Here we’re looking at the 1976 paper “Optimized relative step size random searches” (ORSSRS). The authors build on the earlier FSSRS and ASSRS. FSSRS used a step size of fixed distance to define the hypersphere within which samples would be taken. ASSRS adapts the step size based on the successful and failed samples. ORSSRS proposes a more advanced method for selecting the step size as the optimization progresses.

- Given fitness function “
*f”* - Select a starting point
**x**at random within the solution space. - Let
**best**=**x**. - Generate vector
**d**, a random vector of length**r**(within the dimensions of the solution space). - Calculate a new position
**x**from**x = best + d**. - If
*f(***x***) < f(***best***)*, replace**best**with**x**, replace**r**with**r-δr**(reduce the step size), and continue (from step 4) until termination criteria is reached. - Otherwise, reverse the direction of the search by calculating a new position
**x**from**x = best – d**. - If
*f(***x***) < f(***best***)*, replace**best**with**x**, replace**r**with**r-δr**(reduce the step size), and continue (from step 4) until termination criteria is reached.

The user must provide the initial value of **r **(σ⁰ is used in the paper).

**δr **(α_{r} is used in the paper) is given by a complex derivation provided in the paper. I must confess that I did not fully understand the derivation, so I won’t foster any further confusion on your part by attempting a poor explanation here.

# References

- Schrack 1976 –
*Optimized relative step size random searches*– Schrack, G. & Choit, M. Mathematical Programming (1976) 10: 230. Link.