A New Adaptive Algorithm for Convex Quadratic Multicriteria Optimization

We present a new adaptive algorithm for convex quadratic multicriteria optimization. The algorithm is able to adaptively refine the approximation to the set of efficient points by way of a warm-start interior-point scalarization approach. Numerical results show that this technique is an order of magnitude faster than a standard method used for this problem

A new adaptive algorithm for convex quadratic multicriteria optimization

We present a new adaptive algorithm for convex quadratic multicriteria optimization. The algorithm is able to adaptively refine the approximation to the set of efficient points by way of a warm-start interior-point scalarization approach. Numerical results show that this technique is faster than a standard method used for this problem

Multicriteria global optimization for biocircuit design

One of the challenges in Synthetic Biology is to design circuits with increasing levels of complexity. While circuits in Biology are complex and subject to natural tradeoffs, most synthetic circuits are simple in terms of the number of regulatory regions, and have been designed to meet a single design criterion. In this contribution we introduce a multiobjective formulation for the design of biocircuits. We set up the basis for an advanced optimization tool for the modular and systematic design of biocircuits capable of handling high levels of complexity and multiple design criteria. Our methodology combines the efficiency of global Mixed Integer Nonlinear Programming solvers with multiobjective optimization techniques. Through a number of examples we show the capability of the method to generate non intuitive designs with a desired functionality setting up a priori the desired level of complexity. The presence of more than one competing objective provides a realistic design setting where every design solution represents a trade-off between different criteria. The tool can be useful to explore and identify different design principles for synthetic gene circuits

The proximal point method for locally lipschitz functions in multiobjective optimization with application to the compromise problem

This paper studies the constrained multiobjective optimization problem of finding Pareto critical points of vector-valued functions. The proximal point method considered by Bonnel, Iusem, and Svaiter [SIAM J. Optim., 15 (2005), pp. 953–970] is extended to locally Lipschitz functions in the finite dimensional multiobjective setting. To this end, a new (scalarization-free) approach for convergence analysis of the method is proposed where the first-order optimality condition of the scalarized problem is replaced by a necessary condition for weak Pareto points of a multiobjective problem. As a consequence, this has allowed us to consider the method without any assumption of convexity over the constraint sets that determine the vectorial improvement steps. This is very important for applications; for example, to extend to a dynamic setting the famous compromise problem in management sciences and game theory.Fundação de Amparo à Pesquisa do Estado de GoiásConselho Nacional de Desenvolvimento Científico e TecnológicoCoordenação de Aperfeiçoamento de Pessoal de Nivel SuperiorMinisterio de Economía y CompetitividadAgence nationale de la recherch

Application of general semi-infinite Programming to Lapidary Cutting Problems

We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP) and solved using an interiorpoint method developed by Stein. It is shown, that the convexity assumption needed for the convergence of the algorithm can be satisfied by appropriate modelling. Clustering techniques are used to reduce the number of container constraints, which is necessary to make the subproblems practically tractable. An iterative process consisting of GSIP optimization and adaptive refinement steps is then employed to obtain an optimal solution which is also feasible for the original problem. Some numerical results based on realworld data are also presented

04461 Abstracts Collection -- Practical Approaches to Multi-Objective Optimization

From 07.11.04 to 12.11.04, the Dagstuhl Seminar 04461 ``Practical Approaches to Multi-Objective Optimization\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available