W propose a new approach to convex nonlinear multiobjective optimization that captures the geometry of the Pareto set by generating a discrete set of Pareto points optimally. We show that the problem of finding a maximally uniform representation of the Pareto surface can be formulated as a mathematical program with complementarity constraints. The complementarity constraints arise from modeling...

PURPOSE To introduce a method to simultaneously explore a collection of Pareto surfaces. The method will allow radiotherapy treatment planners to interactively explore treatment plans for different beam angle configurations as well as different treatment modalities. METHODS The authors assume a convex optimization setting and represent the Pareto surface for each modality or given beam set by...

In this paper, evolutionary dynamic weighted aggregation methods are generalized to deal with three-objective optimization problems. Simulation results from two test problems show that the performance is quite satisfying. To take a closer look at the characteristics of the Pareto-optimal solutions in the parameter space, piecewise linear models are used to approximate the definition function in...

We consider Pareto surface based multi-criteria optimization for step and shoot IMRT planning. By analyzing two navigation algorithms, we show both theoretically and in practice that the number of plans needed to form convex combinations of plans during navigation can be kept small (much less than the theoretical maximum number needed in general, which is equal to the number of objectives for o...

This paper presents the strategy for multi-criteria optimization of a prototype. There are taken into account two different optimization criteria. An original computer program was made to make possible the graphic display of regions on the 3D model surface, which exceed a limit for surface roughness, initial established. The computer program allows the automate calculation of optimal position f...

A Pareto optimization study was carried out on a flat pad aerostatic bearing design. Some of the Pareto optimal configurations were then subjected to surface profiling errors including tilt, concavity, convexity and waviness and key performance parameters such as load capacity, stiffness and flow rate determined. From these studies it was concluded that multi-orifice aerostatic flat pad bearing...

| Many, if not most, optimization problems have multiple objectives. Historically , multiple objectives have been combined ad hoc to form a scalar objective function , usually through a linear combination (weighted sum) of the multiple attributes, or by turning objectives into constraints. The genetic algorithm (GA), however, is readily modiied to deal with multiple objectives by incorporating ...

This paper presents an adaptive weighted sum (AWS) method for multiobjective optimization problems. The method extends the previously developed biobjective AWS method to problems with more than two objective functions. In the first phase, the usual weighted sum method is performed to approximate the Pareto surface quickly, and a mesh of Pareto front patches is identified. Each Pareto front patc...