Ranking-Dominance Relation for (Evolutionary) Multi-Objective Optimization

An alternative relation to Pareto-dominance relation is proposed. The new relation is based on ranking a set of solutions according to each separate objective and an aggregation function to calculate a scalar fitness value for each solution. The relation is called as ranking-dominance and it tries to tackle the curse of dimensionality commonly observedin evolutionary multi-objective optimization. Ranking-dominance can beused to sort a set of solutions even for a large number of objectives when Pareto-dominance relation cannot distinguish solutions from one another anymore. This permits search to advance even with a large number of objectives. It is also shown that ranking-dominance does not violate Pareto-dominance. Results indicate that selection based on ranking-dominance is able to advance search towards the Pareto-front in some cases, where selection based on Pareto-dominance stagnates. However, in some cases it is also possible that search does not proceed into direction of Pareto-front because the ranking-dominance relation permits deterioration of individual objectives. Results also show that when the number of objectives increases, selection based on just Pareto-dominance without diversity maintenance is able to advance search better than with diversity maintenance. Therefore, diversity maintenance is connive at the curse of dimensionality.

Objective Evaluation of Nasal Dimensions in Children with Acoustic Rhinometry

Aims: This study was carried out to investigate the usefulness of acoustic rhinometry in the evaluation of intranasal dimensions in children. The aim was to define reference values for school children. In addition, the role of the VAS scale in the subjective evaluation of nasal obstruction in children was studied. Materials and methods: Measurements were done with Acoustic Rhinometry A1. The values of special interest were the minimal cross-sectional area (MCA) and the anterior volume of the nose (VOL). The data for reference values included 124 voluntary school children with no permanent nasal symptoms, aged between 7 and 14 years. Data were collected at baseline and after decongestion of the nose; the VAS scale was filled in before measurements. The subjects in the follow-up study (n=74, age between 1 and 12 years) were receiving intranasal spray of insulin or placebo. The nasal symptoms were recorded and acoustic rhinometry was measured at each control visit. Results: In school children, the mean total MCA was 0.752 cm2 (SD 0.165), and the mean total VOL was 4.00 cm3 (SD 0.63) at baseline. After decongestion, a significant increase in the mean TMCA and in the mean TVOL was found. A correlation was found between TMCA and age, and between TVOL and height of a child. There was no difference between boys and girls. A correlation was found between unilateral acoustic values and VAS at baseline, but not after decongestion. No difference wasfound in acoustic values or symptoms between the insulin and placebo group in the follow-up study of two years. Conclusions: Acoustic rhinometry is a suitable objective method to examine intranasal dimensions in children. It is easy to perform and well tolerated. Reference values for children between 7 and 14 years were established.

Generalized Differential Evolution for Global Multi-Objective Optimization with Constraints

The objective of this thesis work is to develop and study the Differential Evolution Algorithm for multi-objective optimization with constraints. Differential Evolution is an evolutionary algorithm that has gained in popularity because of its simplicity and good observed performance. Multi-objective evolutionary algorithms have become popular since they are able to produce a set of compromise solutions during the search process to approximate the Pareto-optimal front. The starting point for this thesis was an idea how Differential Evolution, with simple changes, could be extended for optimization with multiple constraints and objectives. This approach is implemented, experimentally studied, and further developed in the work. Development and study concentrates on the multi-objective optimization aspect. The main outcomes of the work are versions of a method called Generalized Differential Evolution. The versions aim to improve the performance of the method in multi-objective optimization. A diversity preservation technique that is effective and efficient compared to previous diversity preservation techniques is developed. The thesis also studies the influence of control parameters of Differential Evolution in multi-objective optimization. Proposals for initial control parameter value selection are given. Overall, the work contributes to the diversity preservation of solutions in multi-objective optimization.