Abstract
Applications of optimization methods for optimal design are most efficient when combined with the human engineer’s insight. Visualization is a technique which makes it easier for an engineer to understand the design space and interpret a design found by an optimization algorithm [255]. There are many techniques aimed at visualization of Pareto optimal solutions, especially for the bi-objective problems where a set of solutions, usually referred to as a Pareto front, is a curve in a two-dimensional solution space. The problem of visualization of the sets of optimal decisions is researched not so thoroughly. However, the visualization of a set of Pareto optimal decisions can significantly aid the choice of an appropriate engineering design. In this chapter, we present a case study of a process optimization where the application of a visualization technique was very helpful in the analysis of appropriate design variables.
References
Baronas, R., Žilinskas, A., Litvinas, L.: Optimal design of amperometric biosensors applying multi-objective optimization and decision visualization. Electrochim. Acta 211, 586–594 (2016). doi:10.1016/j.electacta.2016.06.101
Biegler, L., Jiang, L., Fox, G.: Recent advances in simulation and optimal design of pressure swing adsorption systems, separation. Sep. Purif. Rev. 33(1), 1–39 (2005)
Borg, I., Groenen, P.: Modern Multidimensional Scaling: Theory and Applications. Springer, Berlin (1997)
Cox, T., Cox, M.: Multidimensional Scaling. Chapman and Hall, Boca Raton (2001)
Fiandaca, G., Fraga, E., Brandani, S.: A multi-objective genetic algorithm for the design of pressure swing adsorption. Eng. Optim. 41(1), 833–854 (2009)
Haupt, R., Haupt, S.: Practical Genetic Algorithms, 2nd edn. Wiley-Interscience, Hoboken (2004)
Mathar, R., Žilinskas, A.: On global optimization in two dimensional scaling. Acta Appl. Math. 33, 109–118 (1993)
Mockus, J.: Bayesian Approach to Global Optimization. Kluwer Academic Publishers, Dordrecht (1988)
Ruthven, D.: Principles of Adsorption and Adsorption Processes. Wiley-Interscience, New York (1984)
Žilinskas, A., Žilinskas, J.: Optimization based visualization. In: Floudas, C.A., Pardalos, P.M. (eds.) Encyclopedia of Optimization, pp. 2785–2791. Springer, New York (2009)
Žilinskas, A., Žilinskas, J.: Interval arithmetic based optimization in nonlinear regression. Informatica 21(1), 149–158 (2010)
Žilinskas, A., Fraga, E.S., Mackutė, A.: Data analysis and visualisation for robust multi-criteria process optimisation. Comput. Chem. Eng. 30(6–7), 1061–1071 (2006)
Žilinskas, A., Fraga, E., Beck, J., Varoneckas, A.: Visualization of multi-objective decisions for the optimal design of a pressure swing adsorption system. Chemom. Intell. Lab. Syst. 142, 151–158 (2015)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Pardalos, P.M., Žilinskas, A., Žilinskas, J. (2017). Visualization of a Set of Pareto Optimal Decisions. In: Non-Convex Multi-Objective Optimization. Springer Optimization and Its Applications, vol 123. Springer, Cham. https://doi.org/10.1007/978-3-319-61007-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-61007-8_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-61005-4
Online ISBN: 978-3-319-61007-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)