Aircraft range: A supersonic business jet MDO problem for derivative free optimization (DFO) benchmarking

C++ implementation of the multidisciplinary design optimization (MDO) problem described in:

Sobieszczanski-Sobieski, Agte and Sandusky, Bi-Level Integrated System Synthesis (BLISS). NASA/TM-1998-208715, 1998.

This problem has been specifically adapted for benchmarking derivative free optimization algorithms.

The blackbox executable performs a multidisciplinary design analysis (MDA) of a coupled system of disciplines: structures, aerodynamics and propulsion. The objective is maximize the aircraft range computed using the Breguet range equation. The discipline computation relies on analytical expressions typical for an early conceptual design stage.

Two variants of the blackbox are available, depending on how the MDA is managed for solving the disciplines coupling: (I) The coupling can be solved internally within the blackbox source code using a fixed-point iterative method. (II) Alternatively, the backward discipline coupling can be broken by introducing additional variables and consistency equality constraints. Note that the second variant necessitates an optimization algorithm capable of handling equality constraints effectively.

Blackbox evaluation

The blackbox C++ source code needs to be compiled using a C++ compiler to obtain a bb.exe binary file.

The source code of the two variants are in separate directories.

For a given set of variables in an input file, the outputs are obtained on the command line: ./bb.exe x01.txt. The outputs are obtained on the standard output. They are ordered, objective first, followed by inequality constraints and equality constraints (II only).

Problem specifications

For fixed point iterative variant (I)

• Input dimension: 10
• Number of inequality constraints: 10
• Inequality constraints must satisfy the form: gᵢ(x) ≤ 0

For this variant, the blackbox executable returns an extra output for the number of discipline analyses performed to solve the MDA within some accuracy.

For the consistency constraints variant (II) three additional variables and equality constraints are added

• Input dimension: 13
• Number of inequality constraints: 10
• Number of equality constraints: 3
• Consistency equality constraints (II) must satisfy the form: hᵢ(x) = 0.

Initial points

Ten different initial points are provided.

Variable bounds

All variables are scaled and bounded between 0 and 100. Please note that in the blackbox code, the variables are handled in full scale after reading.