Structural Synthesis Using The MINLP
Optimization Approach
Author(s)
S. Kravanja
Abstract
This paper presents a structural synthesis using the Mixed-Integer Non-Linear
Programming (MINLP) approach. The MINLP is a combined
discrete/continuous optimization technique, where discrete binary 0-1 variables
are defined for optimization of discrete alternatives and continuous variables for
optimization of parameters. The MINLP optimization to a structural synthesis is
performed through three steps: i.e. the generation of a mechanical superstructure,
the modelling of an MINLP model formulation and the solution of the defined
MINLP problem. As the discrete/continuous optimization problems are usually
non-convex and highly non-linear, the Modified Outer-Approximation/Equality-
Relaxation (OA/ER) algorithm is selected to be used for the optimization. The
accompanied Linked Multilevel Hierarchical Strategy (LMHS) is developed to
accelerate the convergence of the above-mentioned algorithm. Some examples
are presented at the end of the paper.
1 Introduction
The paper presents structural synthesis using Mixed-Integer Non-Linear
Programming (MINLP) approach. The MINLP handles with continuous and
discrete binary 0-1 variables simultaneously. While continuous variables are
defined for the continuous optimization of parameters (dimensions, stresses,
strains, weights, costs, etc.), discrete variables are used to express discrete
decisions, i.e. usually the existence or non-existence of structural elements inside
the defined structure. Different materials, standard dimensions and rounded
continuous dimensions may also be defined as discrete alternatives. Since
continuous and discrete optimizations are carried out simultaneously, the MINLP
approach also finds optimal continuous parameters, structural topology, material,
standard and rounded dimensions simultaneously.
Keywords
Related Book
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