The movie above shows an animation of the hierarchical Đµxploration of 2D parameter space by **ABAGUS** for the case of a simple parabola test model (keyword '**test=1**'). The acceptable parameter space solution is in the area with radius of about 14 from the global minimum at (0,0) with objective function (OF) cutoff value below 160 (keyword '**cutoff=160**'). The parameter space domain is [-100,100] (keyword '**pardomain=200**') for both model parameters. Only, [-20,20] range is shown in the figure below.

**ABAGUS** performs a series of analyses with different discretization sizes: 10, 5, 2.5, 1.25, etc. The location of the agents is shown by cyan stars (the agents explore the parameter space outside of the shown domain as well.

Response surface of the parabola test function:

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**ABAGUS** performance is compared to **MADS** Monte Carlo analysis using Improved Distributed Latin Hypercube Sampling (**IDLHS**).

Comparison of both methods based on the number of functional evaluations:

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The results demonstrate that **ABAGUS** outperforms the Monte Carlo analysis using Improved Distributed Latin Hypercube Sampling (**IDLHS**).

Comparisons are performed between **LM** (Levenberg-Marquardt), PSO (Particle Swarm Optimization), TRIBES , hPSO and **Squads** to solve **Rosenbrock** and **Griewank** test problem with different dimensionality (i.e. number of adjustable parameters).

Figures below present boxplots for the number of function evaluations for successful runs for 2D, 5D, and 10D **Rosenbrock** and **Griewank** test functions, respectively. In the figures, the boxes represent the 25th to 75th percentile ranges, the bars inside of the boxes represent the median values, and the whiskers represent the minimum and maximum values. The fraction of successful runs out of the attempted runs are presented above the boxes.

The **robustness** of the strategies is defined as the percentage of successful runs.

The **efficiency** of the strategies is defined by the number of functional evaluations required to achieve the global minimum.

**Squads** is as robust or more robust than the other tested strategies (**LM**, PSO, TRIBES, and hPSO) in all cases.

**Squads** is more efficient than PSO, TRIBES, and hPSO in all cases.

For the 2D, 5D, and 10D **Rosenbrock** test functions, **Squads** has comparable efficiency to **LM**.

However, in these cases, the robustness of **Squads** (**100%**) is considerably better than the robustness of **LM** (less than **36%**).

For the 2D, 5D, and 10D **Griewank** test functions, **Squads** is less efficient than **LM** but depending on the initial guesses may converge for the same number of functional evaluations as **LM**.

However, in these cases, the robustness of **Squads** (grater than **80%**) is considerably better than the robustness of **LM** (less than **11%**).

**Squads** is observed to have the best performance when both robustness and efficiency are taken into consideration than the other strategies.