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Often at the earliest stage of an engineering project, a preliminary optimization could be useful, in order to allow the designer to ascertain the envisaged performance of the system under development.Providing an efficient (analytical) tool to quickly define the Pareto-optimal set could be an extremely valuable chance to make the right design decision at the right time.The procedure proposed here to obtain the Pareto-optimal set in analytical form refers mostly to design problems described by a limited number of design variables and a limited number of objective functions and constraints.In the first part of the paper, the analytical derivation of the expression of the Pareto-optimal set for multi-objective optimization problems is dealt with.According to the knowledge of the authors, in the literature, very few papers exist on this topic and related issues. A survey of current continuous multi-objective optimization concepts and methods is presented in Ref. [19]. Some relevant contributions are given in Ref. [17] and Ref. [20] in which some new formulations of the Fritz John first order conditions are proposed and analyzed. In Ref. [30] first and second order conditions are proposed for a convex multi-objective problem via scalarization and in Ref.[1] some second order conditions are analyzed in detail. In Refs. [17,20,30,1,32,26] necessary and/or sufficient conditions are discussed but

A number of experimental activities designed and undertaken for deriving the\ud characteristics of farm tractor tyres are presented. By means of a proprietary measuring hub\ud the three forces and the three moments acting at the hub of a farm tractor wheel have been\ud measured, at different combinations of lateral and longitudinal tyre slips. Tyre steady state\ud characteristics have been derived both on hard asphalt road and on soft soil. The validation of\ud the measurements of tyre characteristics has been performed indirectly by introducing the data\ud referring to tyre characteristics into a detailed mathematical model of a farm tractor. A\ud number of actual manoeuvres have been simulated. The satisfactory agreement between\ud simulated and measured results has provided the necessary condition for the validation of the\ud tyre characteristic measureme nt process

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In the paper, the problem of choosing a single final design solution among a large set of Pareto-optimal solutions is addressed. Two methods, the k-optimality approach and the more general k-ε-optimality method will be introduced. These two methods theoretically justify and mathematically define the designer’s tendency to choose solutions which are “in the middle” of the Pareto-optimal set. These two methods have been applied to the solution of a relatively simple engineering problem, i.e. the selection of the stiffness and damping of a passively suspended vehicle in order to get the best compromise between discomfort, road holding and working space. The final design solution, found by means of the k-ε-optimality approach seems consistent with the solution selected by skilled suspensions specialists. Finally the k-optimality method has proved to be very effective also when applied to complex engineering problems. The optimization of the tyre/suspension system of a sports car has been formulated as a design problem with 18 objective functions. A large set of Pareto-optimal solutions have been computed. Again, the k-optimality approach has proved to be a useful tool for the selection of a fully satisfactory final design solution.

Characteristics of first-round attendees and determinants of reattendance in the Swiss mammography screening pilot programme (1993-1998) were investigated. Data on socio-demographic features, health preventive behaviour and history, prior screening round and referring physicians' attributes were collected at initial attendance among women enrolled in 1993-1995. First-round participants (n = 4,162) were prospectively followed through next screening round. Determinants of reattendance (second-round attendance among first-round participants) were identified by multivariate logistic regression models. The reattendance rate was high (80%). Women most likely to reattend were urban, Swiss residents with a true-negative first-round screening result. The more intensive the initial recruitment efforts, the lesser were the odds of reattendance. Mammography screening prior to screening enrolment increased reattendance. Having a gynaecologist, a female and a younger doctor as a referring physician was positively associated with reattendance. Mammography screening attendance is not only influenced by women-related factors but also by structural factors, and thus requires a global approach. For strategies aimed at improving the impact of organised cancer screening programmes, understanding and quantification of determinants of (re)attendance are key elements to consider.

An application to structural design of an\ud innovative method for optimising stochastic systems is\ud introduced in the paper. The proposed method allows\ud one to carry out both the multi-objective optimisation\ud of a structural element and to improve the robustness of\ud the design. The innovative method is rather general. To\ud show its effectiveness, an ideal cantilever has been designed\ud in order to minimise both mass and deflection. The\ud cantilever is shaped as a beam and is subject to random\ud loads acting at its free end. The beam geometrical dimensions\ud and material properties vary stochastically due to\ud manufacturing tolerances. Different beam cross sections\ud and two different materials (aluminium alloy and steel)\ud have been considered. From the optimisation, it turned\ud out that the optimal solutions are the O and the I beam,\ud depending on the required lightness and stiffness. Compared\ud to steel, aluminium alloy beams have provided better\ud (or at least equal) performance