Search results for "optimality"
showing 10 items of 60 documents
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…
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…
Balanced Asymmetrical Nearly Orthogonal Designs for first and second order effect estimation
2006
Abstract A method for constructing asymmetrical (mixed-level) designs, satisfying the balancing and interaction estimability requirements with a number of runs as small as possible, is proposed in this paper. The method, based on a heuristic procedure, uses a new optimality criterion formulated here. The proposed method demonstrates efficiency in terms of searching time and optimality of the attained designs. A complete collection of such asymmetrical designs with two- and three-level factors is available. A technological application is also presented.
Controlled polyhedral sweeping processes: existence, stability, and optimality conditions
2021
This paper is mainly devoted to the study of controlled sweeping processes with polyhedral moving sets in Hilbert spaces. Based on a detailed analysis of truncated Hausdorff distances between moving polyhedra, we derive new existence and uniqueness theorems for sweeping trajectories corresponding to various classes of control functions acting in moving sets. Then we establish quantitative stability results, which provide efficient estimates on the sweeping trajectory dependence on controls and initial values. Our final topic, accomplished in finite-dimensional state spaces, is deriving new necessary optimality and suboptimality conditions for sweeping control systems with endpoint constrain…
An overview of semi-infinite programming theory and related topics through a generalization of the alternative theorems
1984
We propose new alternative theorems for convex infinite systems which constitute the generalization of the corresponding toGale, Farkas, Gordan andMotzkin. By means of these powerful results we establish new approaches to the Theory of Infinite Linear Inequality Systems, Perfect Duality, Semi-infinite Games and Optimality Theory for non-differentiable convex Semi-Infinite Programming Problem.
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…
Ergativity and Differential Case Marking
2017
Abstract The present chapter discusses patterns of differential case marking in ergative languages, focusing on differential subject marking, which is more prominent in ergative languages (in contrast to accusative languages, where differential object marking is more prominent). It is argued that patterns of (differential) case marking can be accounted two general constraints related to (role)-indexing, on the one hand, and distinguishability (or markedness) on the other hand. This approach correctly predicts asymmetries between differential object marking (DOM) and differential subject marking (DSM) with regard to animacy, definiteness, as well as discourse features. I also show how this a…
Why Use Interactive Multi-Objective Optimization in Chemical Process Design?
2008
Problems in chemical engineering, like most real-world optimization problems, typically, have several conflicting performance criteria or objectives and they often are computationally demanding, which sets special requirements on the optimization methods used. In this chapter, we point out some shortcomings of some widely used basic methods of multi-objective optimization. As an alternative, we suggest using interactive approaches where the role of a decision maker or a designer is emphasized. Interactive multi-objective optimization has been shown to suit well for chemical process design problems because it takes the preferences of the decision maker into account in an iterative manner tha…
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…