Applications of Discrepancy Theory in Multiobjective Approximation

We apply a multi-color extension of the Beck-Fiala theorem to show that the multiobjective maximum traveling salesman problem is randomized 1/2-approximable on directed graphs and randomized 2/3-approximable on undirected graphs. Using the same technique we show that the multiobjective maximum satisfiablilty problem is 1/2-approximable

Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information

Several contributions to the hydrological literature have brought into question the continued usefulness of the classical paradigm for hydrologic model calibration. With the growing popularity of sophisticated 'physically based' watershed models (e.g., landsurface hydrology and hydrochemical models) the complexity of the calibration problem has been multiplied many fold. We disagree with the seemingly widespread conviction that the model calibration problem will simply disappear with the availability of more and better field measurements. This paper suggests that the emergence of a new and more powerful model calibration paradigm must include recognition of the inherent multiobjective nature of the problem and must explicitly recognize the role of model error. The results of our preliminary studies are presented. Through an illustrative case study we show that the multiobjective approach is not only practical and relatively simple to implement but can also provide useful information about the limitations of a model

Meta-heuristic algorithms in car engine design: a literature survey

Meta-heuristic algorithms are often inspired by natural phenomena, including the evolution of species in Darwinian natural selection theory, ant behaviors in biology, flock behaviors of some birds, and annealing in metallurgy. Due to their great potential in solving difficult optimization problems, meta-heuristic algorithms have found their way into automobile engine design. There are different optimization problems arising in different areas of car engine management including calibration, control system, fault diagnosis, and modeling. In this paper we review the state-of-the-art applications of different meta-heuristic algorithms in engine management systems. The review covers a wide range of research, including the application of meta-heuristic algorithms in engine calibration, optimizing engine control systems, engine fault diagnosis, and optimizing different parts of engines and modeling. The meta-heuristic algorithms reviewed in this paper include evolutionary algorithms, evolution strategy, evolutionary programming, genetic programming, differential evolution, estimation of distribution algorithm, ant colony optimization, particle swarm optimization, memetic algorithms, and artificial immune system

Affine arithmetic-based methodology for energy hub operation-scheduling in the presence of data uncertainty

In this study, the role of self-validated computing for solving the energy hub-scheduling problem in the presence of multiple and heterogeneous sources of data uncertainties is explored and a new solution paradigm based on affine arithmetic is conceptualised. The benefits deriving from the application of this methodology are analysed in details, and several numerical results are presented and discussed

SF-SFD: Stochastic Optimization of Fourier Coefficients to Generate Space-Filling Designs

Due to the curse of dimensionality, it is often prohibitively expensive to generate deterministic space-filling designs. On the other hand, when using na{\"i}ve uniform random sampling to generate designs cheaply, design points tend to concentrate in a small region of the design space. Although, it is preferable in these cases to utilize quasi-random techniques such as Sobol sequences and Latin hypercube designs over uniform random sampling in many settings, these methods have their own caveats especially in high-dimensional spaces. In this paper, we propose a technique that addresses the fundamental issue of measure concentration by updating high-dimensional distribution functions to produce better space-filling designs. Then, we show that our technique can outperform Latin hypercube sampling and Sobol sequences by the discrepancy metric while generating moderately-sized space-filling samples for high-dimensional problems

The Kalai-Smorodinski solution for many-objective Bayesian optimization

An ongoing aim of research in multiobjective Bayesian optimization is to extend its applicability to a large number of objectives. While coping with a limited budget of evaluations, recovering the set of optimal compromise solutions generally requires numerous observations and is less interpretable since this set tends to grow larger with the number of objectives. We thus propose to focus on a specific solution originating from game theory, the Kalai-Smorodinsky solution, which possesses attractive properties. In particular, it ensures equal marginal gains over all objectives. We further make it insensitive to a monotonic transformation of the objectives by considering the objectives in the copula space. A novel tailored algorithm is proposed to search for the solution, in the form of a Bayesian optimization algorithm: sequential sampling decisions are made based on acquisition functions that derive from an instrumental Gaussian process prior. Our approach is tested on four problems with respectively four, six, eight, and nine objectives. The method is available in the Rpackage GPGame available on CRAN at https://cran.r-project.org/package=GPGame