- A Microsoft Excel macro with state-of-the art multi-parameter optimization algorithms that outperform the Excel Solver AddIn when the solution domain contains multiple local minima, discontinuous gradient, or regions with constant cost (no gradient).
- The application contains improved versions of the following two optimizers:
- An improved version of the Downhill Simplex algorithm by Nelder-Mead (abbreviated "NM"). The original NM algorithm is known to suffer from stagnation and premature convergence, but this improved version uses successive-approximation (SA-NM) with an extra pseudo-expansion point to guarantee convergence to minima. My own improvements to the SA-NM algorithm include adaptive/optimal factors for shape contraction/expansion/shrinking, an improved shrink method, and shape retension at domain boundaries, vastly improving convergence. For one-dimensional problems, Brent's method is used instead.
- An improved version of the Differential Evolution (abbreviated "DE") algorithm, specifically type "DE/rand-to-pbest/1" with archive, by Jingqiao & Arthur (JA-DE). My own improvements to JA-DE include self-adaptive optimal population size reduction and self-adaptive vector length and crossover likelihood. Each search starts with a population of good candidate points selected from a search of the whole multidimensional solution domain using a scrambled low-discrepancy Faure sequence. This algorithm is slower than NM, but more effective at finding global minima. For one-dimensional problems, pseudo-random Monte-Carlo search is used instead.
- GlobalMinimize lets you use the above two optimizers in three alternative ways.
- Nelder-Mead (NM) only. This is the fastest alternative. This guarantees to find the global minimum for solution domains that are smoothe and are unimodal, but also works very well in solution domains with discontinuous gradient.
- Differential-Evolution (DE) followed by Nelder-Mean (NM). This should be your default option, as it increases the likehood of finding the global minimum, and NM 'polishes off' the optimum with a high degree of accuracy.
- Indefinite repetitions of DE. This option is a Monte Carlo technique; it increases the chances of finding the global optimum for very 'noisy' solution domains with multiple local minima. You can stop the search at any time by pressing the 'stop' button, after which the NM is automatically run to 'polish off' the solution.
- GlobalMinimize is a normal workbook file, not an Excel AddIn, so it does not require any installation. To use GlobalMinimize, you must have two Excel workbooks open at the same time: the GlobalMinimize workbook and your own workbook file containing the cell value that you wish to minimize.
License and warranty
- Distributed free under the CC BY-ND 4.0 license.
- Provided with no warranty of any kind.
Author and copyright
- Buermen A., Tuma T. "Unconstrained derivative-free optimization by successive approximation". Journal of computational and applied mathematics, vol. 223, pp. 62-74, 2009
- Zhang, Jingqiao, and Arthur C. Sanderson. "JADE: adaptive differential evolution with optional external archive." IEEE Transactions on evolutionary computation 13.5 (2009): 945-958.
- Faure H and Tezuka S (2000) "Another random scrambling of digital (t,s)-sequences Monte Carlo and Quasi-Monte Carlo Methods" Springer-Verlag, Berlin, Germany (eds K T Fang, F J Hickernell and H Niederreiter)