# Questions tagged [optimization]

For questions involving mathematical problems that aim to minimize or maximize some objective function, possibly subject to one or more constraints.

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### How to set solver options in Pyomo with GAMS Python API?

Did anyone have experiences with Pyomo and GAMS as solver? I had looked into the pyomo documentation (GAMSShell Solver) and in the CPLEX Manuals, but doesnt find the correct syntax. My Code looks like:...
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### Interger programming using gray encoding

Could anyone suggest me a tool or library which takes an integer programming problem written in DOCPLEX or CVXPY as input and outputs the equivalent problem using Gray binary encoding? I am happy to ...
38 views

### Conditional Objective in PYOMO

Hi, I am trying to set up an optimization problem with an objective function which has a condition: ...
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### Optimizing MIP Parameters For Various Data Sets

I have a MIP that runs for several different data sets. For each data set the MIP runs multiple times, once for each time period in the data set, and each time period is independent. I've experimented ...
9k views

### MATLAB vs. Python in industry

I am a beginning PhD student in math, and I would like to focus on optimization. I am learning programming for the first time, and I have written out some rudimentary optimization algorithms in both ...
1k views

### Recommended books/materials for practical applications of Operations Research in industry

I have a Masters' degree in Mathematics. I've very fair understanding of methods and techniques of Operations Research. I am looking for a good book/material where I can see a lot of examples on Math ...
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### how to apply Big M to model the logic constraint （if-then-else）

I was hoping to get some help in modelling the following logic as an MIP Constraint c_{m,l}^{RC} is binary decision variable. Simplify it：
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### $\nabla_y\nabla_vf(x^*)\geq0$ for any concave $f$ if and only if $y=-v$

$f:\mathbb R^3\to\mathbb R$ is an arbitrary concave function. $H$ is a plane. $v$ is a given vector on $H$. $x^*=\max_{x\in H} f(x)$ Prove that $\nabla_y\nabla_vf(x^*)\geq 0$ if and only if $y=-v$. I ...
307 views

### cvxpy: Code that works for default solver doesn't work for cp.GLPK_MI

The following code works: ...
176 views

### Column Generation algorithm for vehicle routing problem

I want to solve a VRP with a column generation algorithm. The objective of the problem is makespan minimization. In more detail, I want to minimize the arrival time of the last vehicle in the depot. I ...
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### How to decide between a inaccurate system and a accurate system with capacity constraints to do a stream of jobs

Let's say you have a list of at most N Jobs to be done which are coming in a stream. There are two kinds of systems that can do the job: System 1: A very fast system, which however, only does the job ...
184 views

### How would you characterize “optimization data?”

We often hear that in practice, not enough data of sufficient quality, consistency, recency, etc. is available for feeding into mathematical optimization models. Example: my university wanted to plan/...
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### Safety stock calculation with production forecast variance

I am trying to find an safety stock calculation where the expression incorporates: Lead time variance Sales demand variance & Production forecast variance My calculation so far is based on the ...
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### maximum number of BoolVar 's before or-tools is no longer feasible to use

The standard nurse scheduling problem which is used as an example for OR-Tools (see for example https://developers.google.com/optimization/scheduling/employee_scheduling) attempts to assign boolean ...
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### How can this convex optimization problem be proved?

Consider the following maximization problems: $\max_{x} x -\gamma p(x)$ subject to $x \in \Omega_1$ $\max_{x} x-\gamma (p(x) + q(x) )+K$ subject to $x \in \Omega_2$ where $\Omega_1$ and $\Omega_2$...
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### Why is this version of the algorithm more efficient?

I am a student self-studying Optimization, and I am reading about the Conjugate Gradient Method in Numerical Optimization by Nocedal & Wright, and they present two different algorithms for it. ...
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### Mixing time exponent above threshold temperature for Glauber dynamics or annealing

It is well-known that the Glauber dynamics will converge in polynomial time to the Gibbs distribution for, say, the Ising model on a d-regular graph at high enough temperatures $T>T_c$. There are ...
643 views

### Difference between exploration and exploitation in Simulated Annealing algorithm

In evolutionary algorithms, two main abilities maintained which are Exploration and Exploitation. In Exploration the algorithm searching for new solutions in new regions, while Exploitation means ...
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### How to optimize a utility function that contains step function?

I have an optimization problem with an uncommon utility: to find a $\beta$ that maximizes $$r^{T}\cdot H(X\cdot\beta)$$ where $H()$ is a Heaviside step function as in wiki $r$ is a vector of size ...
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### How to linearize a quadratic constraint to add it then via a callback function

Suppose we have a positive continuous variables $0 \le x \le UB$ where $UB$ is a known upper bound. How can we linearize the term $x^2$? Detailled problem: Suppose that via a callback we compute a ...
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### Multiple Knapsacks with splitting

I am trying to solve a problem that I believe is a variation of the multiple knapsacks. Like the classical multiple knapsacks problem, I have a set of items, each one with a weight and a value and I ...
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### Is there any OR way to solve this problem?

For each observations there are 207 variables (binary, either a 'symptom' happened or not), class variable is also binary. For each variable or symptom there is a weight attached (currently set ...
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### How to balance the workload of teachers in OR-Tools (maximization of the minimum)

I am very new to optimization and OR-Tools. I am trying to solve a very simple question. Let's assume that we have $n$ students. Each student needs to be assigned to only one teacher as a supervisor. ...
101 views

### Decision variable transformation in Gurobi

I'm trying to find a way of setting the values of a binary MVar object (which is my decision variable) of size n to {-1,1}. Right now I have a vector that can either take values 0 or 1 (due to binary ...
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### Find a particular optimal solution

After writing an integer linear program in AMPL, I solved it using CPLEX. Now, I have some variables that must necessarily be 1, others that must necessarily be 0 and finally it is possible that some ...
135 views

### Linear objective function with non-linear constraints

I would like to choose a set of $\beta_j$s that maximizes a simple linear objective function of the type $$\underset{\beta_j}{\operatorname{max}}\sum_{j=1}^{J}X_j\beta_j \\$$ subject to the ...