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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14 views

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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0answers
24 views

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 ...
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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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0answers
30 views

Optimization of strongly convex functions with approximate evaluations of gradient and Hessian

Suppose I want to find the minimum of a differentiable, strongly convex function $f:\mathbb{R}^n\to\mathbb{R}$ with constant $\mu>0$. That is, for all $x,y\in\mathbb{R}^n$, I have that: $$f(y) \geq ...
2
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1answer
75 views

Looking for a similar optimization problem

I want to know if there is any already defined problem that could give me a hint on how should I approach the following task. There are N tasks that should be accomplished, each task requires ...
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1answer
68 views

Does this objective function makes sense?

I am wondering if the objective function in the following problem makes sense. The question is posted in CrossValidated, stack exchange as well. I know there is a physical system having an underlying ...
14
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2answers
226 views

How can I approximate a chance constraint in a computationally tractable way?

I want to solve an optimization model that contains a constraint like $$ \Pr[F(x,\xi)\leq0]\geq1-\varepsilon $$ where $x$ are my decision variables, $\xi$ is a random vector, and $\varepsilon\in(0,1)$ ...
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2answers
403 views

How to handle an IP sub-problem with an objective function in Benders Decomposition

I have a question on Benders Decomposition (BD). Suppose I have an MILP model which can be decomposed into a master problem (MP) including integer and continuous variables and a subproblem (SP) ...
2
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1answer
81 views

Specific usecase of two-phase simplex algorithm

The problem below aims to find to most optimal way to transport the fuel : A company Er must transport a type of fuel from its two refineries Ra and Rb to its two points of sale PV1 and PV2. The ...
2
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1answer
109 views

Is my formulation correct and how to formulate this IF-THEN constraint?

I have system with $N_U$ users and $N_T$ transmitters. Multiple transmitters can transmit to a single users and one transmitter can transmit to many users, i.e., two sets of transmitters serving two ...
4
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1answer
138 views

Combinatorial Optimisation, Allocation problem

I am trying to solve a problem (in pyspark/ python) where I need to find two distinct values to allocate, and how to allocate them in a network of stores. The two distinct values can only be integer ...
3
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2answers
180 views

Optimal way of connecting N sensor to M devices in polynomial time?

Let's say I have 3 type of sensors: A, B, C. These sensors can be connected to multiple devices at the same time: let's call them dA, dB and dC. Now, device dA can only accept connections of sensor of ...
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1answer
66 views

How would you linearize this scheduling problem? Or how would you solve this? It is variation of a set coverage problem for OpenSolver

So, it's been about 15 years since I took my OR class in college. I'm not versed in any programming language besides a little bit of VBA. A client of mine is looking to solve the following problem. I ...
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1answer
47 views

Reformulating to locate the second largest decision variable of a set of decision variables

Consider a set of $A_{vn}$ decision variables such that $A_{v1},A_{v2},\cdots,A_{vn}<A$. While this is the standard formulation finding the maximum value of $A_{vn}$, I would also like to find the ...
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1answer
46 views

Formulating indicator constraint set

I am having difficulty formulating the indicator constraints for the following: Consider a set of $A_{n}$ decision variables such that $A_{1},A_{2},⋯,A_{n}<A$. While all of them are integers that ...
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2answers
125 views

Is there efficient way to deal with division by zero?

I am trying to solve an optimization problem in which there is an objective function in the following form: \begin{equation}f(x, y)=x+\left(\frac{1}{y}\right)\end{equation} Where, $x,y$ are positive ...
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2answers
128 views

Constraint $x'Ax = 0$, where $x$ and $A$ are both optimization variables

I'm trying to solve the following optimization problem: $$ \min_{x, \phi} x \quad \text{s.t.} \quad \sum_{s,t = 1}^n \left(m_{s,t} x -v_{s,t} \right)\phi_s \phi_t = 0 , \quad \lVert \phi \rVert = 1$$ ...
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1answer
86 views

How can I have minimum amount of resources wasted in this resource allocation problem?

I have a demand, $d$ I also have supply from 1000 sources. The supplies from those $N$ (for example, $N=1000$) sources are given by $s_1,s_2,s_3,\cdots,s_N$. So,the total supply is : $s_1+s_2+\cdots+...
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0answers
66 views

Fast solvers for LASSO-type non-convex optimization problems

Given $y \in \mathbb{R}^{n \times 1}, X \in \mathbb{R}^{n \times p}$, $p > n$, assume a LASSO-type optimization problem in the form of $$ \hat\beta=\underset{\beta}{\operatorname{argmin}}\frac{1}{2}...
6
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2answers
67 views

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 ...
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7answers
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 ...
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15answers
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 ...
3
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1answer
61 views

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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0answers
44 views

$\nabla_y\nabla_vf(x^*)\geq0$ 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 ...
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1answer
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 ...
4
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2answers
65 views

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 ...
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4answers
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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1answer
84 views

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 ...
4
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1answer
93 views

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 ...
3
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0answers
83 views

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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1answer
147 views

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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1answer
79 views

Radial unboundedness vs convexity

We have a simple problem, namely minimizing: $$f(x) = x_1^2 + x_2^2 - x_1.$$ The gradient is $$\nabla f(x) = \begin{bmatrix} 2x_1 - 1 \\ 2x_2 \end{bmatrix},$$ hence the unique stationary point is: $...
11
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1answer
123 views

Branch and Price algorithm is exact?

I know that the Column Generation algorithm delivers an exact solution when you are solving a linear programming optimization problem. I want to know that, does this column generation approach deliver ...
2
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1answer
53 views

Quasi-convex function must be “partially monotonic”?

$f(x)$ is quasi-convex, $$x^*\in\arg\min_{x\in C}f(x).$$ How to prove that, for any $a\in C$, $f(x) $ is weakly monotonic in the direction of $(x^*-a)$? Is this simple result a part of an ancient ...
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0answers
31 views

Algorithms for finding step sizes which satisfy the Wolfe conditions?

I am a student studying optimization, and I am interested in algorithms which finds step sizes satisfying the Wolfe (or strong Wolfe) conditions. I do know of one book which provides such an algorithm:...
19
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7answers
3k views

What kind of optimization problems are solved most often in practice?

I think that the shortest path problem is probably the problem that is solved most often. But if we move to problems where we need more complicated solvers, like Gurobi, Cplex, and Baron? What are the ...
5
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1answer
92 views

Minimize binary variable's distance with respect to the index values

For a given binary decision variable $x[i,j,k]$ my goal is to get as dense results in terms of k for successive values of j. Distance of k value to be kept as close as possible throughout j values: $d ...
5
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0answers
40 views

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 ...
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2answers
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 ...
3
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1answer
84 views

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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2answers
141 views

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 ...
3
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1answer
80 views

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 ...
2
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3answers
190 views

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 ...
1
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1answer
87 views

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. ...
3
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2answers
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 ...
3
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1answer
69 views

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 ...
6
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2answers
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 ...
3
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1answer
43 views

Feasible sets represented as point clouds

Does the situation in optimization ever occur in which you have a problem whose feasible set is not described in terms of explicit algebraic equations, but instead you have a large set of points that ...
2
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1answer
91 views

Problem with implementing squared terms in the objective function

I'm trying to implement either one of these objective functions, but I'm having a hard time with the squared terms. I'm attaching both so you can take a look at the structure and see if you can give ...

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