how can i write the objective function with constraint given?

hi friends, can anyone help me where can i refer and follow step by step how can i solve this problem.. b'coz i'm not very good in programming i would like to learn more about it.. i have refer this paper to see the result, but i'm totally lost where to start and how to compute this.

P to represent the storage location of each split, and the element pij indicates the storage location of split di, where integer pij ∈ {1; 2; : : : ;N}, in which i = 1; 2; · · · ;m and j = 1; 2; 3.

vector S = {s1; s2; · · · ; sm+r} to represent the final task scheduling scheme, where the ith element indicates that task ti is assigned on server msi , where 1 ≤ si ≤ N and i = 1; 2; · · · ;m + r.

objective function indicates the minimum sum --> NΣk=1(COk − (CSk + NMk × CM + NRk × CR))^2

subject to

1)S{ si ∈ {pi1; pi2; pi3} if i = 1; : : : ; m; sj ∈ {1; 2; : : : ;N} if j = m + 1; : : : ;m + r:

2) NMk = {si si = k; i = 1; 2; : : : ;m}|; where k = 1; 2; : : : ;N:

3)NRk = {si si = k; i = m + 1; : : : ;m + r}|;where k = 1; 2; : : : ;N:

4)CSk + NMk × CM + NRk × CR ≤ 1; where k = 1; 2; : : : ;N:

Constraints (1) expresses that if a map task ti (where i = 1; 2; · · · ;m) is assigned on server msi , then server msi must have stored its corresponding input data.

what i did for the 1st step is

function f = objfun(x)

k=1:N;

f = sum (CO_k - (CS_k + (NM_k * CM)+(NR_k * CR))).^2;

and for constraint part i'm totally stuck and dont know where can i refer to

function [c,ceq] = confun(x)

subject to

S(i): p(i1);p(i2);p(i3);

            S(j): 1:N;

%nonlinear inequality constraints

.....

hope i can find solution and example to do it in .m file coding thank you.

Answer 1

[Alan Weiss]

This is a mixed integer nonlinear programming problem. The only solver in MATLAB toolboxes that addresses this type of problem is ga.

You can take a look at the documentation for integer programming, or an extensive example.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation