9 votes
Accepted

How to Model Path Being Only Through Adjacent Cells

A standard approach for modeling a path from source $s$ to sink $t$ in a directed graph with node set $N$ and arc set $A$ is to let continuous variable $x_{ij} \ge 0$ represent the flow along the arc $...
user avatar
  • 22.2k
8 votes
Accepted

Practical, Short example of Mixed Integer Conic Program

Your opening sentence could be more accurately written as Mixed Integer Conic Programs are a family of Mixed Integer Programs whose continuous relaxations are (convex) conic programs. One easy to ...
user avatar
5 votes

Additional resources for this type of problem formulation

The model looks really linear to me. After substituting out $V_{i,j}$ you have basically terms $x_{i,j}\cdot x_{k,j}$. Solvers may linearize that automatically or you must do it yourself. My guess is ...
user avatar
3 votes

Docplex : How can I get the objective value of the relaxation of an MILP?

Disclaimer: I do not use Docplex (nor Python). That said, the following is in the documentation for LinearRelaxer: Some constructs are not relaxable, for example, piecewise-linear expressions, SOS ...
user avatar
  • 29.7k
3 votes

Approximate Speed-Up With Increasing Cores?

“It depends” absolutely is the answer and while I won’t give you any numbers, I might provide a brief insight into on what it could depend: Whereas continuous LPs gain little from more cores (Gurobi ...
user avatar
3 votes

Approximate Speed-Up With Increasing Cores?

I don't know that anyone can give a meaningful answer. The speedup is definitely a sublinear function of the number of cores or number of threads, and is also problem-specific (and solver-specific). ...
user avatar
  • 29.7k
3 votes
Accepted

Relaxing a relation between variables if one of them reaches its maximal value

Let variable $x_t\in[0,\bar{r}_t]$ be the level of tank $t$, introduce binary variable $y_t$ to indicate whether tank $t$ is full, and introduce variable $z\in[0,r]$. The following constraints do the ...
user avatar
  • 22.2k
3 votes

Is there any open source solver for MILP that can output the top N best results instead of the global best?

No, i am not aware of such a solver. However sequentially excluding previously optimal results comes with an additional pitfall: If the solver discovered symmetries and did cut them away you also ...
user avatar
2 votes

Transfer an integer model to binary

To avoid confusion, I will use $\bar{w}$ for the original (integer) $w$ variable. Assuming you have a constant upper limit $T$ on possible waiting time, you can define your new binary variables via ...
user avatar
  • 29.7k
2 votes

Multiprocessor Scheduling Problem: How to modify some constraints after variable changing?

The condition (*), that every job is assigned to exactly one machine, simply requires $$\sum_{i=k}^n z_{i,k} \ge 1 \quad \forall i=1,\dots,n.$$ That ensures that every job belongs to a cluster. It ...
user avatar
  • 29.7k
1 vote

Docplex : How can I get the objective value of the relaxation of an MILP?

As a simple example to work around what you want the following template would be useful: ...
user avatar
  • 5,833
1 vote
Accepted

gurobi bigM constraint vs. epsilon

Changing the second inequality in (1) as proposed would mean that $w_i \notin (w_j - \epsilon, w_j + \epsilon).$ It would shrink the feasible region in a way that might be detrimental to the solution ...
user avatar
  • 29.7k

Only top scored, non community-wiki answers of a minimum length are eligible