# 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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### Simulation optimisation: Monte carlo simulation, regression, optimise within regression model?

Can you help me identify if this technique has a standard name to help me explore the literature? Suppose I have a black-box stochastic simulation parameterised by $X=[x_1,...,x_p]$ with some single ...
740 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 ...
333 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 ...
119 views

### Run repeatable numerical tests in the cloud

In numerical tests of optimization algorithms, one often reads "We used a XY computer with X GB RAM for the experiments". Usually, when I want to compare my results with theirs, I do not have an XY ...
206 views

### Protein folding and protein design relation

I understand from this active COVID-19 question: Are there any COVID-19 (coronavirus) related optimization problems with input datasets that we can "crowd solve"? that the protein folding ...
223 views

### Simplest way to eliminate redundant constraints due to a new cut

I have a polyhedral set for constraining $x$: \begin{align} \mathcal{P} = \{x \in \mathbb{R}^n_{+} : \ Dx \leq d \} \end{align} where $D \in \mathbb{R}^{m \times n}, d \in \mathbb{R}^m$. I find the ...
291 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 ...
745 views

### What is a “hard problem” in the context of Mixed-integer programming?

As a practical (real-world problems) point of view, it's important we could solve optimization problems as quickly as possible (for instance, to release a daily schedule). Maybe a problem with many ...
1k views

### Allocating credit card points

I’m interested in the idea behind this in general, so I thought this would be the best place to post, though I have a practical and semi-urgent need of allocating the points on my credit card towards ...
471 views

### Expressing a chain of boolean ORs using ILP

How to express a chain of OR operations in an ILP in which each expression is a less than or equal constraint and the left hand side variable in all inequalities is always the same? All the variables ...
2k views

### Performance of a branch and bound algorithm VS branch-cut-heuristics

I was trying to solve a moderate scheduling model using an open-source solver. I did two different ways. A) using pure branch and bound algorithm (disable all options). B) using the default setting ...
1k 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 ...
597 views

### Difference between lazy callbacks and using lazy constraints directly

I'm trying to use lazy constraints to solve an optimization problem. In some software such as CPLEX or GUROBI, they have some tools to handle them directly (in the original model) or using callback ...
454 views

### How to handle an IP sub-problem with an objective function in Benders Decomposition

I have a question on Benders Decomposition (BD). Suppose I have an MILP model which can be decomposed into a master problem (MP) including integer and continuous variables and a subproblem (SP) ...
287 views

### Is my approach to my internship project good? Optimal allocation of product across stores, constrained optimization

Context: I am a CS student currently in a non-CS internship (logistics, supply chain). My manager wants to leverage my knowledge of programming to build a program to solve the following problem: As ...
136 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 ...
362 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 ...
423 views

### Convex Maximization with Linear Constraints

I am doing active research in convex maximization w.r.t. linear constraints. There are many cases which can be efficiently approximately solved, e.g., convex quadratic maximization, log-sum-exp ...
299 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 ...
1k views

### If-then constraints in MIP programming

For continuous variables $x$ and $y$, the constraints are: ...
79 views

### In portfolio optimization, how do we estimate the variance of a new asset?

Say I want to do Portfolio Optimization using the mean-variance approach (i.e Markowitz model), but that some of my assets are new with no returns history. I can use a judgmental (expert knowledge, ...
150 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 ...
189 views

### Looking for books in the same style as Hans Kellerer 2004, Knapsack Problems

I really enjoyed reading Hans Kellerer, David Pisinger, Ulrich Pferschy 2004 book Knapsack Problems. Can anybody recommend books in a similar style, about some other classes of problems / optimisation?...
264 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 ...
99 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 ...
4k views

### Soft constraints and hard constraints

The terms "soft constraints" and "hard constraints" are used in the context of optimization modeling. Is there any standard way to figure out which is which in some of the complicated models?
958 views

### Integer programming problem with simple quadratic objective function in Python

I have $n$ objects that need to be divided among $k$ groups. Each group must receive at least $5$ objects. In addition, the percentage of objects in group $i$ should be as close as possible to $p_i$ ...
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 ...
631 views

### How can I estimate the monetary savings of a operation research application?

Developing operation research applications for industry clients is often very costly since it is in my experience often a custom special development for the client. The cost of developing a running ...
1k 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, ...
348 views

### How difficult is it to understand a Machine Learning method based on integer optimization?

I'm trying to understand a paper called "Supersparse Linear Integer Models for Predictive Scoring Systems" by Ustun, Tracà and Rudin, who introduce a really interesting method for generating an ...
264 views

### Expressing a chain of boolean ORs using ILP involving different variables

How can I express a chain of OR operations in an ILP, given that each operand is an inequality between two binary variables? I have asked a similar question here: Chain of Boolean ORs. In that ...
422 views

### What are the pros and cons of LocalSolver?

LocalSolver is a company which provides a global optimization solver, combining exact and heuristic techniques. The benchmarks on their website are quite impressive. For example, they claim they can ...
122 views

### Is a “multistep” or “multiphase” Newsvendor model possible?

I'm trying to address the question of how many times should I order a product from my supplier, assuming highly stochastic demand. In my mind there would be something like the Newsvendor model, but ...
284 views

### Decoding a Deep Neural Network as an Analytical Expression for Optimization Purpose

This post is not really about a specific question but rather a topic I am curious about to know more. We know that when it comes to integrate machine/statistical learning with optimization for the ...
410 views

### How could we simplify solving the large scale MIPs without using any advanced methods like decompositions?

Many practical optimization models (specially MIPs) are NP-Hard and solving them need much time even with the modern solvers like CPLEX or GUROBI. One of the best way (but not easy) is using ...
226 views

### Is the “reverse search” algorithm of David Avis the state-of-the-art method for finding discrete solutions to a system of linear inequalities?

Is the "reverse search" algorithm of David Avis the state-of-the-art method for finding discrete solutions to a system of linear inequalities? If it is not, then what is? For $m$ inequalities in $d$ ...
653 views

### How to use warm start to solve MIPs efficiently?

I'm working on the scheduling model which takes a long time to solve to optimality (even for a small instance), therefore I would like to use a warm start (MIP start) to solve the problem. I'm using ...
228 views

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### How to maximize “contrast” between nodes on a graph?

I have an undirected graph such as the one shown below. I can make up to 3 choices about the color of each node. The edge weights are equal to the difference between the nodes, given by the "...
345 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.
454 views

### What is the difference between job shop scheduling and resource constrained project scheduling?

I read here https://slideplayer.com/slide/3353960/ that RCPS is a generalized version of job shop scheduling. I'm new to this area and I'm trying to classify a specific variation of these types of ...
209 views

### How can I model regression with an asymmetric loss function?

Mosek provided a concrete example of using the Huber loss function, Huber loss, which is great! One problem I am trying to tackle is to use asymmetric loss, as described in the answer of asymmetric ...
973 views

### Graphical method in linear programming

This page describes the graphical method to solve a linear program. The formulation is as follows. \begin{alignat}{2} \max &\quad Z = 200W + 100B\\ \text{s.t.} &\quad 1W + 0.8B &&\...
163 views

### Use integer/quadratic programming to maximize consecutive zeros in a binary array

A binary array $t = [t_1, t_2, t_3, t_4, t_5]$ with each element a binary integer variable taking values 0 or 1. You can think this vector as slots with 1 representing the slot being taken and 0 ...
130 views

### Algorithmic gap for Hochbaum's (greedy) algorithm for (metric) uncapacitated facility location

In Jain et al. (2003)1, at the bottom of page 801, they construct an instance of (metric) uncapacitated facility location for which they claim the greedy (Hochbaum's) algorithm has gap \$\Omega\left(\...
1k views

### Infinite horizon versus finite horizon MDP

When can we approximate a finite horizon MDP with infinite horizon? Can we use infinite horizon stochastic shortest path problem on a directed acyclic graph?
129 views

### Approaches for choosing a “risk” factor in an Inventory Optimization problem?

I'm working on an Inventory Optimization (Allocation) problem. The decision variable is the amount of inventory budget to allocate for each product, from a set of products. My objective is to ...