8
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Is there a canonical name for Score Folding (multiplying a priority soft constraint by a big weight)?
It's not exactly the same thing, but very close: in goal programming, using a weighted combination of the deviations from goals is often called "Archimedean" (as in "Archimedean" goal programming, or ...
- 40.1k
7
votes
Is there a canonical name for Score Folding (multiplying a priority soft constraint by a big weight)?
The act of moving soft constraint into the objective function using penalties is closely related to Lagrangian Relaxation and Lagrangian Multipliers.
The method penalizes violations of [...] ...
- 2,866
6
votes
How to transform this BIP into LP with the help of penalty function?
You can't. If there were a way to transform a MIP to an LP it would mean MIPs can be solved in polynomial time among many other things (edit: not exactly, see below). You can relax the binaries to ...
- 12.2k
6
votes
Accepted
Difficulties with Finding a Proper Penalty Value for the Progressive Hedging Algorithm
This problem is addressed in some detail in Section 2.1 of the paper Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems by Watson and Woodruff (a non-...
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4
votes
How can I include a penalty to my (linear) model?
You cannot do this within a linear program. If the penalty is a fixed amount (not proportional to the size of $X$ or $Y$), and assuming you can infer upper bounds $M_X$ and $M_Y$ on $X$ and $Y,$ you ...
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4
votes
Accepted
How to model a penalty for exceeding a threshold in a nonlinear optimization problem using IPOPT?
What you want can be expressed mathematically as
$$\text{Penalty} = \lambda * \text{max(}(P_m - P_c)/P_c,0)$$
In this problem, max is being used in a convex manner, so can be handled without ...
- 13.8k
4
votes
Is there a canonical name for Score Folding (multiplying a priority soft constraint by a big weight)?
I’m not sure I’ve heard a canonical name, but that sounds like a multi-objective optimization problem where you’re minimizing the sum of weighted deviations. The weights are based on the constraint ...
- 1,317
4
votes
Is there a canonical name for Score Folding (multiplying a priority soft constraint by a big weight)?
One common way I've seen in the literature to deal with such cases is to multiply the priority constraint by a big weight and add it into the fitness function alongside the lower priority constraint.
...
- 2,130
4
votes
How to transform this BIP into LP with the help of penalty function?
If $A$ is totally unimodular, you can replace the binary restrictions on $b$ with $0 \le b_i \le 1$, and solve as an LP. See https://mathoverflow.net/questions/31367/proving-that-a-binary-matrix-is-...
- 13.8k
3
votes
Extract info from Gurobi binary variables during run-time
We can't modify the optimisation problem while it's being solved. What you could try instead is to solve once (maybe with a lax convergence criterion), add/update the constraints based on that ...
- 12.2k
3
votes
Accepted
Optimization Problem with a Penalty Factor
You have two separate objectives: maximizing terminal value $A$ and minimizing (or at least reducing) initial investment $P.$ You might want to search the web using the phrases "bicriterion ...
- 40.1k
3
votes
Accepted
Assignment Problem - Students and teachers
As in the comments: as it stands, the problem is infeasible. For student 3, they could never be given a class with any teacher, because they have never had at least two classes with any teacher. You ...
- 484
3
votes
How to transform this BIP into LP with the help of penalty function?
This might be a candidate for a binary decision diagram (BDD) approach. It involves building a layered digraph. Each layer involves deciding whether a particular variable $b_i$ will be 0 or 1. Each ...
- 40.1k
1
vote
Accepted
choose constraint from IIS to build penalty function
I think that, when selecting constraints to relax (with penalties), you should look at the IIS from the perspective of the final decision maker. Which constraints do they think absolutely must be ...
- 40.1k
1
vote
How can I include a penalty to my (linear) model?
Obj: $min \ cx + dy + w\epsilon$
3 additional constraints
$y >= w$
$x >= w$
$w >= {{x+y}\over M} - 1$ where we is binary and M could be chosen such that $1 < {{x+y}\over M} <= 2$. My ...
- 3,513
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