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Questions tagged [penalty-based-optimization]

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choose constraint from IIS to build penalty function

Suppose I have a single objective optimization model whose constraints are all composed of linear equations and linear inequalities, and now that it is proven to be infeasible in a calculation using ...
CangWangu's user avatar
2 votes
1 answer
171 views

How to model a penalty for exceeding a threshold in a nonlinear optimization problem using IPOPT?

I'm working on a nonlinear optimization problem where I have a decision variable representing my product's price (P_m) and a constant representing my competitor's price (P_c). I want to introduce a ...
MarcM's user avatar
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3 votes
1 answer
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Optimization Problem with a Penalty Factor

I am working on an investment optimization problem where I'm trying to maximize returns over a 20-year period with a given total budget. The investment involves an initial capital and annual ...
Francesco's user avatar
3 votes
1 answer
195 views

Assignment Problem - Students and teachers

I ran across this problem at work and I'm sure that we can optimize it with OR. I have $n(T) = 4$ teachers and $n(S) = 7$ students that should have a weekly individual class. If a student $s$ has a ...
nickh's user avatar
  • 133
2 votes
2 answers
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How can I include a penalty to my (linear) model?

Is it possible in a linear model to include a penalty if both variables $x$ and $y$ are greater than zero? I would like to have no penalty, if $x$ OR $y$ is zero. For example, I have a model: $$ \...
Lau's user avatar
  • 79
1 vote
3 answers
609 views

How to transform this BIP into LP with the help of penalty function?

I have an BIP problem as below $$\underset{\bf b}{\max}{\bf u}^T\bf b$$ $$\text{subject to}$$ $${\bf Ab}\le1$$ Here, ${\bf b}=\{b_1,b_2,\cdots,b_N\}$ is a column vector of decision/optimization ...
KGM's user avatar
  • 2,377
1 vote
0 answers
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Can I combine two objective functions if they have a relation between them?

I will use a meta-heuristic algorithm, to maximize the following objective functions: Objective function 1 $=\sum\limits_{r=1}^{M} \sum\limits_{s=r+1}^{M} \sum\limits_{j=r+1}^{N} (r_{rj}w_j - r_{sj}...
stevGates's user avatar
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8 votes
1 answer
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Extract info from Gurobi binary variables during run-time

Actually the question below is not specific to Gurobi, but that's the tool I am using. Consider a scheduling problem where a 2D array of binary variables $Z(i,v)$ is defined, where $i$ is index of ...
user22363's user avatar
  • 281
11 votes
1 answer
269 views

Difficulties with Finding a Proper Penalty Value for the Progressive Hedging Algorithm

Recently, I've been working on some two-stage stochastic programming problems. Due to the presence of integer second-stage variables in the model, I've preferred to use the Progressive Hedging ...
Ehsan's user avatar
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10 votes
4 answers
252 views

Is there a canonical name for Score Folding (multiplying a priority soft constraint by a big weight)?

I've regularly encountered that there are too many constraints to categorize into just hard and soft constraints. For example: Physical constraints (very hard), e.g. 1 person can only be at 1 spot ...
Geoffrey De Smet's user avatar