Search results for " Optimality"
showing 10 items of 46 documents
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…
Scope Oriented Thermoeconomic analysis of energy systems. Part II: Formation Structure of Optimality for robust design
2010
This paper represents the Part II of a paper in two parts. In Part I the fundamentals of Scope Oriented Thermoeconomics have been introduced, showing a scarce potential for the cost accounting of existing plants; in this Part II the same concepts are applied to the optimization of a small set of design variables for a vapour compression chiller. The method overcomes the limit of most conventional optimization techniques, which are usually based on hermetic algorithms not enabling the energy analyst to recognize all the margins for improvement. The Scope Oriented Thermoeconomic optimization allows us to disassemble the optimization process, thus recognizing the Formation Structure of Optimal…
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…
NAUTILUS framework : towards trade-off-free interaction in multiobjective optimization
2016
In this paper, we present a framework of different interactive NAUTILUS methods for multiobjective optimization. In interactive methods, the decision maker iteratively sees solution alternatives and provides one’s preferences in order to find the most preferred solution. We question the widely used setting that the solutions shown to the decision maker should all be Pareto optimal which implies that improvement in any objective function necessitates allowing impairment in some others. Instead, in NAUTILUS we enable the decision maker to make a free search without having to trade-off by starting from an inferior solution and iteratively approaching the Pareto optimal set by allowing all obje…
An integrated multiobjective design tool for process design
2006
An integrated multiobjective design tool has been developed for chemical process design. This tool combines the rigorous process calculations of the BALAS process simulator and the interactive multiobjective optimization method NIMBUS. With this design tool, the designer can consider several conflicting performance criteria simultaneously. The interactive nature of this tool allows the designer to learn about the behavior of the problem. To illustrate the possibilities of this design tool, two case studies are considered. One of them is related to paper making while the other one is related to power plants.
A solution process for simulation-based multiobjective design optimization with an application in the paper industry
2014
In this paper, we address some computational challenges arising in complex simulation-based design optimization problems. High computational cost, black-box formulation and stochasticity are some of the challenges related to optimization of design problems involving the simulation of complex mathematical models. Solving becomes even more challenging in case of multiple conflicting objectives that must be optimized simultaneously. In such cases, application of multiobjective optimization methods is necessary in order to gain an understanding of which design offers the best possible trade-off. We apply a three-stage solution process to meet the challenges mentioned above. As our case study, w…
Simultaneous optimization of harvest schedule and data quality
2015
In many recent studies, the value of forest inventory information in harvest scheduling has been examined. In a previous paper, we demonstrated that making measurement decisions for stands for which the harvest decision is uncertain simultaneously with the harvest decisions may be highly profitable. In that study, the quality of additional measurements was not a decision variable, and the only options were between making no measurements or measuring perfect information. In this study, we introduce data quality into the decision problem, i.e., the decisionmaker can select between making imperfect or perfect measurements. The imperfect information is obtained with a specific scenario tree fo…