The partition problem concerns the partitioning of a given set of n vectors in d-space into p parts to maximize an objective function that is convex on the sum of vectors in each part. The problem has broad expressive power and captures NP-hard problems even if either p or d is fixed. In this article we show that when both p d are fixed, the problem is solvable in strongly polynomial time using...

In PET, usually the data are precorrected for accidental coincidence (AC) events by real-time subtraction of the delayed window coincidences. Randoms subtraction compensates in mean for AC events but destroys the Poisson statistics. Furthermore, for transmission tomography the weighted least-squares (WLS) method leads to systematic biases, especially at low count rates. We propose a new “shifte...

In this paper, we present the use of two evolutionary algorithms to estimate fundamental matrices. We first propose a modification of the Hybrid Taguchi Genetic Algorithm (HTGA) that employs a single objective function, either geometric or algebraic distance, for optimization. We then propose to use a multi-objective optimization algorithm, Intelligent Multi-Objective Evolutionary Algorithm (IM...

Bilevel optimization problems with multivalued objective functions in both levels are first replaced by a problem with a parametric lower level using a convex combination of the lower level objectives. Thus a nonconvex multiobjective bilevel optimization problem arises which is then transformed into a parametric bilevel programming problem. The investigated problem has been considered in the pa...

Creating a musical fitness function is largely subjective and can be critically affected by the designer’s biases. Previous attempts to create such functions for use in genetic algorithms lack scope or are prejudiced to a certain genre of music. They also are limited to producing music strictly in the style determined by the programmer. We show in this paper that musical feature extractors, whi...

Genetic algorithms have particular potential as a tool for optimization when the evaluation function is noisy. Several types of genetic algorithm are compared against a mutation driven stochastic hill-climbing algorithm on a standard set of benchmark functions which have had Gaussian noise added to them. Diierent criteria for judging the eeectiveness of the search are also considered. The genet...

In the paper, the problem of multi-objective (MOBJ) learning is discussed. The problem of obtaining apparent (effective) complexity measure, which is one of the objectives, is considered. For the specific case of RBFN, the bounds on the smoothness-based complexity measure are proposed. As shown in the experimental part, the bounds can be used for Pareto set approximation.

Multi-objective as well as dynamic characteristics appear in many real-world problems. In order to use multi-objective evolutionary optimization algorithms (MOEA) efficiently, a systematic analysis of the algorithms’ behavior in dynamic environments by means of dynamic test functions is necessary. These functions can be classified into problems with changing Pareto sets and/or Pareto fronts wit...

The use of different objective functions in hierarchical aggregation procedures is examined in this paper. Specifically, we analyse the use of the original Intramax objective function, the sum-of-flows objective function, the sum-of-proportions-to-intra-regional-flows objective function, Smart’s weighted interaction index, the first and second CURDS weighted interaction indices, and Tolbert and...

A decision-maker who aims to select the ”best” collection of alternatives from the finite set of available ones might be severely restricted in the design of the selection method. If the representation of valuations of available alternatives is subject to invariance under linear scaling, such as the choice of the unit of measurement, a sensible way to compare choices is to compare weighted sums...