Though optimization problems in industrial electromagnetic design are often truly multiobjective, solving them by evolutionary Pareto Optimal Front approximation is often unpractical, due to the high computational cost of objective evaluations. In order to overcome this drawback, an extension of classical single-objective Generalized Response Surface (GRS) methods to Pareto-optimal front approx...

Mainstream surrogate approaches for multi-objective problems build one approximation for each objective. Mono-surrogate approaches instead aim at characterizing the Pareto front with a single model. Such an approach has been recently introduced using a mixture of regression Support Vector Machine (SVM) to clamp the current Pareto front to a single value, and one-class SVM to ensure that all dom...

The mold region of the continuous caster, the most widely used casting device used by the steel industry has been modeled through a combination of a steady-state heat transfer approach and a recently developed pareto-converging genetic algorithm (PCGA). Due to highly non-linear nature of the objective functions, as well as the constraints, locating the pareto-front was quite a challenging job i...

The conventional weighted aggregation method is extended to realize multi-objective optimization. The basic idea is that systematically changing the weights during evolution will lead the population to the Pareto front. Two possible methods are investigated. One method is to assign a uniformly distributed random weight to each individual in the population in each generation. The other method is...

This paper discusses the application of evolutionary multi-objective optimization algorithms namely Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and Modified NSGA-II (MNSGA-II) for solving the Combined Economic Emission Dispatch (CEED) problem with valvepoint loading. The valve-point loading introduce ripples in the input-output characteristics of generating units and make the CEED prob...

We compare two multiobjective evolutionary algorithms, with deterministic gradient based optimization methods for the dose optimization problem in high-dose rate (HDR) brachytherapy. The optimization considers up to 300 parameters. The objectives are expressed in terms of statistical parameters, from dose distributions. These parameters are approximated from dose values from a small number of p...

This paper presents an approach to incorporate Pareto dominance into the differential evolution (DE) algorithm in order to solve optimization problems with more than one objective by using the DE algorithm. Unlike the existing proposals to extend the DE to solve multiobjective optimization problems, our algorithm uses an external archive to store nondominated solutions. In order to generate tri...

This paper presents a Multi-objective Evolutionary Algorithm (MOEA) to derive a set of optimal operation policies for a multipurpose reservoir system. One of the main goals in multiobjective optimization is to find a set of well distributed optimal solutions along the Pareto front. Classical optimization methods often fail in attaining a good Pareto front. To overcome the drawbacks faced by the...

The inverted generational distance (IGD) is a metric for assessing the quality of approximations to the Pareto front obtained by multi-objective optimization algorithms. The IGD has become the most commonly used metric in the context of many-objective problems, i.e., those with more than three objectives. The averaged Hausdorff distance and IGD are variants of the IGD proposed in order to overc...

The hypervolume indicator is widely used to guide the search and to evaluate the performance of evolutionary multi-objective optimization algorithms. It measures the volume of the dominated portion of the objective space which is considered to give a good approximation of the Pareto front. There is surprisingly little theoretically known about the quality of this approximation. We examine the m...