Mixing
Optimization of nonlinear $f(x)$ where $x$ is a vector of binary variables
$begingroup$
I'd like to find a solution (potentially approximate) to the problem
$$
max_{x_{i,j}} sum_{k=0}^Kleft[ 1 - prod_{i=1}^{I} left(1 - prod_{j=1}^{J}(1-b_{k,i,j} , x_{i,j}) right)right]
$$
where the parameters, $b_{k,i,j}$, are continuous on the interval $[0,1]$ and the variables which we are optimizing over $x_{i,j}$ can only take values 0 or 1.
It is a nonlinear, integer-valued, optimization problem. In addition the problem is quite big, I'm thinking of problems where $K$ = 1000, $I$ = 100,000, and $J$ = 20.
My thought for a solution method would be to first try a greedy algorithm, which I would then use to seed a genetic algorithm. But that method won't be able to put bounds on how sub-optimal the answer is. Given the structure of the problem, I thought it might be worth seeing if there is any mathematics that can be used to find a solution efficiently (or provide bounds on how sub-optimal a solution might be using a particular algorithm).
optimization nonlinear-optimization computational-mathematics
asked Jan 22 at 6:23
WetlabStudentWetlabStudent
3821318
$endgroup$
add a comment |
$begingroup$
I'd like to find a solution (potentially approximate) to the problem
$$
max_{x_{i,j}} sum_{k=0}^Kleft[ 1 - prod_{i=1}^{I} left(1 - prod_{j=1}^{J}(1-b_{k,i,j} , x_{i,j}) right)right]
$$
where the parameters, $b_{k,i,j}$, are continuous on the interval $[0,1]$ and the variables which we are optimizing over $x_{i,j}$ can only take values 0 or 1.
It is a nonlinear, integer-valued, optimization problem. In addition the problem is quite big, I'm thinking of problems where $K$ = 1000, $I$ = 100,000, and $J$ = 20.
My thought for a solution method would be to first try a greedy algorithm, which I would then use to seed a genetic algorithm. But that method won't be able to put bounds on how sub-optimal the answer is. Given the structure of the problem, I thought it might be worth seeing if there is any mathematics that can be used to find a solution efficiently (or provide bounds on how sub-optimal a solution might be using a particular algorithm).
optimization nonlinear-optimization computational-mathematics
asked Jan 22 at 6:23
WetlabStudentWetlabStudent
3821318
$endgroup$
$begingroup$
have you tried branch and bound?
$endgroup$
– pointguard0
Jan 22 at 6:56
add a comment |
$begingroup$
I'd like to find a solution (potentially approximate) to the problem
$$
max_{x_{i,j}} sum_{k=0}^Kleft[ 1 - prod_{i=1}^{I} left(1 - prod_{j=1}^{J}(1-b_{k,i,j} , x_{i,j}) right)right]
$$
where the parameters, $b_{k,i,j}$, are continuous on the interval $[0,1]$ and the variables which we are optimizing over $x_{i,j}$ can only take values 0 or 1.
It is a nonlinear, integer-valued, optimization problem. In addition the problem is quite big, I'm thinking of problems where $K$ = 1000, $I$ = 100,000, and $J$ = 20.
My thought for a solution method would be to first try a greedy algorithm, which I would then use to seed a genetic algorithm. But that method won't be able to put bounds on how sub-optimal the answer is. Given the structure of the problem, I thought it might be worth seeing if there is any mathematics that can be used to find a solution efficiently (or provide bounds on how sub-optimal a solution might be using a particular algorithm).
optimization nonlinear-optimization computational-mathematics
asked Jan 22 at 6:23
WetlabStudentWetlabStudent
3821318
$endgroup$
I'd like to find a solution (potentially approximate) to the problem
$$
max_{x_{i,j}} sum_{k=0}^Kleft[ 1 - prod_{i=1}^{I} left(1 - prod_{j=1}^{J}(1-b_{k,i,j} , x_{i,j}) right)right]
$$
where the parameters, $b_{k,i,j}$, are continuous on the interval $[0,1]$ and the variables which we are optimizing over $x_{i,j}$ can only take values 0 or 1.
It is a nonlinear, integer-valued, optimization problem. In addition the problem is quite big, I'm thinking of problems where $K$ = 1000, $I$ = 100,000, and $J$ = 20.
My thought for a solution method would be to first try a greedy algorithm, which I would then use to seed a genetic algorithm. But that method won't be able to put bounds on how sub-optimal the answer is. Given the structure of the problem, I thought it might be worth seeing if there is any mathematics that can be used to find a solution efficiently (or provide bounds on how sub-optimal a solution might be using a particular algorithm).
optimization nonlinear-optimization computational-mathematics
optimization nonlinear-optimization computational-mathematics
asked Jan 22 at 6:23
WetlabStudentWetlabStudent
3821318
asked Jan 22 at 6:23
WetlabStudentWetlabStudent
3821318
asked Jan 22 at 6:23
WetlabStudentWetlabStudent
3821318
asked Jan 22 at 6:23
WetlabStudentWetlabStudent
3821318
asked Jan 22 at 6:23
WetlabStudentWetlabStudent
3821318
3821318
$begingroup$
have you tried branch and bound?
$endgroup$
– pointguard0
Jan 22 at 6:56
add a comment |
$begingroup$
have you tried branch and bound?
$endgroup$
– pointguard0
Jan 22 at 6:56
$begingroup$
have you tried branch and bound?
$endgroup$
– pointguard0
Jan 22 at 6:56
$begingroup$
have you tried branch and bound?
$endgroup$
– pointguard0
Jan 22 at 6:56
add a comment |
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$begingroup$
have you tried branch and bound?
$endgroup$
– pointguard0
Jan 22 at 6:56