Paper Info
Title
A multiobjective approach for finding equivalent inverse images of Pareto-optimal objective vectors
Abstract
Supply bottlenecks or sudden changes in legal regulations may lead to the situation that certain factor com- binations for producing some commodity cannot be used any longer. In this case it is important to know alternative factor combinations leading to a product with identical characteristics represented by a Pareto-optimal objective vector of a multi- objective optimization problem. Here, we present a biobjective approach that finds equivalent inverse images of a given Pareto- optimal objective vector, provided they exist. I. INTRODUCTION Typically, evolutionary multiobjective algorithms (EMOA) deliver a set of objective vectors representing an approxima- tion of the Pareto front. Elements on the Pareto front are characterized by the fact that an improvement with regard to an arbitrary objective must deteriorate at least one of the remaining objective values. Those elements in objective space are important for the product designer as varied values with regard to the objectives typify different products. The inverse images of these objective vectors in decision space determine the factor combinations for producing the com- modity. Consequently, they are of interest for the product engineer being responsible of the production process. Since the mapping from decision space to objective space is not injective in general, it may well happen that different factor combinations may be used to produce equivalent commidities with identical properties as selected by the product designer. If the production is running short of a specific factor due to supply bottlenecks or if new legal regulations prohibit the usage of some factor, the product engineer needs to know these alternative factor combinations to keep the production running. Unfortunately, standard versions of popular EMOAs typ- ically maintain only a single inverse image per objective vector. As a result, equivalent inverse images are not at the product engineer's disposal when they are needed. Therefore we (1), (2) and others (3), (4) have had developed special purpose EMOAs which do not only approximate the Pareto front in objective space; rather, they were designed for covering the Pareto set in decision space as completely as possible. In this case we only need to enumerate the solutions in decision space until we find an equivalent inverse image (if it exists). But actually it is not necessary to approximate the entire Pareto set in decision space. As the product designer selects G¨
Year
DOI
Venue
2009
10.1109/MCDM.2009.4938831
Nashville, TN
Keywords
Field
DocType
Pareto optimisation,Pareto-optimal objective vectors,biobjective approach,equivalent inverse images,multiobjective optimization
Inverse,Distance measurement,Mathematical optimization,Computer science,Multi-objective optimization,Pareto optimal,Multiobjective optimization problem,Artificial intelligence,Probability density function,Machine learning
Conference
ISBN
Citations 
PageRank 
978-1-4244-2764-2
0
0.34
References 
Authors
10
2
Name
Order
Citations
PageRank
Günter Rudolph121948.59
Preuss Mike293381.70