Z-opt

General-Purpose Optimization

Z-opt is a flexible optimization package that can be coupled with virtually any external software through ASCII input/output files or other communication formats. While its primary role is material parameter identification—where it finds the optimal parameter set that minimizes the distance between experimental observations and numerical simulations—it is versatile enough to handle a wide range of optimization problems.

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Applications and Flexibility

Z-opt input files are highly adaptable, making it possible to process data from:

• Standard mechanical tests (tension, creep, uniaxial or multiaxial loading).
• Hybrid databases combining element- or structure-level information.

In practice, Z-opt can:

• Calibrate material parameters by driving external solvers such as Z-sim or any other code.
• Optimize friction coefficients in contact models.
• Estimate convection parameters in thermal simulations.
• Carry out shape optimization tasks.

The workflow begins with an initial parameter set. Z-opt then computes the least-square error between experimental data (stored in files) and simulated results. Based on the chosen optimization strategy, the parameters are updated iteratively until convergence toward an optimal solution.

Standalone Analytical Mode

When the simulated response can be represented analytically, Z-opt can operate without external software. In this case, it directly evaluates the analytical function and runs the optimization internally.

Optimization Algorithms

Z-opt provides a rich set of optimization strategies, covering both gradient-based and heuristic approaches:

• Gradient-driven methods:
  • Levenberg–Marquardt, highly efficient for least-square minimization problems.
  • Sequential Quadratic Programming (SQP), a robust method for constrained optimization.
• Heuristic methods:
  • Simplex method, which does not require gradient information and is well-suited for strongly nonlinear problems.
  • Genetic algorithm, capable of escaping local minima in non-convex landscapes, insensitive to starting values, and able to produce multiple candidate solutions.

In short, Z-opt combines versatility, robustness, and adaptability, making it a powerful tool for parameter calibration and general-purpose optimization across many scientific and engineering applications.