a b s t r a c tNew challenges in engineering design lead to multiobjective (multicriteria) problems. In this context, the Pareto front supplies a set of solutions where the designer (decision-maker) has to look for the best choice according to his preferences. Visualization techniques often play a key role in helping decision-makers, but they have important restrictions for more than two-dimensional Pareto fronts. In this work, a new graphical representation, called Level Diagrams, for n-dimensional Pareto front analysis is proposed. Level Diagrams consists of representing each objective and design parameter on separate diagrams. This new technique is based on two key points: classification of Pareto front points according to their proximity to ideal points measured with a specific norm of normalized objectives (several norms can be used); and synchronization of objective and parameter diagrams. Some of the new possibilities for analyzing Pareto fronts are shown. Additionally, in order to introduce designer preferences, Level Diagrams can be coloured, so establishing a visual representation of preferences that can help the decision-maker. Finally, an example of a robust control design is presented -a benchmark proposed at the American Control Conference. This design is set as a six-dimensional multiobjective problem.Ó 2008 Elsevier Inc. All rights reserved. MotivationIn numerous engineering areas, the task of obtaining suitable designs becomes a multiobjective (or multicriteria) problem. This means it is necessary to look for a solution in the design space that satisfies several specifications (objectives) in the performance space. Generally, these specifications are conflicting, that is, there is no simultaneous optimal solution for all of them. In this context, the solution is not unique, instead there is a set of possible solutions where none is best for all objectives. This set of optimal solutions in the design space is called the Pareto set. The region defined by the performances (the value of all objectives) for all Pareto set points is called the Pareto front.The exact determination of the Pareto front is unrealistic for real-world problems, as it is usually an infinite set. Therefore, it is usual to focus on obtaining a discrete approximation. A common step for solving a multiobjective optimization problem is to obtain the discrete approximation of the Pareto front. This is an open research field where numerous techniques have already been developed [19] and where new techniques are being constantly developed [17,14]. An alternative, and very active research line, is Multiobjective Evolutionary Algorithms [5,9]. In general, these algorithms supply reasonable solutions for Pareto front approximations. Once obtained, the next step for the designer is to select one, or more, solutions inside the Pareto front approximation. The final solution is often selected using methodologies that normally include designer 0020-0255/$ -see front matter Ó

Control engineering problems are generally multi-objective problems; meaning that there are several specifications and requirements that must be fulfilled. A traditional approach to calculate a solution with the desired trade-off is to define an optimisation statement. Multi-objective optimisation techniques deal with this problem from a particular perspective searching for a set of potentially preferable solutions; the designer may then analyse the trade-off among them, and select the best solution according to his/her preferences. In this paper, this design procedure based on evolutionary multiobjective optimisation (EMO) is presented and significant applications on controller tuning are commented on. Through this paper it is noticed that EMO research has been developing towards different optimization statements, but such statements are not commonly used on controller tuning. Therefore gaps between EMO research and EMO applications on controller tuning are detected and suggested as potential trends for research.

This work focuses on development of control algorithms by incorporating energy and water consumption to maintain climatic conditions in greenhouse. Advanced control algorithms can supply solutions to modern exploitations. The new developments usually require accurate models (probably multivariable and nonlinear ones) and control methodologies capable of using these models. As an additional requirement it is important for the final application to be easy to use, so advanced control will not mean an increase in complexity of the manipulation of the installation. This article shows an alternative to classical climate control. It is based on two fundamental elements: an accurate non-linear model and a model based predictive control (MBPC) that incorporate energy and water consumption. Genetic Algorithms (GAs) play a key role in these two elements because functions to solve are non-convex and with local minima. First of all GAs supply a way to adjust the non-linear model parameters obtained from first principles, and finally GAs open the possibility of using non-linear model in the MBPC and of establishing a flexible cost index to minimize energy and water consumption. The results on a plastic greenhouse with arch-shaped roofs and for Mediterranean area are presented, important reduction in energy and water used in the cooling system (nebulization) is obtained.

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Furthermore, for a given controller it is simple to analyse the trade-off achieved between conflicting 8 objectives. By using the multi-objective design technique it is also possible to perform a global compar-9 ison between different control strategies in a simple and robust way. This approach thereby enables an 10 analysis to be made of whether a preference for a certain control technique is justified. This proposal 11 is evaluated and validated in a non-linear MIMO system using two control strategies: a classical PID 12 control scheme and a feedback state controller. DMDecision maker