Home

Modified Double Sum

Two dimensional view

One dimensional view

Function

Latex

A minimization problem:

$$f(x_1 \cdots x_n) = \sum_{i=1}^n (\sum_{j=1}^i (x_j - j)^2)$$

$$-10.24 \leq x_i \leq 10.24$$

$$\text{minimum at }f(1, 2, 3, \cdots, n) = 0$$

Python

def fitnessFunc(self, chromosome):
	"""F4 Modified double sum
	unimodal, asymmetric, inseparable"""
	fitness = 0
	for i in range(len(chromosome)):
		for j in range(i+1):
			fitness += (chromosome[j] - (j+1))**2
	return fitness

Sources

The following may or may not contain the originator of this function.

A novel distributed genetic algorithm implementation with variable number of islands
@inproceedings{varIslandNum07,
author = {Takuma Jumonji and Goutam Chakraborty and Hiroshi Mabuchi and Masafumi Matsuhara},
title = {A novel distributed genetic algorithm implementation with variable number of islands},
booktitle = {IEEE Congress on Evolutionary Computation},
year = {2007},
pages = {4698--4705},
doi = {10.1109/CEC.2007.4425088},
masid = {4737000}
}


Notes