# Optimisation of 2D Toy Functions Using Scilab

0
5598 Scilab has solutions for standard and large scale optimisation problems in engineering. It provides algorithms to solve constrained, unconstrained, continuous and discrete problems.

Optimisation occurs in nature all around us. Water droplets optimise themselves into a sphere, which is the least possible area for any given volume. Migrating flock of birds optimises its use of energy by flying in a V-shaped formation, which reduces air resistance. We continuously learn from nature to artificially engineer things like the honeycomb structure or the flight formation of fighter jets.

To optimise engineering objectives, we use toy functions that are noisy, non-linear and two-dimensional as benchmarks. Scilab is one of the open source platforms in which three-dimensional (3D) plots are possible. Numerical studies followed by visual interpretation help us to understand the efficiency of proposed algorithms. Real world assumptions of engineering problems are bound to truncate broad assumptions into narrow band, making it difficult to solve them using conventional methods. These problems are solved using algorithms benchmarked with toy functions.

Some toy functions from Scilab
In a broad sense, to maximise or minimise an objective function while satisfying some constraints is said to be optimisation. Some of the main toy functions used are:
1. Ackley’s function
2. Levi function
3. Holder-table function
4. Buckin function
The 3D plots for these functions are shown in Figures 1, 2, 3 and 4, respectively, and the equations of each function are shown in Figure 5. 