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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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Inconsistent solutions to linear optimal control problem

Consider the following optimal control problem: \begin{align} J(t) = \inf_{u(t)} \ & \frac{1}{2} \int_0^\infty e^{-\delta t} \left( x(t)^2 + \lambda y(t)^2 \right) dt \\ s.t. \ &u(t) \geq - \...
NC520's user avatar
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53 views

Shift roster (calendar) - mathematic optimization algorithm

I have question about heuristic searching problem - I need to plan shift roster for workers. My solution is to use some bio-inspired algorithm. My implementation is: I created list of timeframes (...
KamikazeNB's user avatar
6 votes
2 answers
645 views

Move circles from initial positions such that they do not overlap and total shift is minimized

I have a set of circles of varying radii residing in 2D space. Some of these circles overlap. I would like to rearrange the circles such that a) they do not overlap; and b) the total distance that the ...
Ike348's user avatar
  • 343
3 votes
2 answers
67 views

Understanding DEA better

we learned something about Data Envolopment Analysis (DEA) and the different models at university today, but somehow I still don't quite understand the basic idea and the scale calculations, as well ...
mingabua's user avatar
0 votes
1 answer
40 views

Is that an optimal solution for this instance of MS-RCPSP (Multi-Skilled Resource-Constrained Project Scheduling Problem)

I'm questioning whether this is the optimal solution for this instance of the MS-RCPSP (Multi-Skilled Resource-Constrained Project Scheduling Problem). I have checked the assignment and would like to ...
John Donald's user avatar
1 vote
1 answer
86 views

How to do the scaling to remove bias in QP problem?

I have a MIQP problem as below minimize $$\min {\bf x}^T{\bf Qx}-{\bf c}^T{\bf x}$$ ${\bf x}$ is a binary variable. The range of values in ${\bf Q}$ and ${\bf x}$ are quite different. The elements of $...
KGM's user avatar
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2 votes
1 answer
30 views

Forecasting based inventory management

In most text books on inventory management and inventory optimisation I have come across, it is assumed that demand follows some known distribution (often a normal distribution). However, when talking ...
Sune's user avatar
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30 views

Need help defining constraints regarding start and end time on job shop scheduling AGV

...
Rami's user avatar
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0 answers
71 views

How to constrain variables to fit a normal distribution

Given a time series $s_t$, I would like to define for each $t$ a perturbation $e_t$ such that the set of all $e_t$ "fits" (within some range) a normal distribution with mean $\mu=0$ and a ...
NormalFit's user avatar
2 votes
1 answer
84 views

Why this ILP and LP are equivalent?

Let's consider a competition with $n$ questions. Each question has a price $p_i$ and a score $v_i$. To advance to the next round of the competition, we need to accumulate a minimum score of $D$. We ...
occasional's user avatar
1 vote
2 answers
88 views

Optimal Methods and LBFGS

I'm working on my thesis in physics. A core part of it is optimizing shapes under electromagnetic (Maxwell's Equations) constraints. To do this, we explore the geometrical space (lets say we have 40-...
James Li's user avatar
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vector number partitioning QUBO formulation

I would like to implement an adaptation of the number partitioning QUBO formulation. The original one is described in this paper as well as this thread on this forum The version of my problem is the ...
user12910's user avatar
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2 answers
85 views

linearizing a constraint involving an absolute function

I would like to know what is the best way to linearize a constraint involving an absolute function. More precisely, imagine I have three binary variables and their relationships is as follows: |x-y| = ...
Sam's user avatar
  • 97
4 votes
3 answers
322 views

How to maximize the number of variables with value at least 0?

Given a matrix $A$ and a vector $b$, I would like to find a vector $x$ satisfying the set of linear constraints $A x \leq b$, and subject to that, contains as many variables as possible with ...
Erel Segal-Halevi's user avatar
-1 votes
1 answer
78 views

How to use gurobi to describe the process of finding the rank of matrix without objective function?

I have a general square matrix [[1,1,0],[1,1,0],[0,0,0]] (the element is on a binary field--Galois Fields) I want to find the rank of this matrix (like the function:...
wenny's user avatar
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0 votes
1 answer
55 views

How to linearize this L0 norm of a vector?

I have an QP optimization problem. $\bf x$ is the binary optimizaion variable of size $12\times 1$. One of the constraints is non-linear/non-convex. The constraint is L0 constraint. The constraint I ...
KGM's user avatar
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2 votes
1 answer
90 views

Approximating a convex program

As I understand it, "approximating" a convex program usually refers to finding a solution that is approximately-feasible approximately-optimal. For example, in the book "Geometric ...
eden hartman's user avatar
2 votes
1 answer
115 views

Modelling L-0 norm of a vector

I have a binary variable $\bf x$ of length 4000. Let ${\bf x}=[x_1,x_2,\cdots, x_{4000}]$. Let's say we have ${\bf y}=[y_1,y_2,y_3,y_4]$, where \begin{align} y_1&=x_1+x_5+x_{9}+\cdots+x_{3997} \\ ...
KGM's user avatar
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0 votes
1 answer
84 views

How to model this constraint for a QP problem?

I have a system with 100 users. There are 6 resources. At any point of time, only 2 resources are made available and those resources can be shared among the users. Some users may not get any resource, ...
KGM's user avatar
  • 2,297
2 votes
2 answers
37 views

use case OR in financial service industry

What are some use cases, with high dollar value impact, of OR and optimization in the financial services industry like life insurance, annuity business? I have seen common use cases of queuing theory ...
janicebaratheon's user avatar
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0 answers
116 views

why this little constraint changes my whole program?

I'm trying to linearize a CP in ILOG CPLEX. I have the following constraint that I want to linearize (I already simplified it with the big M) : ...
Marcocorico's user avatar
1 vote
1 answer
76 views

Understanding (1+ ε) approximation when objective is discrete

Some problems in operations research have (1+ε) approximation algorithms which run in polynomial time. So we have an algorihm that produces a solution which is whose objective is within that factor (1+...
worldsmithhelper's user avatar
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0 answers
66 views

Why are these two constraint equations not equivalent?

I've made a CP Model of an hospital in ILOG CPLEX and I want to test the performance of the CPLEX version of it. In my CP model, I have the following constraint : ...
Marcocorico's user avatar
1 vote
0 answers
36 views

How to convert unit-capacity network flow into transportation problems?

I am working on a problem that can be modeled as a minimum-cost network flow problem where the capacity of edges is 1. I found Exercise 3.8, Chapter 5 of Parallel and Distributed Computation: ...
Recursion's user avatar
1 vote
1 answer
98 views

In Pyomo, how do I modify the Variable if the value is less than 0?

Pyomo does not allow to use if statements that involves variables. I want to create a new dictionary, model.Excess1, which uses the values from model.Excess to ...
xavgo's user avatar
  • 11
0 votes
1 answer
76 views

Scheduling optimization problem - Where to begin?

Class Scheduling Optimization for a Trade School We are exploring ways to model, simulate, and optimize class scheduling for a trade school, focusing on addressing the complex dynamics of managing ...
Evan's user avatar
  • 1
2 votes
1 answer
114 views

Optimizing a Route Selection Problem with Multiple Constraints and Objectives

I'm developing a solution to optimize a vehicle routing problem where each stop has an associated score (priority), specific geo coordinates, and a required stop duration. The goal is to maximize the ...
Rastislav's user avatar
  • 131
0 votes
0 answers
44 views

Lagrange Duality in Robust Optimization

I am learning Robust Optimization and been stuck on this example. I've brushed up on my knowledge of Lagrange duality and referred to a couple of textbooks on Linear Programming but not able to ...
stuckinlocal's user avatar
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0 answers
35 views

When does local search algorithm for SMT (1-Steiner algorithm) not output the optimal solution?

I am trying to find an example where the 1-steiner algorithm (local search algorithm for Steiner Minimum Tree) does not output the optimal solution, but each instance I find seems to be optimal.
Marie's user avatar
  • 9
2 votes
1 answer
154 views

How to pass the values of a variable of the first model to a parameter of the second model?

I am working on a scheduling problem which is NP-hard problem. Therefore, I decided to implement two-stage strategy to speed up the solution process. I need to pass the values of a variable from the ...
Baghban's user avatar
  • 131
2 votes
1 answer
578 views

Is mathematical programming synonymous with algebraic modelling?

Based on my on-again-off-again internet search of optimization problems over the past few years, the two terms seem to cover largely the same way of representing problems, if not the identically. I'm ...
user2153235's user avatar
1 vote
2 answers
74 views

How to maximise black-box function defined on a subset of integers, with access to its derivative?

The basic form of my problem is as follows. Let $S = \{ 1, 2, ..., 30 \}$. I have an integer-valued function $f$, whose argument is an integer-valued vector $\vec{x} \in S^{200}$. I also know that ...
j x's user avatar
  • 111
0 votes
0 answers
99 views

How to Find Optimal Way to Allocate a Budget? [duplicate]

How can I find the optimal or close to optimal way to allocate a budget if I have revenue and spending data? I was thinking of using linear programming, but I'm assuming it wouldn't work as the ...
user13229's user avatar
4 votes
3 answers
3k views

I have found so many tools that can solve optimization problems, I want to know which workflow is the best or the most practical?

I have found so many tools that can solve optimization problems (wikipedia also has one page "List of optimization software"), I want to know which workflow is the best or $\color{blue}{\...
138 Aspen's user avatar
  • 197
1 vote
1 answer
118 views

0-1 Knapsack optimization problem

Can anyone explain how the writer rewrite the objective function in (7) to be written as (8)?
AhmedHassan's user avatar
0 votes
2 answers
70 views

Sewing lines orders assignment

What are the algorithms used to assign orders to sewing lines based on order priority, line capacity, time taken to sew garments, due dates, specialization of lines etc.
Tharindu Kariyawasam's user avatar
0 votes
0 answers
46 views

monte carlo for a selection problem

What type of Monte Carlo simulation is suitable for solving this problem? Also, how can we select results after simulation to guarantee feasibility?
Mohammad Reza Salehizadeh's user avatar
0 votes
2 answers
104 views

Are Metaheuristics Global Optimizer?

In recent years, we experience an explosion in the publication of metaheuristics. They claim finding the global optimum of the optimization problems they are applied on. Is that claim correct? Can ...
Clement's user avatar
  • 2,252
0 votes
2 answers
68 views

Problem 8.17 of Korte and Vygen

An airline wants to conduct a given set of scheduled flights with as few airplanes as possible. All available airplanes are of the same type. For each flight we know the departure time and the flight ...
Nico Konrad's user avatar
1 vote
1 answer
121 views

How to turn off tree search in fico xpress ? Couldn't see relevant documentation

trying to solve a very large problem , using heuremphasis as 3 , cutfreq=0 , scaling =4, run time reduced significantly however , solver spends 400 seconds in tree search , but couldn't see any ...
21vs's user avatar
  • 489
1 vote
0 answers
42 views

satisfactory vs optimal decision making

In most classical game theoretic problems (situations in which more than one decision maker impacts the state of the environment), we assume that the decision-makers optimize their objective function. ...
Mohammad Reza Salehizadeh's user avatar
0 votes
1 answer
146 views

PuLP is ignoring constraints, and setting everything to 0 for minimization problem

I have a multi-objective optimization problem I am trying to solve with competing objectives. I am trying to model a network of industrial businesses which can share wastewater rather than sending it ...
Caleb O's user avatar
  • 13
3 votes
2 answers
184 views

Can an Operations Research model optimize on a vector's indexes?

Theoretical model Suppose that I have an input vector $E_{t}\in\mathbb R^n$ for $n\in \mathbb N$ Suppose that I want to optimize $\displaystyle\max_{t,x} E_tx$. That is, my decision variables are the ...
JKHA's user avatar
  • 679
2 votes
0 answers
160 views

Global optimizers handling minimization of an expression arising from the likelihood of a multivariate normal

I am interested in converting the following optimisation problem into a form that an exponential cone and/or SDP solver such as MOSEK can handle. This is a multivariate version of the question I ...
cfp's user avatar
  • 259
3 votes
1 answer
829 views

Scipy.optimize can't get correct answer when objective is Piecewise Linear Function and Equality Constraint

I'm encountering a puzzling issue with SciPy's minimize function in a constrained optimization problem. My objective is to optimize a piecewise linear function with ...
Yiyuan Chen's user avatar
2 votes
1 answer
84 views

Optimizing for an unknown conjugation matrix

I am trying to find the invertible matrix $M$ satisfying: $$v_t'= MA_tM^{-1}v_t$$ For a dataset of observed transformations $(v_t',A_t,v_t)_t$. Note, there is a different linear transformation $A_t$ ...
hamza keurti's user avatar
0 votes
1 answer
29 views

Grouping of a list of elements in fixed order to maximize the total return of all the groups

I'd like to ask about if there's an existing type of problems that fits to my question. (Searching it for a while but cannot get to the point) Basic Problem Description: Given a sequenced list (order ...
X.Arthur's user avatar
  • 103
0 votes
0 answers
43 views

Can ADMM be applied to "latently coupled" variables?

I've been studying a paper where the authors employ the ADMM in a way that has left me somewhat perplexed. The paper focuses on addressing a robust principal component analysis (RPCA) problem, ...
Piko Mone's user avatar
5 votes
2 answers
173 views

Global optimizers handling minimization of expressions like $\log{v}+\frac{1}{v}$

Consider the simple problem of maximum likelihood estimation of the variance of a mean zero normal distribution. The expression to be minimised is: $$N \log{v}+\frac{1}{v}\sum_{n=1}^N{b_n^2},$$ where $...
cfp's user avatar
  • 259
2 votes
2 answers
100 views

benders decomposition master problem scale large

I am dealing with a benders decomposition problem, in which there are 100 sub-problems that need to be solved. During each iteration, 100 new optimal cuts will be added to the master problem. I would ...
XXia's user avatar
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