Javier Sanchis

A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization

New 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.

Integrated multiobjective optimization and a priori preferences using genetic algorithms

One of the tasks of decision-making support systems is to develop methods that help the designer select a solution among a set of actions, e.g. by constructing a function expressing his/her preferences over a set of potential solutions. In this paper, a new method to solve multiobjective optimization (MOO) problems is developed in which the users information about his/her preferences is taken into account within the search process. Preference functions are built that reflect the decision-makers (DM) interests and use meaningful parameters for each objective. The preference functions convert these objective preferences into numbers. Next, a single objective is automatically built and no weight selection is performed. Problems found due to the multimodality nature of a generated single cost index are managed with Genetic Algorithms (GAs). Three examples are given to illustrate the effectiveness of the method.

Multiobjective evolutionary algorithms for multivariable PI controller design

A multiobjective optimisation engineering design (MOED) methodology for PI controller tuning in multivariable processes is presented. The MOED procedure is a natural approach for facing multiobjective problems where several requirements and specifications need to be fulfilled. An algorithm based on the differential evolution technique and spherical pruning is used for this purpose. To evaluate the methodology, a multivariable control benchmark is used. The obtained results validate the MOED procedure as a practical and useful technique for parametric controller tuning in multivariable processes.

Comparison of design concepts in multi-criteria decision-making using level diagrams

In this work, we address the evaluation of design concepts and the analysis of multiple Pareto fronts in multi-criteria decision-making using level diagrams. Such analysis is relevant when two (or more) design concepts with different design alternatives lie in the same objective space, but describe different Pareto fronts. Therefore, the problem can be stated as a Pareto front comparison between two (or more) design concepts that only differ in their relative complexity, implementation issues, or the theory applied to solve the problem at hand. Such analysis will help the decision maker obtain a better insight of a conceptual solution and be able to decide if the use of a complex concept is justified instead of a simple concept. The approach is validated in a set of multi-criteria decision making benchmark problems.

Hybrid DE algorithm with adaptive crossover operator for solving real-world numerical optimization problems

In this paper, the results for the CEC 2011 Competition on testing evolutionary algorithms on real world optimization problems using a hybrid differential evolution algorithm are presented. The proposal uses a local search routine to improve convergence and an adaptive crossover operator. According to the obtained results, this algorithm shows to be able to find competitive solutions with reported results.

Applied Pareto multi-objective optimization by stochastic solvers

It is well known that many engineering design problems with different objectives, some of which can be opposed to one another, can be formulated as multi-objective functions and resolved with the construction of a Pareto front that helps to select the desired solution. Obtaining a correct Pareto front is not a trivial question, because it depends on the complexity of the objective functions to be optimized, the constraints to keep within and, in particular, the optimizer type selected to carry out the calculations. This paper presents new methods for Pareto front construction based on stochastic search algorithms (genetic algorithms, GAs and multi-objective genetic algorithms, MOGAs) that enable a very good determination of the Pareto front and fulfill some interesting specifications. The advantages of these applied methods will be proven by the optimization of well-known benchmarks for metallic supported I-beam and gearbox design.

Design of continuous controllers using a multiobjective differential evolution algorithm with spherical pruning

Controller design has evolved to a multiobjective task, i.e., today is necessary to take into account, besides any performance requirement, robustness requisites, frequency domain specifications and uncertain model parameters in the design process. The designer (control engineer), as Decision Maker, has to select the best choice according to his preferences and the trade-off he wants to achieve between conflicting objectives. In this work, a new multiobjective optimization approach using Differential Evolution (DE) algorithm is presented for the design of (but not limited to) Laplace domain controllers. The methodology is used to propose a set of solutions for an engineering control benchmark, all of them non-dominated and pareto-optimal. The obtained results shows the viability of this approach to give a higher degree of flexibility to the control engineer at the decision making stage.

Physical programming for preference driven evolutionary multi-objective optimization

Graphical abstractDisplay Omitted HighlightsWe deal with preference driven evolutionary multi-objective optimization statements.Our approach uses physical programming to include preferences in the optimization.Preferences and constraints are included in a meaningful way for the designer.The implemented algorithm shows its usefulness to compute a pertinent Pareto front. Preference articulation in multi-objective optimization could be used to improve the pertinency of solutions in an approximated Pareto front. That is, computing the most interesting solutions from the designers point of view in order to facilitate the Pareto front analysis and the selection of a design alternative. This articulation can be achieved in an a priori, progressive, or a posteriori manner. If it is used within an a priori frame, it could focus the optimization process toward the most promising areas of the Pareto front, saving computational resources and assuring a useful Pareto front approximation for the designer. In this work, a physical programming approach embedded in an evolutionary multi-objective optimization is presented as a tool for preference inclusion. The results presented and the algorithm developed validate the proposal as a potential tool for engineering design by means of evolutionary multi-objective optimization.

Evolutionary multi-objective optimisation with preferences for multivariable PI controller tuning

We present an evolutionary multiobjective optimisation approach for PI controller tuning.This approach incorporates designers preferences into the optimisation process.The methodology is evaluated in a multivariable process.It is possible to improve pertinency of the approximated Pareto front. Multi-objective optimisation design procedures have shown to be a valuable tool for control engineers. They enable the designer having a close embedment of the tuning process for a wide variety of applications. In such procedures, evolutionary multi-objective optimisation has been extensively used for PI and PID controller tuning; one reason for this is due to their flexibility to include mechanisms in order to enhance convergence and diversity. Although its usability, when dealing with multi-variable processes, the resulting Pareto front approximation might not be useful, due to the number of design objectives stated. That is, a vast region of the objective space might be impractical or useless a priori, due to the strong degradation in some of the design objectives. In this paper preference handling techniques are incorporated into the optimisation process, seeking to improve the pertinency of the approximated Pareto front for multi-variable PI controller tuning. That is, the inclusion of preferences into the optimisation process, in order to seek actively for a pertinent Pareto front approximation. With such approach, it is possible to tune a multi-variable PI controller, fulfilling several design objectives, using previous knowledge from the designer on the expected trade-off performance. This is validated with a well-known benchmark example in multi-variable control. Control tests show the usefulness of the proposed approach when compared with other tuning techniques.

Multiobjective optimization algorithm for solving constrained single objective problems

In this paper, the results for the CEC 2010 Competition and Special Session on Constrained Real-Parameter Optimization using the multiobjective differential evolution algorithm with spherical pruning (sp-MODE) are presented. According to the obtained results, the sp-MODE shows to be able to find feasible solutions in highly constrained search spaces.