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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8
votes
1answer
101 views

Scheduling events in order to maximize preparation time

Problem statement I'm given a set of events $E$, and $\forall e \in E$ also: a set of plausible dates on which the event can happen $D_e$ importance (weight) $w_e$ ideal preparation time duration $...
6
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4answers
143 views

Sequential quadratic programming source

What are the good text books to learn SQP? Are there any online courses that you can suggest?
9
votes
1answer
162 views

How to classify and model this problem?

I was given the task to model the following problem and find a solution for it, but as I do not have any experience in this field, I already have trouble classifying it. There are a number of ...
10
votes
2answers
979 views

Linear programming: objective function with “buckets”

I had a linear programming problem with the following objective function $$f(x) = \sum_{j}x_jq_jp_j - \sum_{i}\left(\sum_{j}x_jq_jC_{ij} \right) c_i$$ Where $q, p, C, c$ are known. This problem was ...
6
votes
1answer
70 views

How to minimize a weighted sum of RMSE-like terms?

I am trying to solve the following problem: \begin{align} \min&\quad f(x) = \sum_{i=1}^{n}{a_ix_i} + \sum_{i=1}^{n}{b_i\sqrt{\sum_{j=1}^{m}{\left(y_{i,j}-x_i\right)^2}}}\\\text{s.t.}&\quad x_{...
3
votes
1answer
40 views

defining Mixed integer linear inequalities for a set of variables

The problem is described as follows: considering $n$ variables which are continuous and bounded such that $$L_i \le x_i \le U_i\quad \forall i=1,2,\dots,n.$$ How can i define a set of mixed integer ...
11
votes
2answers
3k views

Is it necessary to study rigorous math courses in OR?

I am a business student with engineering background and I am studying papers published in some journals like Management Science, Operations Research, Math of OR and they use some notations and ...
13
votes
2answers
662 views

What is the difference between optimization software APIs based on performance and speed?

The state-of-art solvers like CPLEX or Gurobi and some of the open-source solvers have had the different APIs (like Python, C/C++, Java, etc.) in which users could write their MP model in own ...
6
votes
1answer
110 views

Optimal Energy Charging/discharging Scheduling Problem

I'm new to IBM CP optimizer. I want to make charging / discharging scheduling based on cost (value will change on time) and my objective function is $$\sum_{t=1}^{24}\sum_{j=1}^5x(1)^{(t,j)}x(2)^{(t,j)...
8
votes
3answers
618 views

Bin packing variant

I am currently struggling with a bin packing variant, where we have fuel and compartments of a tank truck. Some industry constraints apply, but the whole picture is that you must fit the total volume ...
5
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3answers
906 views

Solving continuous Minimax Optimization problem

I want to solve a linear programming minimax problem here mathematically without using software: $$\begin{align*} \text{min}\ \text{max} \quad & \{x_1,x_2,x_3\} \\ \text{s.t.} \...
6
votes
0answers
50 views

Semi-definite Programming, non standard notation

The usual way to define a semi-definite program (SDP), e.g., as given in Boyd and Vandenberghe's convex optimization book, is: $$ \begin{array}{cl} \min & c^\top x \\ \mathrm{s.t.} & 0 \succeq ...
5
votes
2answers
63 views

AMPL implement constraint

I'm trying to implement the following in AMPL: $$ i \in [N], j \in[N] \backslash \{i\}, t \in [T] $$ I have so far written the following: ...
7
votes
1answer
70 views

Aggregate production planning

I'm looking for an optimization model about production planning that takes the following into consideration: Single site Multi products One machine/resource Sequence-dependent Fixed batch ...
8
votes
2answers
1k views

How to formulate problems in the language of mathematical programming?

The question says it all. I am having difficulties formulating general problems (meaning no numbers just variables). When I read the solution, I understand but I can't figure how to formulate myself ...
4
votes
0answers
61 views

Continue on “Is there a known MILP to schedule routes after routes are made”

I have made some progress on my previous question (Is there a known MILP to schedule routes after routes are made). I have derived the sets of the problem, which are: 1) Itineraries of vehicle: $i \in ...
6
votes
1answer
96 views

How to write a constraint for a directed graph?

I'm working on an optimization problem regarding a directed acyclic graph. The constraint looks in pyomo like this: ...
6
votes
2answers
261 views

Assignment problem where assignments must be done sequentially

I have a weird planning problem. I think it falls under the assignment category, but I'm not sure because I'm not familiar with assignment problems, and also because there is a "temporal" angle to it, ...
12
votes
2answers
145 views

Is there a known MILP to schedule routes after routes are made

I am trying to create a mixed integer model that has as an objective to schedule routes for a single vehicle within its timeline. Let me try to elaborate. Let's say we have a single vehicle vrp and ...
4
votes
0answers
307 views

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

The following code works: ...
7
votes
1answer
60 views

Expressing a chain of boolean if-then with logical ANDs using MIP

How to express a chain of boolean If-then as MIP such as: If $(x_{10} \ge b_1$ and $x_{11} \le b_1)$ AND $(x_{20} \ge b_2$ and $x_{21} \le b_2)$... AND... then $y_1 = 1$ else $y_1 = 0$. So basically,...
7
votes
1answer
163 views

Custom Nurse Rostering Problem

I've asked this question also on Math Stack Exchange. It's a custom nurse rostering problem: $N$ is a set of nurses; $S$ is the set of shift-type (morning, afternoon, night, rest) $n_\mathrm{...
5
votes
1answer
192 views

How to express this constraint?

I have the constraint \begin{align}\max&\quad\gamma\\\text{s.t.}&\quad a\ge\gamma b\\&\quad\gamma\le 1\end{align} where $\gamma$ is an optimization variable and $a$ is a function of some ...
10
votes
2answers
337 views

Current Issues of Interest

What are some current issue of interest in Operations Research? I am interested in current topics that experts in the field are interested in researching.
6
votes
1answer
134 views

GUROBI Re-optimize a model

(For Linear Programming) I am aware of CPLEX's reoptimize methods. If I am not wrong, if you solve a problem and after that you add a new constraint, then you can call the reoptimize method for not to ...
7
votes
1answer
92 views

Variant of job shop scheduling problem

I'm looking to identify a problem in the literature that I'm currently solving. I have a set of jobs each having a set of operations. Each operation has a duration. An operation may be done by a ...
9
votes
1answer
143 views

How to remove or replace sub tour elimination constraints in the VRP variant models?

In many of vehicle routing problems variant (VRP), which can be formulated using MIPs, to avoid creating sub tour, we need to use sub tour elimination constraints (SEC). One of the known SEC is (I ...
7
votes
1answer
227 views

Finding the optimal, spatially compact set of grid cells

I have a regular grid of cells, maybe square, maybe hexagonal. Each cell has a numeric value associated with it. How can I find a subset of cells that are: a connected, compact set and have an ...
9
votes
1answer
85 views

Problem solvable $\Rightarrow$ subproblems solvable if feasible region closed, convex?

Let $c \in \mathbb{R}^n$, $M \subseteq \mathbb{R}^n$ such that the problem \begin{align}P:\quad\min_{x \in \mathbb{R}^n}&\quad c^\intercal x\\\textrm{s.t.}&\quad x \in M\end{align} is solvable....
8
votes
1answer
60 views

Speed of convergence for minimizing Rosenbrock's function

I am minimizing $f(x_1,x_2) = 100(x_2-x_1^2)^2 + (1-x_1)^2$, where I try many algorithms to compare with each other. All of the algorithms find the optimal solution $(1,1)$ quickly, so I am not ...
8
votes
1answer
564 views

Travelling salesman problem with given number of locations to visit

There's a great example here of how to find a solution to the travelling salesman problem: ...
5
votes
2answers
560 views

Integer programming problem

I have the following exercise: Stockco is considering four investments. Investment 1 will yield a net present value (NPV) of \$16,000; investment 2, an NPV of \$22,000; investment 3, an NPV of \$12,...
5
votes
1answer
235 views

How is Big M calculated?

Because of excessive pollution on the Momiss River, the state of Momiss is going to build pollution control stations. Three sites (1, 2, and 3) are under consideration. Momiss is interested in ...
4
votes
3answers
685 views

Shortest path problem

At the beginning of year 1, a new machine must be purchased. The cost of maintaining a machine $i$ years old is given in Table 5. The cost of purchasing a machine at the beginning of each year is ...
4
votes
2answers
437 views

Shortest path problem with boxes

A company sells seven types of boxes, ranging in volume from 17 to 33 cubic feet. The demand and size of each box is given in the following table. The variable cost (in dollars) of producing each box ...
3
votes
0answers
64 views

How can I do this in GAMS?

I am mimicking a GAMS model that was introduced in Soler et al. (2013)1 to compare my new model with its results. In a nutshell, assume we have a variable $t$ that is supposed to only take certain ...
8
votes
2answers
269 views

How can I transform this MILP into an LP problem?

I have a MILP problem with one of the constraints is given below. Sometimes, even for a small-sized problem, the solver takes a very long time to find a solution. What could be an efficient ...
8
votes
1answer
205 views

Speedup or Caching for a Multi-Iteration MIP problem

I'm solving an MIP: \begin{align}\mathrm{arg\,min}&\quad\sum\limits_{i}{x_i}\\\text{s.t.}&\quad A\,x\geq1,\end{align} where both the matrix $A$ and vector $x$ are boolean valued, and $A$ is ...
11
votes
1answer
291 views

Minimize number of pieces required to cover distances, with overlap

The specific optimization problem I'm trying to solve is this: Find the minimum integer number of $2$m pieces required to cover $2$ or $4$ distances of length $D$ given that adjacent pieces must have ...
12
votes
3answers
894 views

Does it make sense to use strict equality constraint in optimization?

Once I learned from some post that the strict equality constraint in optimization problem does not make much sense. We should always use $\le$ constraint. How far this is true. If I must have a ...
14
votes
2answers
231 views

Search approach to solve optimization problem with only a minimum where time series get scaled

Currently, I am working on a relatively simple optimization problem: There is a set of time series (red) that get summed up to a cumulated time series (blue). The red time series have different forms ...
11
votes
1answer
217 views

Linearization of the product of two real valued variables - Binary expansion approach

I want to minimize the following objective function: \begin{align}\min &\quad x\cdot y\\\text{s.t.}&\quad2 \le x \le 5\\&\quad5 \le y \le 10.\end{align} Since the objective function is ...
11
votes
0answers
83 views

Armijo Line Search Parameters

I am trying to compare many unconstrained optimization algorithms like gradient method, Newton method with line search, Polak-Ribiere algorithm, Broyden-Fletcher-Goldfarb-Shanno algorithm, so on so ...
11
votes
2answers
285 views

Black-box optimization with linear programming?

In my research, I do a black-box optimization based on a simulation model with nonlinear properties. The simulation model gets an operation plan for a time period and then returns a time series, which ...
7
votes
0answers
56 views

KKT conditions validation- one dual variable equating to two values

I have the following optimization problem: \begin{alignat}2\min &\quad A(t)\cdot x(t)-B(t)\cdot y(t)+C(t)\cdot z(t)-D(t)\cdot k(t)\\\text{s.t.}&\quad z(t)+z_1(t)-y(t)-y_1(t)+x(t) = k(t);&...
11
votes
1answer
353 views

Suggested Resources for Non-Linear Optimization

I recently completed an undergraduate course in Linear Programming and Operations Research. I am willing to look into advanced concepts and Non-Linear Optimization algorithms and also, their method of ...
12
votes
3answers
1k views

YALMIP-like modeling environment in Python

What are the handiest optimization parsers out there? Is COIN-OR's PyPy being used actively? I am currently trying to do an optimization project in Python, but I am used to using MATLAB + YALMIP ...
8
votes
1answer
153 views

GLPK: meaning of the "marginal' column in the solution output

I'm using GLPK to solve an LP. I use it through its standalone solver, that I call with the glpsol command, and I get the solution detail written in a file using ...
12
votes
0answers
244 views

Categorization of optimization models

For many families of optimization problems there is some sort of classification scheme. I am thinking about the triple notation for machine scheduling introduced in "Optimization and approximation in ...
17
votes
3answers
887 views

TSP with revenue maximization

How to approach a travelling salesman problem with an aim to maximize revenue at each town visited in a certain number of days (total number of towns is greater than what can be visited in the given ...

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