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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2answers
725 views

"Types" of Problems where Evolutionary Algorithms (significantly) Outperform Non-Evolutionary Algorithms

In the field of Optimization and Operations Research : Are there "Types" any Problems where Evolutionary Algorithms (significantly) Outperform Non-Evolutionary Algorithms? For instance: ...
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1answer
46 views

"Sensitivity Analysis" vs. "Machine Learning"

I have the following question that compares how "Sensitivity Analysis" is perceived in the field of Optimization compared to that of Machine Learning. Sensitivity Analysis in Machine ...
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2answers
316 views

History of the (Famous) Simplex Algorithm?

What Real Life Problems Motivated the Creation of the (Famous) Simplex Algorithm? I was reading about the (famous) Simplex Algorithm : My Question: Were there any real world problems that people (e.g....
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0answers
75 views

Reference of Optimization in the Bible : Moses and Coins

A few days ago, I was reading some articles/stackexchange posts on the "history and origins of optimization". Somewhere, there was an interesting reference to a biblical/old testament story ...
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Optimal stopping with two variables

I'm not sure if this is a question more appropriate for QF or OR but here we go: Assume we have some money and we would like to make more money with this amount! We have two options: leave this amount ...
9
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3answers
2k views

Are Metaheuristics and Evolutionary Algorithms the "Gold Standard" for the Traveling Salesman Problem?

Are Metaheuristics and Evolutionary Algorithms the "Gold Standard" for the Traveling Salesman Problem? I am interested in learning more about how we have been able to solve the (famous) ...
4
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1answer
407 views

Is the Travelling Salesman Problem Considered as "Gradient Free Optimization"?

I was thinking about the Traveling Salesman Problem the other day - for such types of discrete combinatorial optimization problems, do they have a "loss function"? It seems that there is ...
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1answer
42 views

Assignment Problems With More than One Class of Resource

I am working on a dispatch optimization problem in the trucking industry. I have a first algorithm - a vehicle routing algorithm - that produces a series of tours. I will need a second algorithm that ...
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2answers
151 views

Eliminating Variables in Semidefinite Programs Using Equality Constraints

Suppose I have an SDP \begin{align}\min_{X \in \mathbb{S}^{n}_{+}}&\quad f(X)\\\text{s.t.} &\quad X_{i,j} = c_{i,j} \quad \forall (i,j) \in I,\end{align} where $I \subseteq [n] \times [n]$ and ...
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How to plug the obtained solutions of a pyomo model in a model

I am working on the data-driven robust optimization approach. I generated a set of robust solutions using Pyomo. Now, I want to evaluate robust solutions. To do so, I quantify the uncertain parameters ...
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2answers
308 views

Optimization Solution Framework

I am working through Pascal Van Hentenryck's excellent discrete optimization course on Coursera. While the course certainly touches on it in some ways, I am looking for more of a framework in terms of ...
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0answers
72 views

Optimization algorithms for problems with variable objective function

Let us assume a single objective binary optimization problem, where you need to solve it 20,000 times (approx) in order to tune some coefficients. The objective function includes two components. The ...
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2answers
48 views

sensitivity analysis in python + Docplex

I want to do a sensitivity analysis for the following problem. I know how to add new variables or constraints, but I do not know how I can change the right-hand side (RHS) of the constraint. ...
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0answers
64 views

Linear program with an additional second-degree utility term

I would like to solve a problem obtained from a LP by adding a second degree term to its utility. A simple example would be the following (with $c_i > 0$): $$ \min xy - c_1 z_1 - c_2 z_2 \\ \...
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3answers
186 views

optimize days between work shift

For a work shift optimization problem, I've defined a binary variable in PuLP as follows: pulp.LpVariable.dicts('VAR', (range(D), range(N)), 0, 1, 'Binary') where ...
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3answers
1k views

Solving Logic puzzles through optimization

I have the following "logic puzzle" (I think this is considered as a "scheduling problem"): In this problem, there are 5 basketball players - provided some clues about their ...
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0answers
37 views

Constructive proof for the Hyperplane Separating Theorem (HST)?

HST is usually proven through the existence of a unique minimum-norm vector in a nonempty closed convex set. I think this is an existential proof. However, to actually apply the result in a real world ...
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0answers
29 views

How to construct a restriction for a blending problem that has 2 inputs that are blended, and as result we get 2 outputs?

THE PROBLEM A refinery has 10 million barrels of type A crude and 6 million barrels of Type B crude oil. The refinery has 3 plants to produce Gasoline (it makes a profit of 2 USD / barrel) and Naphtha ...
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0answers
51 views

GENIUS (General Insertion (GENI) + Unstringing / Stringing (US) - Anyone familiar with the procedure? I have questions

I am currently trying to understand the concept of GENIUS. It was a method devoloped to solve the tsp. The first step seems logical to me: GENI (construction phase): start of with an tour of 3 nodes ...
3
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1answer
239 views

Mixed Integer Programming/Optimization using the Genetic Algorithm

I am working with the R programming language. Given a data set ("my_data"), I am trying to use an mixed integer optimization algorithm (e.g. genetic algorithm) to find out which filters ...
3
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1answer
119 views

How to retrieve the variable's value in DOCplex

I am trying to write a simple optimization problem by using DOCPLEX. I am pretty new on python+DO and What I have tried to do is: ...
3
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0answers
118 views

Good book to get familiar with the key concepts of Operations Research for a person which didn't enjoy a good math education in university?

I am currently reading research papers on optimization problems in logistics and struggle to understand the math notation. Any good beginner friendly books you would recommend? This is the paper I ...
4
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1answer
150 views

How to construct the linear programing representation of a blending problem?

THE PROBLEM A refinery has 10 million barrels of type A crude and 6 million barrels of Type B crude oil. The refinery has 3 plants to produce gasoline (it produces a profit of 2 USD / barrel) and ...
0
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1answer
86 views

Gurobi Environment should be Common or Unique for concurrent optimization problems?

Thanks for the amazing performance of Gurobi. Actually we are using Gurobi Cloud (via its python binding - Gurobipy) for our optimization requirements. Due to our ...
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2answers
167 views

How to perform clustering of two different sets of entities?

I need to perform clustering of two different entities. Lets say we have transmitters and users. The relation between a transmitters and user is defined by a weight, for example, the weight between ...
4
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1answer
118 views

Adding a group constraint to binary decision variables

I have a problem where I have N binary decision variables where each one of them belongs to a group (Where the number of groups G is less than N) and I have to choose a subset of them to maximize some ...
3
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1answer
67 views

Optimize parametric Log-Likelihood with a Tree

Suppose there are some objects with features, and the target is parametric density estimation. Density estimation is model-based. Parameters are obtained by maximizing log-likelihood. $$\operatorname{...
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0answers
64 views

Minimizing the number of machine starts

Please, if somebody has another approach to a similar MIP problem... Assume we have some machines $m$ and their activity could be interpreted by the boolean decision variable $x_{i,j} \ i \in m, j \in ...
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143 views

Why do we use the square root as a proportional measure?

I originally posted this on the Mathematics Stack Exchange site, but I think it fits more on the OR-site. I'm reading a paper where the goal is to determine the weights of a weighted arithmetic mean ...
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0answers
90 views

struggling to understand why this is a bi-objective function

i am working on a network-design problem. Where Containerflow between 2 Origin-Destination-Port-Pairs has to be fullfilled via some hub-ports. Sure, you want to pick a hub-port based on the distance, ...
3
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1answer
218 views

What does nonconvex multilinear mean?

I am not a math student so I am sometimes a bit confused when it comes to math lingo. For me non-convex would mean its concave which means functions have local minima in case of a minimization problem....
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0answers
42 views

Indeterminacy Reduction for MINLP

I am considering a Mixed Interger NonLinear Program (MINLP), and using a solver to obtain admissible solutions. Is there a general method to reduce indeterminacy of solutions (e.g. by adding ...
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1answer
125 views

Is this integer optimization problem still NP?

I have the following integer optimization problem \begin{align}\min&\quad\sum_ix_i\\ \text{s.t.}&\quad Ax \geq b\\ &\quad x \geq 0,\\ &\quad x \in \mathbb{Z}^n\end{align} where $b$ is ...
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1answer
61 views

Maximizing the number of nonnegative coordinates of $Wx$

I want to find good incumbent solutions to the following problem: $\newcommand{\RR}{\mathbb{R}}$ $\newcommand{\norm}[1]{\left\Vert#1\right\Vert}$ Given a matrix $W \in \RR^{m \times n}$, find the ...
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3answers
225 views

Scheduling for the shortest days using ILP

I've tried Or-Tools and MILP solvers a couple of different ways on this, but they take a surprisingly long time to realize that the solution they generated fairly quickly is in fact minimal. Is there ...
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0answers
35 views

Estimation of Vandermonde matrix

Cross-posted on Mathematics SE. I would like to discuss how to tackle an optimization problem to learn a Vandermonde matrix. In particular, I have an optimization problem in the following form: \...
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1answer
83 views

Spatial complexity of optimization algorithm

How can I calculate the space complexity of an optimization algorithm? Otherwise, what would happen if the complexity exceeds the machine capacity, and can I use the hardware instead of RAM? In this ...
3
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1answer
172 views

If variable falls below a certain value, include difference to set value in objective

I think its easiest to describe my goal first and continue with my implementation and the resulting problems! My goal: Using Pyomo as interface and Gurobi as solver, if a variable $x_{i,t}$ falls ...
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2answers
153 views

No value for uninitialized NumericValue object

I'm working on an optimization model in python with the pyomo library. However I'm getting an error message in python that I cannot seem to understand. The code and error message is below. My code is <...
6
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1answer
331 views

Optimize for bonuses within a group (knapsack)

I am trying to create an LP problem which is like the knapsack problem but with groups of items. Let's say there are 10 groups of items each with up to 5 items. Each group has one special item and you ...
5
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1answer
262 views

Is it possible to identify all possible Irreducible Infeasible Sets (IIS) for an infeasible Integer Linear Programming problem? (ILP)?

For an Integer Linear Programming problem (ILP), an irreducible infeasible set (IIS) is an infeasible subset of constraints, variable bounds, and integer restrictions that becomes feasible if any ...
2
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1answer
52 views

Capacitated Facility Location problem with a dynamic set up cost

I am trying to solve a Capacitated Facility Location Problem (CFLP) with a dynamic setup cost in R. The problem statement is this: I have the transport cost The ...
3
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1answer
84 views

How to formulate this optimisation problem that has time varying components?

I've been working on a optimisation problem at work regarding blending. Essentially we have different types of grain stock with different properties and we bought them for different amounts. We then ...
5
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1answer
306 views

How to optimize on a fixed-cost based on number of results?

I am trying to create an LP problem which is like the knapsack problem but where there is a fixed bonus/penalty based on the number of items chosen. There are 20 items to choose from with some weight ...
3
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2answers
129 views

Defining multiple constraints compactly where some index combinations are not defined

My question is about how usual/strange defining constraints compactly can be (in a scientific document). Formally, I define constraints $$f_{i,j,k}(x) \leq 0, \quad \forall i \in [I], \ \forall j \in [...
2
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1answer
115 views

How to solve a minimum cost flow problem with time constraints

In the following picture, the decision-maker has to make deliveries to node $V=\{1,2,3,4,5,6\}$. He has two options: use cars or bikes. In both cases, he has to make a stop at a relay point where the ...
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1answer
71 views

Formulating a linear programming problem, with indicator variables. (Solution verification)

A factory creates different types of oils and mixes them together. There exists two types of vegetarian oils (veg1,veg2) and three types of non-vegetarian oils (oil1,oil2,oil3), the price of each oil (...
4
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0answers
91 views

Weighted nuclear norm minimization

The problem. Let $X,A \in\mathbb{R}^{n\times m}$ and let $W\in\mathbb{R}^{nm\times nm}$ be a positive definite matrix. I want to know if there is a closed-form solution to this problem $$ \min_{X} \...
2
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2answers
93 views

How to prove that optimizing each component of a system separately gives suboptimal result?

The black-box system shown below has 3 components. They run sequentially to generate a final output from the input. Each component has its own parameters to optimize for better intermediate results (...
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1answer
42 views

How to compute Generational Distance, Inverted Generational Distance, Epsilon Indicator, and Hypervolume for a Pareto front?

In order to find the quality indicators like Generational Distance, Inverted Generational Distance, Epsilon Indicator, and HyperVolume for a Pareto front I want to normalize the values of ...

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