NIMBUS is a Nondifferentiable Interactive Multiobjective BUndle-based optimization System

NIMBUS has been developed at the University of Jyväskylä, Department of Mathematical Information Technology. This is a fourth version of the WWW interface.

NIMBUS is suitable for both differentiable and nondifferentiable multiobjective and single objective optimization problems subject to nonlinear and linear constraints with bounds for the variables. The problems to be solved are of the form

where k is the number of the objective functions, m is the number of the nonlinear constraints, decision variable vector x and its lower and upper bounds are n-dimensional vectors, b is an l-dimensional vector and A is an l x n-dimensional matrix of linear constraint coefficients. Integer variables can also be handled.

When the objective functions are to be minimized, the user is assumed to prefer less to more in the objective function values.

Pareto optimality and weak Pareto optimality are used as optimality concepts.

In the NIMBUS method, the idea is that the user examines the values of the objective functions calculated at a current solution and divides the objective functions into up to five classes. The classes are functions whose values

A new subproblem is formed according to the classification and the connected information. This problem is solved alternatively by a multiobjective proximal bundle (MPB) method or genetic algorithms.

The flowchart of the NIMBUS algorithm is the following.

Note: Every WWW-NIMBUS -page includes a help page.

For further information, contact

Current NIMBUS usage statistics

Old NIMBUS usage statistics