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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4
votes
1answer
114 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:
4
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0answers
83 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}...
4
votes
1answer
107 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 ...
2
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1answer
100 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 ...
5
votes
1answer
213 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
votes
2answers
71 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 ...
11
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1answer
187 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
votes
1answer
65 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 ...
2
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0answers
39 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:...
5
votes
1answer
106 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 ...
7
votes
1answer
155 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. ...
5
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0answers
44 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 ...
7
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2answers
821 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
votes
1answer
246 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 ...
3
votes
1answer
189 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 ...
1
vote
1answer
124 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. ...
5
votes
2answers
192 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
votes
2answers
174 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
votes
1answer
107 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 ...
2
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3answers
208 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 ...
3
votes
1answer
44 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 ...
6
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2answers
193 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 ...
2
votes
1answer
96 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 ...
2
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1answer
77 views

AdaGrad - Sparsity of parameters

I read on Wikipedia: AdaGrad (for adaptive gradient algorithm) is a modified stochastic gradient descent algorithm with per-parameter learning rate, first published in 2011. Informally, this ...
1
vote
1answer
70 views

How to get detail about 'OptimizationStatus.ERROR' in MIP module in Python?

I am using MIP (Mixed Integer Programming) module in Python to solve one of my optimization problems. for some of the scenarios, model returns "ERROR" (OptimizationStatus.ERROR) status after ...
3
votes
3answers
365 views

SLSQP Optimisation loop takes several iterations to compute error function despite jacobian

I have an error function $f : w \rightarrow f(w)$ that I want to minimize, $w$ being a vector of length 211. There are some constraints on $w$. I managed to compute the jacobian $J$ and even with it ...
3
votes
1answer
102 views

Can Deep RL be used to find optimal division point in an application?

I need to optimise the end-to-end latency for a multi-service application while distributing it on multiple devices. The application is a series of services interconnected to each other. The goal is ...
14
votes
4answers
196 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/...
1
vote
1answer
76 views

Find minimum cost problem

The problem below aims to find the minimum cost for the network architecture: We want to build a network where client terminals are connected to servers by cabling which is very expensive. The network ...
2
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0answers
151 views

Operation hours optimization for circular schedule

Here is my problem. A store has X = 15 electical devices with the ability to work non-stop, fully charged, up to 8 hours. Their battery charge lasts 2 hours and the operating hours of the store differ ...
2
votes
1answer
55 views

Specify the criteria of the optimal solution

I have three variables $x_{1},x_{2},x_{3}$ and a function $f : D \rightarrow \mathbb{R}$ where $D$ is defined as such : $$D = (x_{1},x_{2},x_{3})$$ such that $$x_{1}+x_{2}+x_{3}=1$$ and $$x_{1}>x_{...
4
votes
2answers
198 views

Output of binary variable greater than one

I am working on a shipping demurrage problem that uses a binary variable to denote the date a specific vessel can be loaded (I have been kindly helped by Wesley on OR before with this). I am confident ...
3
votes
2answers
138 views

Limit number of switches in employee scheduling problem

Here is a scheduling problem I need to solve. Given the demand for 2 positions in 1 week with 3 shifts per position, I need to allocate the employees accordingly with some extra operational ...
2
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0answers
46 views

Algorithm for Trainyard Marshall optimization problem

The problem I am trying to solve is the 2014 RAS problem. The link is the following The problem Trains come to the humpyard where each compartment of a train gets humped or disassembled and then each ...
3
votes
1answer
119 views

How to optimize with “if” constraints

The minimizing problem is the following : $$ \underset{w}{\operatorname{argmin}} \sum_{i=1}^{n}\left[w_{i}\times (\frac{Vw}{\sigma})_{i} - b_{i}\right]^{2}$$ with $V$ a $n\times n$ matrix (covariance ...
0
votes
1answer
55 views

How to deal with the sub-problem with zero reduced cost in D-W decomposition

The specific linear programme has an optimal solution as $x_1 = 0.66$, $x_2 = 1.33$, $x_3 = 12.2$, $x_4 = 0.0$ and the objective value is $33.3$. While the problem is solved by D-W decomposition ...
2
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1answer
147 views
2
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1answer
133 views

Representing Date Variables in Pulp

I am working on an optimisation problem that involves minimising shipping demurrage. I am struggling to model how to represent the difference, (x-y) between dates where the ship is ready to be loaded ...
2
votes
0answers
46 views

Decision-making algorithm for dynamic load balancing

I'm researching a subject of balancing the load between two black-box systems (with some twists). I thought that I could record latest response time log from each of those systems and process such a ...
3
votes
2answers
778 views

Fast algorithm for Transportation Problem in Python?

The Transportation Problem can be solved with a simplex algorithm, but it's time-consuming. I'm wondering if there exists a specific Python-implemented algorithm with low complexity.
3
votes
1answer
133 views

Resource constraint with MIP model

My question is how to model a resource constraint with MIP model (how should I modify it?) A factory is making blocks. If there is space left at that time, the block can be assembled. (If the factory ...
11
votes
1answer
2k views

An approximate answer to the right question or an exact answer to the wrong question

There is a quote from John Tukey in one of his papers on data analysis Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, ...
4
votes
1answer
236 views

Creating an Optimisation Problem to Optimise Water Flow

A water tank needs to be refilled with an electric pump when the water level gets below a certain level. The pump can operate at variable flow rates. Further, there is a time-variant electric billing ...
2
votes
1answer
152 views

Pulp Python: How to formulate a time-based variable for shipping demurrage

I am working on a shipping optimisation problem that aims to minimise demurrage charges as a result of low/insufficient inventory. I have daily vessel requirement (sales) data in the format ...
6
votes
1answer
202 views

Convert summation of min functions into linear constraints for optimization

I have the following optimization problem: $$ \mbox{maximize } j^{*} \mbox{ subject to:} \sum_{j^{*}\leq j\leq J} \min({\bf A}_j,{\bf B}_j) \geq \lambda, \lambda \in \mathbb{R} \mbox{ and } {\bf A}_j,{...
1
vote
1answer
321 views

How to allow multiple assignments for jobs in Hungarian Algorithm?

In the Hungarian Algorithm, the assignment for a bipartite graph considers the restriction of assigning a single job to a single person for example. Can this restriction be relaxed? I would like to ...
8
votes
2answers
2k views

How to convince people that OR can help them?

When talking to people who are not familiar with what OR is and what it is about, and you want to convince them that it might be useful for them/their industry, what do you tell them in order to ...
2
votes
1answer
197 views

Defining and comparing utilization rates for delivery service

I'm currently working on a case for a food delivery service and wondered whether my notion of "driver utilization" makes any sense. My data set contains an hourly overview of the number of active ...
6
votes
1answer
222 views

Can Operations Research applications scale?

What do I mean by scaling? Let's say you developed a software for an operations research application for an industry client. Now you want to make a product out of this and sell it for other clients. ...
5
votes
0answers
353 views

What is the difference between root relaxation and LP relaxation

(I apologize. I saw this question but, I do not know these may be the same or not.) I am trying to solve a MIP problem and have an issue about that. The problem's LP relaxation has the objective ...

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