NIMBUS - Optimizers

As explained briefly in NIMBUS - Info -page, the classification information obtained from a decision maker is used to create a subproblem, that is then solved with an objective optimization method. At the moment this single-objective subproblem can be solved alternatively by local proximal bundle (MPB) method or global method based on genetic algorithm. There exists also a hybrid method combining these two optimizers.

Local (PB):

The local solver is proximal bundle method developed for nondifferentiable optimization. The method can find a local minimum of a locally Lipschitz continuous function (subject to linear and nonlinear constraints). It is a descent method based on a piecewise linear model constructed via subgradients. Thus, the method cannot be used if subgradients are not available.

Global:

The global solver used by the NIMBUS system is based on a genetic algorithm. There is two different versions of the global solver, named as Global 1 and Global 2. The underlaying genetic algorithm in is identical in both global solvers, they differ only by their constraint handling routines.

Global 1:

The global solver is genetic algorithm together with the constraint handling technique suggested by Deb. Infeasible solutions are avoided in the selection phase so that feasible solutions are always preferred to infeasible ones. If the selection is to be done between two infeasible solutions, the one closer to the feasible region is selected. This constraint handling technique involves no additional parameters.

Global 2:

The global solver is genetic algorithm together with the method of adaptive penalties (AP) for handling constraints. The AP method tries to avoid infeasible solutions by adjusting the penalty coefficient. The penalty is increased if all the best solutions of a pre-specified number of past iterations are infeasible whereas the penalty is decreased if all of them are feasible.

Hybrid:

In a hybrid method the global and local methods have been combined. In a hybrid method the problem is first solved with and global solver, and then the obtained solution is solved the local method.

Global 1 + Local (PB):

In Global 1 + Local (PB) method the Global 1 has been combined with the Local (PB) method. These methods are described earlier.

Global 2 + Local (PB):

In Global 2 + Local (PB) method the Global 2 has been combined with the Local (PB) method. These methods are described earlier.

References:

Mäkelä M.M., Neittaanmäki P. Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control, World Scientific Publishing Co., Signapore, 1992.
Hadj-Alouane A.B., Bean J.C, A Genetic Algorithm for the Multiple-Choice Integer Program, Operations Research, Vol 45, pp. 92-101, 1997.
Deb K., An Efficient Constraint Handling Method for Genetic Algorithms, Computer Methods in Applied Mechanics and Engineering, Vol 186, pp. 311-338, 2000.
Miettinen K., Mäkelä M.M., Toivanen J. Numerical Comparison of Some Penalty-Based Constraint Handling Techniques in Genetic Algorithms, Journal of Global Optimization, Vol 27(4), pp. 427-446, 2003.

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