Quasiconvex Constrained Multicriteria Continuous Location Problems: Structure of Nondominated Solution Sets

In this paper, we consider constrained multicriteria continuous location problems in two-dimensional spaces. In the literature, the continuous multicriteria location problem in two-dimensional spaces has received special attention in the last years, although only particular instances of convex functions have been considered. Our approach only requires the functions to be strictly quasiconvex and inf-compact. We obtain a geometrical description that provides a unified approach to handle multicriteria location models in two-dimensional spaces which has been implemented in MATHEMATIC

An axiomatization of the Euclidean compromise solution

The utopia point of a multicriteria optimization problem is the vector that specifies for each criterion the most favourable among the feasible values. The Euclidean compromise solution in multicriteria optimization is a solution concept that assigns to a feasible set the alternative with minimal Euclidean distance to the utopia point. The purpose of this paper is to provide a characterization of the Euclidean compromise solution. Consistency plays a crucial role in our approach.Consistency; Euclidean compromise solution; Multicriteria optimization

Exploring parameter sensitivities of the land surface using a locally coupled land-atmosphere model

This paper presents a multicriteria analysis that explores the sensitivity of the land surface to changes in both land and atmospheric parameters, in terms of reproducing surface heat fluxes and ground temperature; for the land parameters, offline sensitivity analyses were also conducted for comparison to infer the influence of land-atmosphere interactions. A simple "one-at-a-time" sensitivity analysis was conducted first to filter out some insensitive parameters, followed by a multicriteria sensitivity analysis using the multiobjective generalized sensitivity analysis algorithm. The models used were the locally coupled National Center for Atmospheric Research (NCAR) single-column community climate model and the offline NCAR land surface model, driven and evaluated by a summer intensive operational periods (IOP) data set from the southern Great Plains. As expected, the results show that land-atmosphere interactions (with or without land-atmosphere parameter interactions) can have significant influences on the sensitivity of the land surface to changes in the land parameters, and the single-criterion sensitivities can be significantly different from the multicriteria sensitivity. These findings are mostly model and data independent and can be generally useful, regardless of the model/data dependence of the sensitivities of individual parameters. The exceptionally high sensitivities of the selected atmospheric parameters in a multicriteria sense (and in particular for latent heat) appeal for adequate attention to the specification of effective values of these parameters in an atmospheric model. Overall, this study proposes an effective framework of multicriteria sensitivity analysis beneficial to future studies in the development and parameter estimation of other complex (offline or coupled) land surface models. Copyright 2004 by the American Geophysical Union

Indicators and Evaluation Tools for the Assessment of Urban Sustainability

This paper attempts to provide an explanation of why reductionistic approaches are not adequate to tackle the urban sustainability issue in a consistent way. Concepts such as urban environmental carrying capacity and ecological footprint are discussed. Multicriteria evaluation is proposed as a general multidimensional framework for the assessment of urban sustainability. This paper deals with the following main topics: · definition of the concept of urban sustainability, · discussion of relevant sustainability indicators, · multicriteria evaluation as a framework for the assessment of urban sustainability, · an illustrative example.Urban environmental carrying capacity, ecological footprint, multicriteria evaluation, NAIADE method

Primitive Zonotopes

We introduce and study a family of polytopes which can be seen as a generalization of the permutahedron of type $B_d$. We highlight connections with the largest possible diameter of the convex hull of a set of points in dimension $d$ whose coordinates are integers between $0$ and $k$, and with the computational complexity of multicriteria matroid optimization.Comment: The title was slightly modified, and the determination of the computational complexity of multicriteria matroid optimization was adde

Multicriteria VMAT optimization

Purpose: To make the planning of volumetric modulated arc therapy (VMAT) faster and to explore the tradeoffs between planning objectives and delivery efficiency. Methods: A convex multicriteria dose optimization problem is solved for an angular grid of 180 equi-spaced beams. This allows the planner to navigate the ideal dose distribution Pareto surface and select a plan of desired target coverage versus organ at risk sparing. The selected plan is then made VMAT deliverable by a fluence map merging and sequencing algorithm, which combines neighboring fluence maps based on a similarity score and then delivers the merged maps together, simplifying delivery. Successive merges are made as long as the dose distribution quality is maintained. The complete algorithm is called VMERGE. Results: VMERGE is applied to three cases: a prostate, a pancreas, and a brain. In each case, the selected Pareto-optimal plan is matched almost exactly with the VMAT merging routine, resulting in a high quality plan delivered with a single arc in less than five minutes on average. VMERGE offers significant improvements over existing VMAT algorithms. The first is the multicriteria planning aspect, which greatly speeds up planning time and allows the user to select the plan which represents the most desirable compromise between target coverage and organ at risk sparing. The second is the user-chosen epsilon-optimality guarantee of the final VMAT plan. Finally, the user can explore the tradeoff between delivery time and plan quality, which is a fundamental aspect of VMAT that cannot be easily investigated with current commercial planning systems