Search results for "Pareto optimal"
showing 10 items of 50 documents
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…
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…
An Interactive Evolutionary Multiobjective Optimization Method: Interactive WASF-GA
2015
In this paper, we describe an interactive evolutionary algorithm called Interactive WASF-GA to solve multiobjective optimization problems. This algorithm is based on a preference-based evolutionary multiobjective optimization algorithm called WASF-GA. In Interactive WASF-GA, a decision maker (DM) provides preference information at each iteration simple as a reference point consisting of desirable objective function values and the number of solutions to be compared. Using this information, the desired number of solutions are generated to represent the region of interest of the Pareto optimal front associated to the reference point given. Interactive WASF-GA implies a much lower computational…
Decision Making on Pareto Front Approximations with Inherent Nondominance
2011
t Approximating the Pareto fronts of nonlinear multiobjective optimization problems is considered and a property called inherent nondominance is proposed for such approximations. It is shown that an approximation having the above property can be explored by interactively solving a multiobjective optimization problem related to it. This exploration can be performed with available interactive multiobjective optimization methods. The ideas presented are especially useful in solving computationally expensive multiobjective optimization problems with costly function value evaluations. peerReviewed
ANOVA-MOP: ANOVA Decomposition for Multiobjective Optimization
2018
Real-world optimization problems may involve a number of computationally expensive functions with a large number of input variables. Metamodel-based optimization methods can reduce the computational costs of evaluating expensive functions, but this does not reduce the dimension of the search domain nor mitigate the curse of dimensionality effects. The dimension of the search domain can be reduced by functional anova decomposition involving Sobol' sensitivity indices. This approach allows one to rank decision variables according to their impact on the objective function values. On the basis of the sparsity of effects principle, typically only a small number of decision variables significantl…
Treed Gaussian Process Regression for Solving Offline Data-Driven Continuous Multiobjective Optimization Problems
2023
Abstract For offline data-driven multiobjective optimization problems (MOPs), no new data is available during the optimization process. Approximation models (or surrogates) are first built using the provided offline data and an optimizer, e.g. a multiobjective evolutionary algorithm, can then be utilized to find Pareto optimal solutions to the problem with surrogates as objective functions. In contrast to online data-driven MOPs, these surrogates cannot be updated with new data and, hence, the approximation accuracy cannot be improved by considering new data during the optimization process. Gaussian process regression (GPR) models are widely used as surrogates because of their ability to pr…
Potential of interactive multiobjective optimization in supporting the design of a groundwater biodenitrification process
2019
The design of water treatment plants requires simultaneous analysis of technical, economic and environmental aspects, identified by multiple conflicting objectives. We demonstrated the advantages of an interactive multiobjective optimization (MOO) method over a posteriori methods in an unexplored field, namely the design of a biological treatment plant for drinking water production, that tackles the process drawbacks, contrarily to what happens in a traditional volumetric-load-driven design procedure. Specifically, we consider a groundwater denitrification biofilter, simulated by the Activated Sludge Model modified with two-stage denitrification kinetics. Three objectives were defined (nitr…
An Introduction to Multiobjective Optimization
2016
Multiobjective optimization in industry has rapidly grown in importance, as it provides the possibility for a designer or an engineer to consider the problem in hand as a whole. Solution to a multiobjective optimization problem involves several optimal solutions with different trade-offs. As a result upon optimization s(he) can understand the trade-offs between different solutions and subsequently choose the most preferred solution. In this paper, we provide a bird’s eye view of the different methods available in the literature to solve multiobjective optimization problems. Specifically, in literature there exists at least two different research fields i.e. multiple criteria decision making…