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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