Nonlinear multiple objective optimization: An algorithm and some theory

This paper presents an algorithm and the supporting theory for solving a class of nonlinear multiple criteria optimization problems using Zionts—Wallenius type of interaction. The Zionts—Wallenius method, as extended in this paper, can be used for solving multiple criteria problems with concave objective and (implicit) value functions and convex feasible regions. Modifications of the method to handle nonconvex feasible regions and general nonlinear objective functions are also discussed.This research was supported, in part, by a Faculty Research Development Award and by a Council of 100 Research Grant from Arizona State University (Roy), and by a grant from Y. Jahnsson Foundation, Finland (Wallenius). The research was performed while the second author was a Visiting Professor at Arizona State University.     

Behaviour of239,240Pu and241Am in the Baltic Sea; Measurements and interpretation in 1980–1984

Concentrations of^239,240Pu and²⁴¹Am in filtered seawater, particulate fraction and sediment were measured. Methods for determination of these nuclides were critically chequed and a new rapid method for²⁴¹Am in sediment was developed. Due to seasonal variation a significant decrease of plutonium and americium concentrations in surface water takes place in summer. Americium is more efficiently associated with particulate matter than plutonium. From May 1980 to September 1984 soluble plutonium in the water was reduced to about half. The residence half-time of^239,240Pu in the water of Baltic Sea is of the order of 5 years. About similar concentrations of^239,240Pu and²⁴¹Am were found in particulates in water as in the surface layer of the sediment. The average K_d-values for plutonium and americium were 10⁵ and 10⁵–10⁶ ml/g, respectively.     

Can a linear value function explain choices? An experimental study

We investigate in a simple bi-criteria experimental study, whether subjects are consistent with a linear value function while making binary choices. Many inconsistencies appeared in our experiment. However, the impact of inconsistencies on the linearity vs. non-linearity of the value function was minor. Moreover, a linear value function seems to predict choices for bi-criteria problems quite well. This ability to predict is independent of whether the value function is diagnosed linear or not. Inconsistencies in responses did not necessarily change the original diagnosis of the form of the value function. Our findings have implications for the design and development of decision support tools for Multiple Criteria Decision Making problems.     

Connections Between Single-Level and Bilevel Multiobjective Optimization

The relationship between bilevel optimization and multiobjective optimization has been studied by several authors, and there have been repeated attempts to establish a link between the two. We unify the results from the literature and generalize them for bilevel multiobjective optimization. We formulate sufficient conditions for an arbitrary binary relation to guarantee equality between the efficient set produced by the relation and the set of optimal solutions to a bilevel problem. In addition, we present specially structured bilevel multiobjective optimization problems motivated by real-life applications and an accompanying binary relation permitting their reduction to single-level multiobjective optimization problems.     

Wettability conversion on the liquid flame spray generated superhydrophobic TiO2 nanoparticle coating on paper and board by photocatalytic decomposition of spontaneously accumulated carbonaceous overlayer

Titanium dioxide (TiO₂) is a photoactive material with various interesting and useful properties. One of those is the perfect wettability of TiO₂ surface after ultraviolet (UV) illumination. Wettability of a solid surface plays an important role in the field of printing, coating, and adhesion among others. Here we report on a superhydrophobic and photoactive liquid flame spray (LFS) generated TiO₂ nanoparticle coating that can be applied on web-like materials such as paper and board in one-step roll-to-roll process. The LFS TiO₂ nanoparticle coated paper and board were superhydrophobic instantly after the coating procedure because of spontaneously accumulated carbonaceous overlayer on TiO₂, and thus there was no need for any type of separate hydrophobization treatment. The highly photoactive LFS TiO₂ nanoparticle coating could be converted steplessly from superhydrophobic to superhydrophilic by UV-illumination, and the coating gave strong response to natural daylight illumination even in the shade. The superhydrophobic LFS TiO₂ coated surface can be used as an intelligent substrate, where photo-generated hydrophilic patterns guide the fluid setting and figure formation. Our study reveals that the wettability changes on the LFS TiO₂ surface were primarily caused by the photocatalytic removal of the carbonaceous material from TiO₂ during the UV-illumination and spontaneous accumulation of the carbonaceous material on the surface of the metal oxide during storage in the dark. The latter mechanism was found to be a temperature activated process which could be significantly speeded up by heat treatment. If other mechanisms such as surface oxidization, increment of hydroxyl groups, or charge separation played a role in the wetting phenomena on TiO₂, their effect was rather secondary as the removal and accumulation of the carbonaceous material dominated the wettability changes on the surface. Our study gives valuable information on the complex issue of photo-induced wettability changes on TiO₂.     

Switchable water absorption of paper via liquid flame spray nanoparticle coating

Surface wetting/anti-wetting and liquid absorption are relevant properties of many porous solids including paper and other cellulose-based materials. Here we demonstrate how surface wetting by water and water absorption of commercially available kraft paper can be altered by thin nanoparticle coatings fabricated by liquid flame spray in facile and continuous one-step process. Surface wettability and absorption properties of paper increased with silica and decreased with titania (TiO₂) nanoparticle coatings. Moreover, the water-repellent (superhydrophobic) TiO₂ nanoparticle coated paper could be switched to superhydrophilic and water absorbing by ultraviolet illumination. The experiments revealed that although surface wetting and liquid absorption of nanoparticle coated paper are strongly related to each other, they are two distinct phenomena which do not necessarily correlate. We propose wetting regimes on the nanoparticle coated paper samples on the basis of the experimental observations.     

A Decision Model for the Multiple Criteria Group Secretary Problem: Theoretical Considerations

A decision model is developed for solving the discrete multiple criteria group secretary problem. The model extends the single decision-maker progressive algorithm by Korhonen, Moskowitz and Wallenius to group contexts. As the original progressive algorithm, it relaxes the usual assumption of a fixed set of available decision alternatives and complete knowledge of a decision-maker's preference structure (value function). The decision-makers are requested to settle on a compromise, if possible. The model then proceeds with determining the likelihood of finding possibly/surely better settlements (compromises). Linear value functions, linear prospect theory-type value functions, and quasiconcave value functions are considered.