Test Problems

Test Problems#

The test problems provided by moospread can be accessed via moospread.tasks. We include several commonly used multi-objective optimization benchmark problems.

The provided reference points (used for hypervolume computation) are suitable for specific settings. For other settings, a reference point can be specified when defining the problem (e.g., RE21(ref_point=[..., ...])). Please refer to our paper for recommended reference points for each optimization setting.

Problem

Variables

Objectives

Pareto Front Shape

Recommended Setting

ZDT1

\(d \ge 2\)

2

Convex

Online Setting

ZDT2

\(d \ge 2\)

2

Concave

Online Setting

ZDT3

\(d \ge 2\)

2

Disconnected

Online Setting

DTLZ2

\(d \ge 2\)

\(m \ge 3\)

Concave

Online Setting

DTLZ4

\(d \ge 2\)

\(m \ge 3\)

Concave

Online Setting

DTLZ7

\(d \ge 2\)

\(m \ge 3\)

Disconnected

Online Setting

RE21 (Four-bar truss design)

4

2

Convex

Offline Setting

RE33 (Disc brake design)

4

3

Offline Setting

RE34 (Vehicle crashworthiness design)

5

3

Offline Setting

RE37 (Rocket injector design)

4

3

Offline Setting

RE41 (Car side impact design)

7

4

Offline Setting

BraninCurrin

2

2

MOBO Setting

Penicillin

7

3

MOBO Setting

VehicleSafety

5

3

MOBO Setting