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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1answer
20 views

CPLEX log always the same after hours (“Gap” and “Best Integer” always blanks)

I'm using the Java API of CPLEX 12.6.1 (with license) to solve a MILP (Mixed-Integer Linear Programming) maximization problem. The point is that, after 21 hours, CPLEX has consumed 32 GB of RAM and ...
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0answers
14 views

Capacitated Maximum Coverage Location Problem, Python and Gurobi

I am building a variant of the maximum coverage location model and want to limit the amount of points that each "facility" can cover. I am using Gurobi optimization . I have tried using the ...
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0answers
21 views

Binary variable with two criteria in Gurobi (Java)

I have the following problem in Gurobi (Java). I have a binary variable $b$ that is supposed to be $1$ or $0$ depending on my optimisation variable $x$. It should be true that $b = 1$ if $c_1 \le x \...
5
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1answer
87 views

Solver Recommendation : Discrete Variables and Quadratic Constraints

I would like some solver recommendations to solve a problem with boolean/integer variables, mostly linear constraints but also some quadratic constraints. I also have an objective to minimize which is ...
1
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1answer
37 views

Employee allocation based on ranking: Mathematical Model

Suppose I have three employees and I have to assign three employees based on their ranks. If an employee has rank 1 that means he is best. Say, I have the following table ...
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0answers
42 views

Combinatorial Analysis : How can I demonstrate the following proposition [closed]

I have to demonstrate the following proposition, but I cant figure out how I might start with it. Can anyone please help me demonstrating the following mathematical proposal : The number $g_{s}$ of ...
3
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0answers
61 views

Simplified risk game: writing a pratical Minimax objective for mixed integer programming

Problem To ensure fairness of the game, I am writing a bot that plays against itself. I have trouble rewriting a minimax objective to a pratical maximization in mixed integer programming. The amount ...
5
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1answer
104 views

How to partition a graph with optimal number of groups?

I have a graph with $N=12$ nodes. Some nodes may not have any edge between them. every edge has a weight. How to find the optimal partitioning of the graph so that total weight in the system is ...
2
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1answer
57 views

Black-box optimization of a single parameter function with high cost evaluation

I need to solve a series of single parameter black-box minimization problem. The underlying cost functions are quite simple. They always have the same shape: a global minimum inside a fixed interval (-...
5
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0answers
112 views

Water quality component optimization

I have an optimization problem that I'm attempting to tackle. As you can see in the image below, there's a graph network through which water flows. I've drawn out the problem in the image to explain ...
7
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1answer
86 views

Terrain Ruggedness Index for optimization problem

If I want to study the smoothness of the energy landscape of a cost function, is there any metric similar to Terrain Ruggedness Index used in geology?
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2answers
62 views

multiple cranes scheduling optimization [closed]

So i'm working on my school project and The problem is described as follow: we have 31 baths and 4 cranes '1 axis of movement'. figure 1: a crane imageimagen_2021-06-01_120450.png figure 2: baths ...
2
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2answers
68 views

Docplex, CPLEX Warning 1036 :

I am trying to solve a large-scale MIP problem. I have the following errors, I know, it's about the data, but I can't change the data. Is there a method to deal with it? ...
6
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1answer
132 views

Two equivalent soft constraint implementations

Take the following optimization problem: \begin{align}\min_x&\quad f(x)\\\text{s.t.}&\quad g(x)\le0\end{align} with $f$ and $g$ nonlinear functions. Suppose I want to relax the constraint by ...
2
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2answers
86 views

Transformations that leave the linear program unchanged

A typical linear program is written as $$L_0:\min_{x \geq 0; A^\top x \leq b}c^\top x.$$ Here, $x \in \mathbb{R}^n$, $c \in \mathbb{R}^n$, $A \in \mathbb{R}^{m \times n}$, and $b \in \mathbb{R}^m$. ...
2
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3answers
74 views

Convex optimization on the unit hypercube with gradients and a bounded minimum

I'd like to find the minimum of a smooth, continuous function inside the unit hypercube (the dimensionality of which could go into the hundreds or even thousands). The function is convex (Hessian $\...
10
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1answer
592 views

Linear Optimization Library for C++ with GPU Support

Does anyone know any linear optimization libraries for C++ supporting GPUs for parallelization? If multiple, which do you recommend? The GPU support is important to me since I am dealing with large ...
2
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1answer
53 views

Returning the best possible value found when the search direction is becoming too small (IPOPT via Pyomo)

I'm using Pyomo to solve an optimization problem and I'm using as a solver IPOPT. Now I'm getting an error from IPOPT. EXIT: Search Direction is becoming Too Small. according to the docs, this means:...
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1answer
52 views

Trouble implementing a line-search algorithm

I am trying to implement a simple line-search algorithm in Julia. I am new to Julia programming, so I am learning it on the go. I'd like to ask for some help, if possible, to correct an error while ...
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1answer
89 views

Multiple If else constraints in Mixed integer programming

How to formulate the following as constraints in MILP? a[0][0] = y, if x[0]= 0, a[0][0] = 0, if x[0] != 0, . . . . a[i][j] = b[i][j-1] + y, if x[j]=i, a[i][j] = a[i][j-1], if x[j] != i, ... . . . b[0]...
3
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2answers
82 views

Literature for building solver portfolios

A portfolio of solvers is collection of solvers with different configuration that share CPU time, CPU cores and memory resources and try to get an answer as soon as possible. Solvers might also ...
3
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1answer
93 views

Method of Multipliers: Why is the next iterate always dual feasible?

I am reading this expository paper on ADMM by Boyd, et. al. Consider the problem \begin{align*} &\min f(x)\\ & \ \text{s.t.} \ \ \ Ax = b \end{align*} with Lagrangian $L(x, \lambda) = f(x) + \...
2
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1answer
90 views

Recovering Primal Solution from Dual solution

Consider the problem \begin{align*} &\min f(x)\\ & \ \text{s.t.} \ \ \ Ax = b \end{align*} In this expository paper, Boyd claims (top of page $8$) that if: $\lambda^*$ is a dual optimal ...
2
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1answer
47 views

Length of intervals in Fibonacci Line Search

I am self-learning basic optimization techniques and trying to implement the 1-dimensional line search algorithms from the book - Algorithms for Optimization by Kochenderfer and Wheerler, MIT Press. I ...
2
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2answers
113 views

What kind of scheduling/packing problem is this?

I have the following problem which seems to be a mixture of a resource constrained scheduling and packing problem. There is a set of activities $A_1,\ldots,A_n$ and given precedences $P$, where $(A_i,...
3
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1answer
97 views

Finding the global minimum of $f(\mathbf{x})=\|(1-x_1,x_1-x_2,x_2-x_3,\ldots,x_{n-1}-x_n,x_n-2)\|_2^2$

I am self-learning optimization algorithms. A certain assignment problem is as follows: Show that the $n$-dimensional function $f(\mathbf{x})=\|(1-x_1,x_1-x_2,x_2-x_3,\ldots,x_{n-1}-x_n,x_n-2)\|_2^2$ ...
0
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1answer
72 views

How to solve this clustering problem with heuristic or meta-heuristic approach?

I have clustering problem with servers and users. This is different to the one posted in https://math.stackexchange.com/questions/4088441/what-will-be-an-efficient-joint-clustering-solution-to-this-...
1
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1answer
50 views

Integral of PWL-Constraint in Gurobi (Java)

In my optimization model, I use piecewise-linear constraints with the output of $y[m]$. The question or problem I have now is whether there is a way in Gurobi (Java) to form the integral for this PWL ...
3
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1answer
46 views

Non-Convex QCP model - Used Method in Gurobi

I have the following question: I have a non-convex QCP model. In the parameter description for method it says that "Only barrier is available for continuous QCP models". However, the dual ...
2
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1answer
70 views

Accessing Lagrange Multipliers in CPLEX

I want to get the lagrange multipliers for a solution from cplex. I am using it via Python. The problem is continuous with a linear objective function and elements of solution vector $x$ are ...
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2answers
99 views

Why do we need SCED in addition to SCUC in RTO/ISO electricity markets?

I understand that we use SCUC (Security Constrained Unit Commitment) and SCED (Security Constrained Economic Dispatch) in day ahead electricity market – According to the literature, SCUC is used to ...
4
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1answer
305 views

Is there any automatic way to spot contradictory constraints in linear programming?

Let's have the following trivial linear program: \begin{align}\max&\quad z=20A+30B\\\text{s.t.}&\quad A\le60\\&\quad B\le50\\&\quad A+2B\ge220\\&\quad A,B\ge0\end{align} It's easy ...
5
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2answers
76 views

MAX-CUT: are there any algorithms or codes for classical computers, that cater to this specific case?

I missed the opportunity to ask this on OR.SE by 24 days! I asked it at CS.SE on 6 May 2019 and OR.SE entered Private Beta on 30 May 2019. It's a problem about minimizing a sum of terms that are ...
2
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1answer
94 views

How to deal with log0 in optimization problem

I am adding some constraints to my model described in my previous post, where a discontinuous piecewise-quadratic functions is the objective to be minimized in cvx. Here I have an additional terms, ...
5
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1answer
186 views

Subtour elimination constraint in Travelling Salesman Problem

I am trying to understand travelling salesman problem, the Dantzig, Fulkerson, Johnson(1954) formulation. In the general formulation given below I am having trouble to implement subtour elimination in ...
3
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2answers
148 views

How to reformulate a discontinuous piecewise-quadratic functions

I am trying to develop a model, solving an optimization problem which has the following objective function: variable p(i); minimize sum(cost) subject to p>=0 ...
1
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1answer
38 views

How to interpret no-overlap constraints with rotation as a mixed integer programming

Suppose, we want to locate some given facilities $\left \{ (i,j) \ |\ (i,j) \in \text[{1,\cdots, N}]\right \}$ in a specific area. Each facility has a predefined dimension with a length $l_{i}$ and ...
2
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2answers
80 views

Relationship aware task scheduling heuristics

I have a task scheduling/assignment on machines problem (like a classic bin packing problem) with a twist in which the placement/assignment of one task affects the placement/assignment of other tasks (...
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0answers
55 views

Quadratic optimization in Gurobi with constraint

I have a question of understanding in Gurobi: I have an objective function in which my optimization variable x is squared. I have solved this bsiher by a quadratic objective function with $x$, $x$. ...
3
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3answers
103 views

warmstarting simplex algorithm- how much can problems differ from each other?

I'm working on an implementation of the simplex algorithm. I want to solve problems in real time every 30 minutes. They could be interpreted as a classic transportation problem. I couldn't really say ...
3
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1answer
44 views

Control & Experimental Group Selection Methodology using STDEV and T-Test?

I would like to know if my methodology was 'correct': I am trying to conduct an experiment on my stores. I would like to find out the effect of a marketing campaign on the number of transactions. Only ...
2
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1answer
159 views

How to convexify log(convex) function?

I have the following optimization problem: \begin{align}\max_x&\quad\log_2(1+|a+bx|^2+cx^2)\\\text{s.t.}&\quad0\le x\le1\\&\quad(1-x^2)\ge\text{constant}\end{align} where $a$ and $b$ are ...
3
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3answers
658 views

Model if-else statement

I need to build a if-else constraint for this statement, where $x_P$ and $x_I$ are decision variables, and $C$ is a constant: if $x_P \ge C$ then $x_I = x_P - C$ else $x_I = 0$. Any help is greatly ...
1
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1answer
48 views

Find an upper bound for an objective function

My objective function is $\log_2(1+{x^2y^2})$ and I found two upper bounds for $x^2$ and $y^2$. For example, assumed that we have the following upper bounds: $x^2\leq\text{constant}_1^2$ and $y^2\leq\...
1
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1answer
113 views

fpl and constraints about centers

Does anybody know how we could optimise fpl problems with additional constraints?
0
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1answer
109 views

Invalid solutions to Piecewise Mccormick Envelope Implementation

I am currently trying to implement a piecewise McCormick envelope in Drake (c++). The current issue I am having is that the solution produced by the optimization does not produce a valid $x$ and $y$ ...
2
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3answers
122 views

Linearizing a Max Function in the constraint - not working

I have a minimization function which is in its simplest form looks like below. I am including the index of the variables. ...
5
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2answers
90 views

Is $\min \ x^3 \ \mathrm{s.t.}\ x \geq 0$ a convex problem?

The problem $$\min \ x^3 \ \mathrm{s.t.} \ x \geq 0$$ is sometimes said to be a convex optimization problem. $f(x) = x^3$ is not a convex function. However, in the domain of $x\geq 0$ it is convex. So ...
4
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2answers
200 views

Mixed-integer optimization with bilinear constraint

So I have an optimization problem of the following form: \begin{aligned} \max_{x,y} \quad & \sum_i x_i \\ \text{s.t.} \quad & \sum_i x_iy_i \leq a \\ \quad & x_{\min} \leq x \leq x_{\max} ...
3
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1answer
64 views

Clustering problem involving multidepots and customers requiring commodities located exclusively in an specific depot

I'm trying to solve a clustering problem that's similiar to a VRP Pickup and Delivery problem with multiple depots and customers. Each customer demands a commodity that is exclusively found on one ...

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