# A comparison of global optimization algorithms with standard benchmark functions and real-world applications using Energy Plus

## Abstract

There is an increasing interest in the use of computer algorithms to identify combinations of parameters which optimise the energy performance of buildings. For such problems, the objective function can be multi-modal and needs to be approximated numerically using building energy simulation programs. As these programs contain iterative solution algorithms, they introduce discontinuities in the numerical approximation to the objective function. Metaheuristics often work well for such problems, but their convergence to a global optimum cannot be established formally. Moreover, different algorithms tend to be suited to particular classes of optimization problems. To shed light on this issue we compared the performance of two metaheuristics, the hybrid CMA-ES/HDE and the hybrid PSO/HJ, in minimizing standard benchmark functions and real-world building energy optimization problems of varying complexity. From this we find that the CMA-ES/HDE performs well on more complex objective functions, but that the PSO/HJ more consistently identifies the global minimum for simpler objective functions. Both identified similar values in the objective functions arising from energy simulations, but with different combinations of model parameters. This may suggest that the objective function is multi-modal. The algorithms also correctly identified some non-intuitive parameter combinations that were caused by a simplified control sequence ofmore »

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- Environmental Energy Technologies Division

- OSTI Identifier:
- 988173

- Report Number(s):
- LBNL-3909E

TRN: US201018%%294

- DOE Contract Number:
- DE-AC02-05CH11231

- Resource Type:
- Journal Article

- Journal Name:
- Modelica 2009

- Additional Journal Information:
- Conference: Modelica 2009

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 32; ALGORITHMS; APPROXIMATIONS; BENCHMARKS; COMPUTERS; CONVERGENCE; ENERGY SYSTEMS; OPTIMIZATION; PERFORMANCE; SIMULATION; optimisation; algorithm; application using EnergyPlus; Covariance Matrix Adaptation Evolution Strategy Algorithm (CMA-ES) and Hybrid Differential Evolution (HDE); Particle Swarm Optimisation (PSO) and Hooke-Jeeves (HJ); building energy minimisation

### Citation Formats

```
Kamph, Jerome Henri, Robinson, Darren, and Wetter, Michael.
```*A comparison of global optimization algorithms with standard benchmark functions and real-world applications using Energy Plus*. United States: N. p., 2009.
Web.

```
Kamph, Jerome Henri, Robinson, Darren, & Wetter, Michael.
```*A comparison of global optimization algorithms with standard benchmark functions and real-world applications using Energy Plus*. United States.

```
Kamph, Jerome Henri, Robinson, Darren, and Wetter, Michael. Tue .
"A comparison of global optimization algorithms with standard benchmark functions and real-world applications using Energy Plus". United States. https://www.osti.gov/servlets/purl/988173.
```

```
@article{osti_988173,
```

title = {A comparison of global optimization algorithms with standard benchmark functions and real-world applications using Energy Plus},

author = {Kamph, Jerome Henri and Robinson, Darren and Wetter, Michael},

abstractNote = {There is an increasing interest in the use of computer algorithms to identify combinations of parameters which optimise the energy performance of buildings. For such problems, the objective function can be multi-modal and needs to be approximated numerically using building energy simulation programs. As these programs contain iterative solution algorithms, they introduce discontinuities in the numerical approximation to the objective function. Metaheuristics often work well for such problems, but their convergence to a global optimum cannot be established formally. Moreover, different algorithms tend to be suited to particular classes of optimization problems. To shed light on this issue we compared the performance of two metaheuristics, the hybrid CMA-ES/HDE and the hybrid PSO/HJ, in minimizing standard benchmark functions and real-world building energy optimization problems of varying complexity. From this we find that the CMA-ES/HDE performs well on more complex objective functions, but that the PSO/HJ more consistently identifies the global minimum for simpler objective functions. Both identified similar values in the objective functions arising from energy simulations, but with different combinations of model parameters. This may suggest that the objective function is multi-modal. The algorithms also correctly identified some non-intuitive parameter combinations that were caused by a simplified control sequence of the building energy system that does not represent actual practice, further reinforcing their utility.},

doi = {},

journal = {Modelica 2009},

number = ,

volume = ,

place = {United States},

year = {2009},

month = {9}

}