A comparison of building energy optimization problems and mathematical test functions using static fitness landscape analysis

ABSTRACT

Computational optimization is gaining popularity in energy-efficient building design. For choosing an algorithm or setting its parameters, often mathematical test functions are employed. This study, therefore, investigates differences and similarities between such test functions and building energy optimization (BEO) problems. A fitness landscape analysis (FLA) is conducted with existing and newly proposed metrics, shedding light on the characteristics of optimization problems. We use the COCO testbed and compare it to BEO problems from the literature. Results suggest that for most FLA metrics there is no statistical difference between the set of test functions and BEO problems. Also, characterizing an archetypical BEO problem appears infeasible due to the high heterogeneity we can observe in FLA metric scores. However, using hierarchical clustering we can identify similarities between test functions and groups of BEO problems. Such knowledge may be exploited for selecting or calibrating an algorithm, thus facilitating its effective use in practice.

KEYWORDS:

• Fitness landscape analysis
• sensitivity analysis
• simulation-based optimization
• building energy simulation
• EnergyPlus

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Christoph Waibel  http://orcid.org/0000-0001-6077-1411

Notes

1. He describes the landscapes as projections of multi-dimensional problems onto the X- and Y-axes.

2. Version 8.5.0.

3. ϵ in % gives the cost values normalized by the minimal and maximal cost values found by all random walks and the LP${}_{\mathrm{T}}$ sequence.

4. We perform mean normalization before the PCA.

5. As we did for the PCA, the data has been mean normalized before the clustering.

Additional information

Funding

This work was supported by the Swiss Commission for Technology and Innovation within SCCER FEEB&D [grant number CTI 1155002539]; and by the Swiss Competence Center for Energy and Mobility project SECURE [grant number CCEM 914].