The focus of this research is to provide an efficient approach to deal with computationally expensive Multiobjective Optimization Problems (MOP’s). Typically, approximation or surrogate based techniques are adopted to reduce the computational cost. In such cases, the original expensive objective function is replaced by a cheaper mathematical model, where this model mimics the behavior/input-output (i.e. design variable – objective value) relationship. However, it is difficult to model an exact substitute of the targeted objective function. Furthermore, if this kind of approach is used in an evolutionary search, literally, the number of function evaluations does not reduce (i.e. The number of original function evaluation is replaced by the number of surrogate/approximate function evaluation). However, if a large number of individuals are considered, the surrogate model fails to offer smaller computational cost. / To tackle this problem, we have reformulated the concept of surrogate modeling in a different way, which is more suitable for the Multiobjective Evolutionary Algorithm(MOEA) paradigm. In our approach, we do not approximate the objective function; rather we model the input-output behavior of the underlying MOEA itself. The model attempts to identify the search path (in both design-variable and objective spaces) and from this trajectory the model is guaranteed to generate non-dominated solutions (especially, during the initial iterations of the underlying MOEA – with respect to the current solutions) for the next iterations of the MOEA. Therefore, the MOEA can avoid re-evaluating the dominated solutions and thus can save large amount of computational cost due to expensive function evaluations. We have designed our approximation model as a variation operator – that follows the trajectory of the fronts and can be “plugged-in” to any kind of MOEA where non-domination based selection is used. Hence it is termed– the “Pareto-Following Variation Operator (PFVO)”. This approach also provides some added advantage that we can still use the original objective function and thus the search procedure becomes robust and suitable, especially for dynamic problems. / We have integrated the model into three base-line MOEA’s: “Non-dominated Sorting Genetic Algorithm - II (NSGA-II)”, “Strength Pareto Evolutionary Algorithm - II (SPEAII)”and the recently proposed “Regularity Model Based Estimation of Distribution Algorithm (RM-MEDA)”. We have also conducted an exhaustive simulation study using several benchmark MOP’s. Detailed performance and statistical analysis reveals promising results. As an extension, we have implemented our idea for dynamic MOP’s. We have also integrated PFVO into diffusion based/cellular MOEA in a distributed/Grid environment. Most experimental results and analysis reveal that PFVO can be used as a performance enhancement tool for any kind of MOEA.
| Identifer | oai:union.ndltd.org:ADTP/245036 |
| Date | January 2008 |
| Creators | Talukder, A. K. M. K. A. |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | Restricted Access: Abstract and Citation Only Available |
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