Multi-objective optimization: Difference between revisions

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This is perhaps the most intuitive approach to solving the multiobjective problem. The basic idea is to combine all of the objective functions into a single functional form, called the AOF. A well-known combination is the weighted linear sum of the objectives. One specifies scalar weights for each objective to be optimized, and then combines them into a single function that can be solved by any single-objective optimizer (such as SQP, pattern search etc.). Clearly, the solution obtained will depend on the values (more precisely, the relative values) of the weights specified. For example, if we are trying to maximize the strength of a machine component and minimize the production cost, and if we specify a higher weight for the cost objective compared to the strength, our solution will be one that favors lower cost over higher strength. The solutions obtained using the weighted sum are always Pareto optimal, but coming up with meaningful combinations of weights can be challenging.<ref> A. Messac, A. Ismail-Yahaya, and C. A. Mattson. The Normalized Normal Constraint Method for Generating the Pareto Frontier. Structural and Multidisciplinary Optimization, 25(2):86–98, 2003. </ref>

* Normal Boundary Intersection (NBI) method <ref> I. Das and J. E. Dennis. Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems. SIAM Journal on Optimization, 8:631–657, 1998. </ref>

* Normal Constraint (NC) method .

* Multiobjective GeneticOptimization Evolutionary Algorithms (MOGAMOEA). <ref>Deb, K. Deb,Multi-Objective A.Optimization using Evolutionary Algorithms John Wiley & PratapSons, S2001.</ref> Agarwal,<ref>Coello andCoello, TC. MeyarivanA.; ALamont, FastG. andB. Elitist& MultiobjectiveVan GeneticVeldhuizen, Algorithm:D. NSGA-IIA. IEEEEvolutionary TransactionsAlgorithms onfor EvolutionarySolving Computation,Multi-Objective 6(2):182–197Problems Springer, 2002. 2007</ref>

==See also==