Search results for "optimality"

A New Hybrid Mutation Operator for Multiobjective Optimization with Differential Evolution

2011

Differential evolution has become one of the most widely used evolution- ary algorithms in multiobjective optimization. Its linear mutation operator is a sim- ple and powerful mechanism to generate trial vectors. However, the performance of the mutation operator can be improved by including a nonlinear part. In this pa- per, we propose a new hybrid mutation operator consisting of a polynomial based operator with nonlinear curve tracking capabilities and the differential evolution’s original mutation operator, to be efficiently able to handle various interdependencies between decision variables. The resulting hybrid operator is straightforward to implement and can be used within most evoluti…

PAINT : Pareto front interpolation for nonlinear multiobjective optimization

2011

A method called PAINT is introduced for computationally expensive multiobjective optimization problems. The method interpolates between a given set of Pareto optimal outcomes. The interpolation provided by the PAINT method implies a mixed integer linear surrogate problem for the original problem which can be optimized with any interactive method to make decisions concerning the original problem. When the scalarizations of the interactive method used do not introduce nonlinearity to the problem (which is true e.g., for the synchronous NIMBUS method), the scalarizations of the surrogate problem can be optimized with available mixed integer linear solvers. Thus, the use of the interactive meth…

A Surrogate-assisted Reference Vector Guided Evolutionary Algorithm for Computationally Expensive Many-objective Optimization

2018

We propose a surrogate-assisted reference vector guided evolutionary algorithm for computationally expensive optimization problems with more than three objectives. The proposed algorithm is based on a recently developed evolutionary algorithm for many-objective optimization that relies on a set of adaptive reference vectors for selection. The proposed surrogateassisted evolutionary algorithm uses Kriging to approximate each objective function to reduce the computational cost. In managing the Kriging models, the algorithm focuses on the balance of diversity and convergence by making use of the uncertainty information in the approximated objective values given by the Kriging models, the distr…

Integrating risk management tools for regional forest planning : an interactive multiobjective value at risk approach

2018

In this paper, we present an approach employing multiobjective optimization to support decision making in forest management planning under risk. The primary objectives are biodiversity and timber cash flow, evaluated from two perspectives: the expected value and the value-at-risk (VaR). In addition, the risk level for both the timber cash flow and biodiversity values are included as objectives. With our approach, we highlight the trade-off between the expected value and the VaR, as well as between the VaRs of the two objectives of interest. We employ an interactive method in which a decision maker iteratively provides preference information to find the most preferred management plan and lea…

Flexible Data Driven Inventory Management with Interactive Multiobjective Lot Size Optimization

2021

We study data-driven decision support and formalise a path from data to decision making. We focus on lot sizing in inventory management with stochastic demand and propose an interactive multi-objective optimisation approach. We forecast demand with a Bayesian model, which is based on sales data. After identifying relevant objectives relying on the demand model, we formulate an optimisation problem to determine lot sizes for multiple future time periods. Our approach combines different interactive multi-objective optimisation methods for finding the best balance among the objectives. For that, a decision maker with substance knowledge directs the solution process with one’s preference inform…

On Dealing with Uncertainties from Kriging Models in Offline Data-Driven Evolutionary Multiobjective Optimization

2019

Many works on surrogate-assisted evolutionary multiobjective optimization have been devoted to problems where function evaluations are time-consuming (e.g., based on simulations). In many real-life optimization problems, mathematical or simulation models are not always available and, instead, we only have data from experiments, measurements or sensors. In such cases, optimization is to be performed on surrogate models built on the data available. The main challenge there is to fit an accurate surrogate model and to obtain meaningful solutions. We apply Kriging as a surrogate model and utilize corresponding uncertainty information in different ways during the optimization process. We discuss…

Multiobjective shape design in a ventilation system with a preference-driven surrogate-assisted evolutionary algorithm

2019

We formulate and solve a real-world shape design optimization problem of an air intake ventilation system in a tractor cabin by using a preference-based surrogate-assisted evolutionary multiobjective optimization algorithm. We are motivated by practical applicability and focus on two main challenges faced by practitioners in industry: 1) meaningful formulation of the optimization problem reflecting the needs of a decision maker and 2) finding a desirable solution based on a decision maker’s preferences when solving a problem with computationally expensive function evaluations. For the first challenge, we describe the procedure of modelling a component in the air intake ventilation system wi…

Handling expensive multiobjective optimization problems with evolutionary algorithms

2017

Multiobjective optimization problems (MOPs) with a large number of conflicting objectives are often encountered in industry. Moreover, these problem typically involve expensive evaluations (e.g. time consuming simulations or costly experiments), which pose an extra challenge in solving them. In this thesis, we first present a survey of different methods proposed in the literature to handle MOPs with expensive evaluations. We observed that most of the existing methods cannot be easily applied to problems with more than three objectives. Therefore, we propose a Kriging-assisted reference vector guided evolutionary algorithm (K-RVEA) for problems with at least three expensive objectives. The alg…

Approximation through interpolation in nonconvex multiobjective optimization

2011

Probabilistic Selection Approaches in Decomposition-based Evolutionary Algorithms for Offline Data-Driven Multiobjective Optimization

2022

In offline data-driven multiobjective optimization, no new data is available during the optimization process. Approximation models, also known as surrogates, are built using the provided offline data. A multiobjective evolutionary algorithm can be utilized to find solutions by using these surrogates. The accuracy of the approximated solutions depends on the surrogates and approximations typically involve uncertainties. In this paper, we propose probabilistic selection approaches that utilize the uncertainty information of the Kriging models (as surrogates) to improve the solution process in offline data-driven multiobjective optimization. These approaches are designed for decomposition-base…