MILP models for objective reduction in multi-objective optimization: Error measurement considerations and non-redundancy ratio

Abstract A common approach in multi-objective optimization (MOO) consists of removing redundant objectives or reducing the set of objectives minimizing some metrics related with the loss of the dominance structure. In this paper, we comment some weakness related to the usual minimization of the maximum error (infinity norm or δ-error) and the convenience of using a norm 1 instead. Besides, a new model accounting for the minimum number of Pareto solutions that are lost when reducing objectives is provided, which helps to further describe the effects of the objective reduction in the system. A comparison of the performance of these algorithms and its usefulness in objective reduction against principal component analysis + Deb & Saxena's algorithm (Deb & Saxena Kumar, 2005) is provided, and the ability of combining it with a principal component analysis in order to reduce the dimensionality of a system is also studied and commented.

[1]  Gonzalo Guillén-Gosálbez,et al.  Systematic approach for the life cycle multi-objective optimization of buildings combining objective reduction and surrogate modeling , 2016 .

[2]  Agnar Aamodt,et al.  Case-Based Reasoning: Foundational Issues, Methodological Variations, and System Approaches , 1994, AI Commun..

[3]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[4]  Thomas L. Saaty,et al.  Decision making with dependence and feedback : the analytic network process : the organization and prioritization of complexity , 1996 .

[5]  A. Charnes,et al.  Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis , 1984 .

[6]  Thomas L. Saaty,et al.  Decision Making for Leaders: The Analytical Hierarchy Process for Decisions in a Complex World , 1982 .

[7]  L. Lasdon,et al.  On a bicriterion formation of the problems of integrated system identification and system optimization , 1971 .

[8]  Karl Pearson F.R.S..  LIII. On lines and planes of closest fit to systems of points in space , 1901 .

[9]  Gerald Rebitzer,et al.  IMPACT 2002+: A new life cycle impact assessment methodology , 2003 .

[10]  Gonzalo Guillén-Gosálbez,et al.  On the use of Principal Component Analysis for reducing the number of environmental objectives in multi-objective optimization: Application to the design of chemical supply chains , 2012 .

[11]  Eckart Zitzler,et al.  Are All Objectives Necessary? On Dimensionality Reduction in Evolutionary Multiobjective Optimization , 2006, PPSN.

[12]  Eckart Zitzler,et al.  Objective Reduction in Evolutionary Multiobjective Optimization: Theory and Applications , 2009, Evolutionary Computation.

[13]  Eckart Zitzler,et al.  Dimensionality Reduction in Multiobjective Optimization with (Partial) Dominance Structure Preservation: Generalized Minimum Objective Subset Problems , 2006 .

[14]  Indraneel Das.  A preference ordering among various Pareto optimal alternatives , 1999 .

[15]  Rubén Ruiz-Femenia,et al.  MILP method for objective reduction in multi-objective optimization , 2018, Comput. Chem. Eng..

[16]  G Guilln-Goslbez.  A novel MILP-based objective reduction method for multi-objective optimization: Application to environmental problems , 2011 .

[17]  Eckart Zitzler,et al.  On Objective Conflicts and Objective Reduction in Multiple Criteria Optimization , 2006 .