Search results for "tavoite"
showing 10 items of 143 documents
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 …
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 …
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…
A Visualizable Test Problem Generator for Many-Objective Optimization
2022
Visualizing the search behavior of a series of points or populations in their native domain is critical in understanding biases and attractors in an optimization process. Distancebased many-objective optimization test problems have been developed to facilitate visualization of search behavior in a two-dimensional design space with arbitrarily many objective functions. Previous works have proposed a few commonly seen problem characteristics into this problem framework, such as the definition of disconnected Pareto sets and dominance resistant regions of the design space. The authors’ previous work has advanced this research further by providing a problem generator to automatically create use…
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
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…
Demonstrating the Applicability of PAINT to Computationally Expensive Real-life Multiobjective Optimization
2011
We demonstrate the applicability of a new PAINT method to speed up iterations of interactive methods in multiobjective optimization. As our test case, we solve a computationally expensive non-linear, five-objective problem of designing and operating a wastewater treatment plant. The PAINT method interpolates between a given set of Pareto optimal outcomes and constructs a computationally inexpensive mixed integer linear surrogate problem for the original problem. We develop an IND-NIMBUS R PAINT module to combine the interactive NIMBUS method and the PAINT method and to find a preferred solution to the original problem. With the PAINT method, the solution process with the NIMBUS method take …
Interactive Multiobjective Optimization in Lot Sizing with Safety Stock and Safety Lead Time
2021
In this paper, we integrate a lot sizing problem with the problem of determining optimal values of safety stock and safety lead time. We propose a probability of product availability formula to assess the quality of safety lead time and a multiobjective optimization model as an integrated lot sizing problem. In the proposed model, we optimize six objectives simultaneously: minimizing purchasing cost, ordering cost, holding cost and, at the same time, maximizing cycle service level, probability of product availability and inventory turnover. To present the applicability of the proposed model, we consider a real case study with data from a manufacturing company and apply the interactive NAUTI…
A Computationally Inexpensive Approach in Multiobjective Heat Exchanger Network Synthesis
2010
We consider a heat exchanger network synthesis problem formulated as a multiobjective optimization problem. The Pareto front of this problem is approximated with a new approximation approach and the preferred point on the approximation is found with the interactive multiobjective optimization method NIMBUS. Using the approximation makes the solution process computationally inexpensive. Finally, the preferred outcome on the Pareto front approximation is projected on the actual Pareto front. 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…