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1- It is likely that the performance will be improved, but it is not guaranteed. In general I would always recommend to provide a start solution. 2- You can use the Start attribute. An example would ...

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I would add an auxiliary variable $z\in\{0,1\}$: $$z \geq a_i \ \ \forall a_i \in A$$ Then you can write: $$b_j \leq 1-z \ \ \forall b_j \in B$$ If $z=0$, then the constraint is redundant. However,...

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When defining multiple components in an objective function, you should take care of a couple of items: All elements (i.e.e $a \cdot x_1$, $b\cdot x_2$ etc.) should have the same unit. This sounds ...

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This sounds like parametric programming to me. In short, you can calculate a set of regions, typically called &quot;critical regions&quot;, within which the same set of constraints is active. This in ...

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The problem is that you create a tuplelist of a list. The function addVars returns a list of variables objects already. This means, you should be able to simply do: contribution = LinExpr(coefficients,...

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You can control the branching priorities in Gurobi using the BranchPriority attribute, which you can then store in an .ord file. This file can then be provided as an input using the InputFile ...

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Honestly, there is not that much in general that I am aware of. The best resource (other than the ones you mentioned) that comes to mind is Fischetti's modeling book &quot;Introduction to Mathematical ...

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You should model this using a set of constraints. Off the cuff you could try this: \begin{equation} \begin{array}{ll} \text{minimize} &amp; \sum_{i} c_ib_i \\ \text{subject to} &amp; a \leq A_i \...

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Here is the list of blogs and social media that I regularly check [in no particular order]: https://www.zverovich.net/ https://yetanothermathprogrammingconsultant.blogspot.com/ https://orinanobworld....

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The easiest would probably be to model it as follows: $$S_m \leq a + bx_m \\ S_m \geq ax_m$$ where $a$ is the switch and $a+b$ is the upper bound for variable $S_m$. In this case, if $S_m&lt; a$, ...

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In my view, mathematical optimization is inherently explainable for various reasons: The model is &quot;white-box&quot;, i.e. it is developed by a person defining all the variables and constraints. ...

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In my experience, it does not matter much for in terms of speed. The reason is that the size of an optimization really does not correlate with the time it takes to solve the model. There are even ...

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In order to query the GRB_DoubleAttr_UnbdRay attribute, you need to optimize the problem with the InfUnbdInfo parameter set to 1.

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TL;DR: You can do a lot with data QA, but it may not cover everything. Let's assume that you have written your model &quot;correctly&quot;, i.e. there are no typos etc. Then, any infeasibility will ...

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TL;DR: Some optimization problems are tough, and it requires a lot of work to get them solved. First, let me answer your questions: Yes, this is NP-hard, but that does not say anything about whether ...

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Disclaimer: I did my PhD on the topic below and was the author of one of the toolboxes I mention below. This sounds a lot like you are interested in multi-parametric programming, i.e. solving your ...

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In the order of importance (my opinion): Solution quality/optimality Speed Robustness towards numerically challenging problems API and model creation speed The first three you can do through ...

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In my opinion your best bet is to define an auxiliary variable $z_{ijk}$ such that: \begin{equation} z_{ijk} \geq x_{ji} + y_{kj} -1 \\ z_{ijk} \leq x_{ji} \\ z_{ijk} \leq y_{kj} \end{equation} Now ...

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When dealing with infeasibility, I like to do two things: a) Create the Irreducible Infeasible Subset (IIS). I don't think PuLP directly allows you to create that, however you could export your model ...

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Disclaimer: I have worked for 3 years as an optimization software developer at a utility company and now work for Gurobi. Is the expectation for entry level positions, that the applicant is able to ...

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The only way (to my knowledge) to get all feasible points for the binary components of a MIP is as follows: Solve the problem. Let $y$ denote the optimal solution Add the following integer cut to ...

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The solution to an LP is given directly by its active set, $I = \{i_1,i_2,...,i_n\}$, which forms a system of equations that recovers the solution $x^*$. If your solution varies, then the question is ...

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Disclaimer: I work as an optimization specialist in a large utility company in Denmark. Look for "Data Scientist", "Data Engineer", "Optimization specialist", "Operations Research Specialist" or ...

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I think there is three angles to attack this problem. A complete solution will probably feature each one of them Large set of (hard) test cases: If you are worried about the hard instances, then I ...

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In my opinion, fuzzy sets inherently suggest a notion of uncertainty, e.g. a statement may be “half-true” as it cannot be clearly determined whether it is true or not. This type of uncertainty is ...

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Mathematically, mixed-integer programs (MIPs) are non-convex, for the very reason you stated: the set $x \in \{0,1\}$ is inherently non-convex. In fact, for a convex optimization problem (e.g. linear ...

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Not sure about CP solvers, but for FICO Xpress the .NET .dll also works for .NET core. So I would suspect that similar transferability is also applicable for CP solvers. The reason is in my opinion ...

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In my opinion, OR is definitely broadening in scope, but let me try to be a bit more concrete (N.B.: all of this is my opinion, and I hope others will add their views as well): OR is a relatively "...

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