SPATIALLY DIFFERENTIATED RESTRAINING FORCES APPROACH AND M…

2010

The growing interest in sheet metal stamping processes, particularly in the automotive industry has led to three main issues in this field:*request of very complex shapes; *growing interest in springback control; *solution of multi-objective problems. These issues make a sheet metal stamping processes design very difficult and proper design methodologies to reduce times and costs are highly required. In this paper, a computer aided approach aiming to satisfy the mentioned issues is proposed. In particular, a progressive design approach based on the integration between numerical simulations, Response Surface Methodology (RSM) and Pareto optimal solutions search techniques was applied in orde…

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 …

2021

One of the problems that hinder emergency in developing countries is the problem of monitoring a number of activities on inter-urban roadway networks. In the literature, the use of control points is proposed in the context of these countries in order to ensure efficient monitoring, by ensuring a good coverage while minimizing the installation costs as well as the number of accidents across these road networks. In this work, we propose an optimal deployment of these control points from several optimization methods based on some evolutionary multi-objective algorithms: the non-dominated sorting genetic algorithm-II (NSGA-II); the multi-objective particle swarm optimization (MOPSO); the streng…

Experiments with classification-based scalarizing functions in interactive multiobjective optimization

2006

In multiobjective optimization methods, the multiple conflicting objectives are typically converted into a single objective optimization problem with the help of scalarizing functions and such functions may be constructed in many ways. We compare both theoretically and numerically the performance of three classification-based scalarizing functions and pay attention to how well they obey the classification information. In particular, we devote special interest to the differences the scalarizing functions have in the computational cost of guaranteeing Pareto optimality. It turns out that scalarizing functions with or without so-called augmentation terms have significant differences in this re…

Interactive Nonconvex Pareto Navigator for Multiobjective Optimization

2019

Abstract We introduce a new interactive multiobjective optimization method operating in the objective space called Nonconvex Pareto Navigator . It extends the Pareto Navigator method for nonconvex problems. An approximation of the Pareto optimal front in the objective space is first generated with the PAINT method using a relatively small set of Pareto optimal outcomes that is assumed to be given or computed prior to the interaction with the decision maker. The decision maker can then navigate on the approximation and direct the search for interesting regions in the objective space. In this way, the decision maker can conveniently learn about the interdependencies between the conflicting ob…

Improving Computing Systems Automatic Multiobjective Optimization Through Meta-Optimization

2016

This paper presents the extension of framework for automatic design space exploration (FADSE) tool using a meta-optimization approach, which is used to improve the performance of design space exploration algorithms, by driving two different multiobjective meta-heuristics concurrently. More precisely, we selected two genetic multiobjective algorithms: 1) non-dominated sorting genetic algorithm-II and 2) strength Pareto evolutionary algorithm 2, that work together in order to improve both the solutions’ quality and the convergence speed. With the proposed improvements, we ran FADSE in order to optimize the hardware parameters’ values of the grid ALU processor (GAP) micro-architecture from a b…