New answers tagged reference-request
5
If I understand correctly, you can obtain the desired linear constraints via conjunctive normal form. Explicitly, suppose $f(\bar{x}_1,\dots,\bar{x}_n)=1$, and let $S_0 = \{j\in\{1,\dots,n\}:\bar{x}_j = 0\}$ and $S_1 = \{j\in\{1,\dots,n\}:\bar{x}_j = 1\}$. You want to enforce $$\left[\left(\bigwedge_{j\in S_0} \lnot x_j\right) \bigwedge \left(\bigwedge_{j\...
5
There is a good reference that has been published by Alireza Soroudi.
Power System Optimization Modeling in GAMS
3
The state-of-the-art method for solving the vehicle routing problem with split deliveries is in fact LBBD as can be seen in the following papers:
https://www.sciencedirect.com/science/article/abs/pii/S037722171400352X
https://pubsonline.informs.org/doi/abs/10.1287/trsc.2018.0825
Although the authors do not refer to their algorithms as LBBD, their methods can ...
2
For the case of mixed integer programs, I would recommend the following paper:
Klotz, E., & Newman, A. M. (2013). Practical guidelines for solving difficult mixed integer linear programs. Surveys in Operations Research and Management Science, 18(1-2), 18-32.
As the abstract says:
"Even with state-of-the-art hardware and software, mixed integer ...
3
There's also the Octeract Reformulator repository, where we host a growing collection of scripts to automatically apply reformulations to non-linear problems, e.g.:
from octeract import *
# Linearize bilinear term x*y where x,y binary
# =============================================
# x*y = w
# w <= x
# w <= y
# x + y - 1 <= w
# 0 <= w <= 1
# ...
3
I would also add "Optimization in Engineering" as a reference. It offers a good overview on LPs, MILPs and convex programming, focusing on applications. It is also a good resource in best practises, see for example Chapter 3.3 "Linearizing Nonlinearities Using Binary Variables".
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