Multi-objective optimization: Difference between revisions

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* Constructing a single aggregate objective function (AOF)

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. Thus, it may be noticed that the weighted sum method is essentially subjective, in that a decision manager (DM) needs to supply the weights. The objective way of solving multiobjective problems require a Pareto-compliant ranking method, favouring non-dominated solutions, as seen in thecurrent MOEAsmultiobjective evolutionary approaches such as NSGA-II and SPEA2. Here, no weights are required and thus no a priori information on the problem is needed.

<ref> Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. Wiley,

2002. </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><ref>[http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19970005647_1997005080.pdf Normal-Boundary Intersection: An Alternate Method For Generating Pareto Optimal Points In Multicriteria Optimization Problems]</ref>

* Normal Constraint (NC) method.

* Multiobjective Optimization Evolutionary Algorithms (MOEA).<ref>Deb, K. Multi-Objective Optimization using Evolutionary Algorithms John Wiley & Sons, 2001.</ref><ref>Coello Coello, C. A.; Lamont, G. B. & Van Veldhuizen, D. A. Evolutionary Algorithms for Solving Multi-Objective Problems Springer, 2007.</ref><ref>Das, S.; Panigrahi, B. K. Multi-objective Evolutionary Algorithms, Encyclopedia of Artificial Intelligence, (Eds. J. R. Rabuñal, J. Dorado & A. Pazos), Idea Group Publishing, 3:1145 – 1151, 2008.</ref>

Evolutionary algorithms are very popular approaches in multiobjective optimization. Nowadays, most evolutionary optimizers apply Pareto-based ranking schemes. Genetic algorithms such as the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and Strength Pareto Evolutionary Approach 2 (SPEA-2) have become standard approaches, although some schemes based on particle swarm optimization and simulated annealing are significant.

* PGEN (Pareto surface generation for convex multiobjective instances)<ref> D. Craft, T. Halabi, H. Shih, and T. Bortfeld. Approximating convex Pareto surfaces in multiobjective radiotherapy planning. Medical Physics, 33(9):3399–3407, 2006.</ref>

* [[IOSO]] (Indirect Optimization on the basis of Self-Organization)