A Posteriori Methods
A posteriori methods aim at producing all the Pareto optimal solutions or a representative subset of the Pareto optimal solutions. Well-known examples are the Normal Boundary Intersection (NBI), Modified Normal Boundary Intersection (NBIm), Normal Constraint (NC), Successive Pareto Optimization (SPO) and Directed Search Domain (DSD) methods that solve the multi-objective optimization problem by constructing several scalarizations. The solution to each scalarization yields a Pareto otpimal solution, whether locally or globally. The scalarizations of the NBI, NBIm, NC and DSD methods are constructed with the target of obtaining evenly distributed Pareto points that give a good evenly distributed approximation of the real set of Pareto points.
Evolutionary algorithms are popular approaches to generating Pareto optimal solutions to a multiobjective optimization problem. Currently, most evolutionary multiobjective optimization (EMO) algorithms apply Pareto-based ranking schemes. Evolutionary algorithms such as the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and Strength Pareto Evolutionary Algorithm 2 (SPEA-2) have become standard approaches, although some schemes based on particle swarm optimization and simulated annealing are significant. The main advantage of evolutionary algorithms, when applied to solve multiobjective optimization problems, is the fact that they typically generate sets of solutions, allowing computation of an approximation of the entire Pareto front. The main disadvantage of evolutionary algorithms is their lower speed and the Pareto optimality of the solutions cannot be guaranteed. It is only known that none of the generated solutions dominates the others.
Other a posteriori methods are:
- PGEN (Pareto surface generation for convex multiobjective instances)
- IOSO (Indirect Optimization on the basis of Self-Organization)
- SMS-EMOA (S-metric selection evolutionary multiobjective algorithm)
- Reactive Search Optimization (using machine learning for adapting strategies and objectives), implemented in LIONsolver
- Benson's algorithm for linear vector optimization problems
- Multiobjective particle swarm optimization
Read more about this topic: Multi-objective Optimization
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