Cat-Suite: a collection of optimization problems with categorical and quantitative variables for benchmarking

Under construction!

This repository contains 32 mixed-variable analytical problems with categorical and quantitative variables for benchmarking. Half of the problems are constrained.

Summary and problem characteristics

The following two tables present the characteristics of the unconstrained and constrained problems, respectively. The star symbol represents a user-chosen parameter.

Table 1: Unconstrained test problems.

| Name | $n^{\text{cat}}$ | $\ell$ | $n^{\text{int}}$ | $n^{\text{cont}}$ | Smooth | Ref. | Original problem | |---------|------------|--------|------------------|--------------------|--------|------|----------------------| | Cat-1 | 2 | 9 | 2 | $\star$ | No | [2] | Ackley | | Cat-2 | 2 | 9 | 2 | 3 | No | [2] | Beale | | Cat-3 | 2 | 4 | 2 | 2 | Yes | [5] | Augmented-Branin | | Cat-4 | 2 | 4 | 2 | 4 | No | [2] | Bukin-6 | | Cat-5 | 1 | 6 | 1 | 3 | Yes | [3] | EVD-52 | | Cat-6 | 2 | 9 | 0 | 2 | Yes | [5] | Goldstein | | Cat-7 | 3 | 16 | 3 | 2 | No | [2] | Goldstein-Price | | Cat-8 | 1 | 4 | 1 | 5 | Yes | [3] | HS78 | | Cat-9 | 2 | 9 | 2 | $\star$ | No | [2] | Rastrigin | | Cat-10 | 2 | 6 | 2 | $\star$ | No | [2] | Rosenbrock | | Cat-11 | 1 | 4 | 1 | 4 | Yes | [3] | Rosen-Suzuki | | Cat-12 | 1 | 5 | $\star$ | $\star$ | No | [2] | Styblinski-Tang | | Cat-13 | 1 | 10 | 0 | 4 | Yes | [4] | Toy | | Cat-14 | 1 | 10 | 0 | 8 | No | [4] | Toy | | Cat-15 | 1 | 5 | 3 | 4 | Yes | [3] | Wong-1 | | Cat-16 | 2 | 9 | 2 | $e$ | No | [2] | Zakharov |

Table 2: Constrained test problems.

| Name | $n^{\text{cat}}$ | $\ell$ | $n^{\text{int}}$ | $n^{\text{cont}}$ | $m$ | Smooth | Ref. | Original problem | |---------------|------------|--------|------------------|--------------------|-----|--------|------|------------------------| | Cat-cstrs-1 | 2 | 9 | 2 | 3 | 3 | No | [2] | Beale | | Cat-cstrs-2 | 2 | 4 | 2 | 2 | 1 | Yes | [5] | Augmented-Branin | | Cat-cstrs-3 | 2 | 9 | 2 | 4 | 2 | No | [2] | Bukin-6 | | Cat-cstrs-4 | 1 | 4 | 4 | 4 | 3 | Yes | [3] | Dembo-5 | | Cat-cstrs-5 | 1 | 6 | 1 | 3 | 1 | No | [3] | EVD-52 | | Cat-cstrs-6 | 2 | 9 | 2 | 3 | 4 | Yes | [1] | G-09 | | Cat-cstrs-7 | 2 | 9 | 0 | 2 | 1 | Yes | [5] | Goldstein | | Cat-cstrs-8 | 2 | 25 | 2 | 2 | 2 | Yes | [2] | Himmelblau | | Cat-cstrs-9 | 2 | 4 | 3 | 5 | 4 | Yes | [3] | HS-114 | | Cat-cstrs-10 | 1 | 3 | 2 | 4 | 6 | Yes | [3] | Pentagon | | Cat-cstrs-11 | 1 | 8 | 2 | 2 | 3 | Yes | [1] | Pressure-Vessel | | Cat-cstrs-12 | 2 | 25 | 1 | 2 | 2 | Yes | [1] | Reinforced-Concrete | | Cat-cstrs-13 | 2 | 6 | 2 | $\star$ | 1 | No | [2] | Rosenbrock | | Cat-cstrs-14 | 1 | 5 | $\star$ | $\star$ | 2 | No | [2] | Styblinski–Tang | | Cat-cstrs-15 | 1 | 10 | 0 | 4 | 2 | Yes | [4] | Toy | | Cat-cstrs-16 | 1 | 6 | 4 | 6 | 3 | Yes | [3] | Wong-2 |

Best known feasible values: 13 June 2025

Table 3: Best known values for unconstrained problems.

| Problem | $f(x_{\text{best}})$ | |-----------|----------------------| | Cat-1 | 21.71 | | Cat-2 | 3.12E-12 | | Cat-3 | 4.87 | | Cat-4 | 1.06E4 | | Cat-5 | -31250.5 | | Cat-6 | 38.08 | | Cat-7 | 5 | | Cat-8 | -152 | | Cat-9 | -2 | | Cat-10 | 1.03 | | Cat-11 | -113.71 | | Cat-12 | -102.51 | | Cat-13 | -0.71 | | Cat-14 | 0.14 | | Cat-15 | -1942.82 | | Cat-16 | 1 |

Table 4: Best known feasible values for constrained problems.

| Problem | $f(x_{\text{best}})$ | |---------------|----------------------| | Cat-cstrs-1 | 1.27E-03 | | Cat-cstrs-2 | -5.1273 | | Cat-cstrs-3 | 4.30E-03 | | Cat-cstrs-4 | -24245741.22 | | Cat-cstrs-5 | -77237.8 | | Cat-cstrs-6 | 555.58 | | Cat-cstrs-7 | 38.8 | | Cat-cstrs-8 | 10 | | Cat-cstrs-9 | -1256527.34 | | Cat-cstrs-10 | 1.47E-09 | | Cat-cstrs-11 | 6184.75 | | Cat-cstrs-12 | 303.4 | | Cat-cstrs-13 | 19210.88 | | Cat-cstrs-14 | -66.68 | | Cat-cstrs-15 | 3 | | Cat-cstrs-16 | -9721.58 |

References

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[4] M. Munoz Zuniga and D. Sinoquet.
Global optimization for mixed categorical-continuous variables based on Gaussian process models with a randomized categorical space exploration step.
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[5] J. Pelamatti, L. Brevault, M. Balesdent, E.-G. Talbi, and Y. Guerin.
Efficient global optimization of constrained mixed variable problems.
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