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10
votes
2answers
309 views

Many-to-many Breadth First Search

There is a directed social network with large number of nodes and arcs and there are many instances of the network (nodes are same but arcs change in each instance). You can think of it as a ...
16
votes
6answers
2k views

List of Implementations for common OR problems

For the TSP there famously is the concord solver (http://www.math.uwaterloo.ca/tsp/concorde.html) which is argubly the fastest exact solver for the TSP. There are many other problems that also show ...
25
votes
4answers
1k views

“Best practices” for formulating MIPs

Often there are many alternatives ways for formulating a MIP. For example: The model contains inequality constraints that must hold with equality in an optimal solution. The model contains ...
11
votes
2answers
432 views

Finding an optimal set without forbidden subsets

Given $n$ items, I want to select a set items $S\subseteq\{1,2,\dots,n\}$ that maximize profit. The profit of item $i\in\{1,2,\dots,n\}$ is given by $p_i$ and may be assumed to be non-negative. ...
11
votes
1answer
99 views

Suggestion of some courses in sequential decision making

I am studying about sequential decision making and I am willing to know if there is any course which is recorded and is publically available covering topics in dynamic programming (DP), reinforcement ...
10
votes
2answers
119 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?
18
votes
2answers
230 views

Mathematically creating the 'perfect' permutation for reservations in a hostel

I am working at a hostel which uses a reservation system for each room and the beds in the room (e.g. $14$ beds in one room, bed numbers $1-14$.) When we get bookings for multiple people, we assign ...
16
votes
2answers
274 views

What are some real-world applications of QUBO?

QUBO (Quadratic Unconstrained Binary Optimization) is the minimization of a quadratic function of binary variables. It has been used for computer vision, Ramsay numbers, factoring numbers, the ...
9
votes
0answers
68 views

Modelling resource dependency in the assignment problem

The assignment problem is well-studied and has a nice polynomial time algorithm. I'm interested in an extension of this problem where all edges are in a certain group and taking multiple edges from ...
14
votes
1answer
587 views

When is the McCormick envelope exact?

I know that given $S$ of the form $$ S = \{ (x,y,z) \in \mathbb R^3: \ell_x \leq x \leq u_x; \ell_y \leq y \leq u_y; z = xy\} $$ with finite lower and upper bounds, the McCormick envelope of $S$ ...
13
votes
1answer
569 views

What is quadratization?

In the context of discrete optimization, what exactly does it mean to "quadratize" a function? The term seems to be used mainly by operations researchers, in my experience.
11
votes
3answers
212 views

How to write a mixed-integer linear programming formulation in Python using Gurobi?

I can remember that I spent some time in understanding how to formulate my first model. So I aimed at presenting a complete model here, wishing to save some time for students or researchers needing it....
11
votes
2answers
182 views

Is deciding the presence of mixed-integer points in the relative interior of a polyhedron in NP?

Given $P = \{x\in\mathbb R^n: Ax \leq b\}$, I want to decide if $(\mathbb Z^\ell \times \mathbb R^{n-\ell}) \cap \operatorname{relint}(P)$ is non-empty. Is this problem in NP? One idea is to check ...
8
votes
1answer
95 views

Read an LP/MPS file in the PuLP

I was trying to read a MPS file by using the PuLP package in the Python, but I can't find any related documents on it. Does ...
15
votes
2answers
116 views

Bound on the number of constraints to be generated (lazy constraints)

I am working on a very large optimisation problem. All variables are continuous, the objective is linear and the constraints convex, but I have many such constraints (on the order of $2^n$ — actually, ...
11
votes
2answers
197 views

Can SOCPs approximate better than LPs?

Are there any classes of NP-hard combinatorial optimization problems where Second order cone programs (SOCP) gives a better approximation than linear programs (LP)? I am looking for results in the ...
15
votes
3answers
890 views

Bin Packing with Relational Penalization

There are $ N $ bins with equal capacity $ C $. In addition, there are $ N $ objects $x_1, x_2, \dots, x_N $ that need to be accomodated using the least amount of bins. Each object $x_i$ has a volume $...
8
votes
1answer
178 views

How do I access the value of a variable in PuLP?

In Python's PuLP package, how can I get the value of a decision variable? For example, if I declare a variable— ...
12
votes
1answer
126 views

QA techniques for optimization problem coding

I often spend much, much, more time QAing and debugging my code than I do actually writing the optimization problem or shaping my data. Are there any tools or techniques to make it easier? I am asking ...
11
votes
3answers
213 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 ...
10
votes
3answers
611 views

Graph problems as integer programs

Suppose I give a solver (CPLEX, Gurobi, SCIP or anything else) an IP which is a reformulation of a stable set problem (or vertex cover problem or coloring problem) of some graph, is there a way I can ...
11
votes
1answer
126 views

Heuristics for mixed integer linear and nonlinear programs

What are some primal heuristics that mixed-integer linear and nonlinear program solvers use to quickly obtain a reasonably good feasible solution?
22
votes
2answers
537 views

How to select a Constraint Programming Solver

I would like to clarify that I am absolutely not an expert when it comes to constraint programming (I happen to use it when it seems to be the right tool for the right job). It is my understanding ...
5
votes
0answers
76 views

maximum eigenvalue across subsamples

I have an $N$-dimensional vector of data, say $X_{t}$, with $1 \leq t \leq T$. Of this vector $X_{t}$, I want to consider sub-vectors, say $X_{t}^{b}$, which are $m$-dimensional combinations of ...
6
votes
1answer
56 views

Minimizing a project costs through nonlinear optimization

I have a project and I want to minimize the costs. I am are responsible for the inspection of 1000 miles of sewer grid in Canada. My goal is to provide time high quality inspection reports. I tried to ...
7
votes
1answer
291 views

KKT inequality conditions

Let's say I have an objective function $$f(x_1,x_2, \cdots, x_n)$$ and $N$ constraints $$x_i \ge 0. $$ I am trying to solve it with KKT conditions. Now the objective function becomes $$f(x_1,x_2,...
19
votes
5answers
1k views

Ordered list of OR journals

Is there any compact resource that includes a list of all academic journals in the OR/MS space, ranked by journal importance? Although there are some helpful features offered by publisher websites ...
10
votes
2answers
124 views

Global optimality condition of non-convex quadratic programs

We know that a convex quadratic maximization (not minimization!) on a polyhedron has its global optimal value on a vertex. Also, I have read in some papers that checking whether a vertex is globally ...
12
votes
1answer
419 views

How to formulate maximum function in a constraint?

How to formulate (linearize) a maximum function in a constraint? Suppose $C = \max \{c_1, c_2\}$, where both $c_1$ and $c_2$ are variables. If the objective function is minimizing $C$, then it can be ...
13
votes
6answers
600 views

Are metaheuristics ever practical for continuous optimization?

All of the applications of metaheuristics that I can think of are for discrete optimization (usually combinatorial optimization) problems. Are metaheuristics ever practical tools for continuous ...
8
votes
2answers
357 views

Gurobi's “Out of memory” error without exhausting the RAM?

I wrote a branch-and-price algorithm in Python 2.7 which solves several small LP and MIP models by Gurobi 8.1 in each node. The algorithm runs fine at first, it produces both lower bound and upper ...
11
votes
1answer
381 views

Prove that these linear programming problems are bounded by $O(k^{1/2})$

Prove that these linear programming problems are bounded by $O(k^{1/2})$ The expanded partial sums of the Möbius inverse of the Harmonic numbers have two out of three properties in common with this ...
5
votes
1answer
74 views

Python PuLP - Unable to Model Non-Square Matrix

I am having issues with setting up constraints using both input arrays from excel and variable arrays within PuLP. It appears the model only works with square matrices and my final code has a matrix ...
16
votes
3answers
353 views

As an Operations Research professional, how is your time divided when working on an optimization project?

When working on an optimization project, what is the typical time division (in percentage) between the various tasks that you have to work on: Problem understanding/definition (figuring out what is ...
31
votes
6answers
2k views

How to determine the correct level of detail when modelling?

"All models are wrong, but some are useful" - George E. P. Box I usually work on what one could call operational problems. There I usually do not have too much trouble figuring out the level of ...
12
votes
1answer
134 views

When is the original BFGS algorithm still better than the Limited-Memory version?

I have been going through Andrew NG's original data science course on Coursera. I learned the BFGS algorithm at some point in my OR education, but not the Limited Memory version that Andrew NG focuses ...
11
votes
2answers
139 views

partitioning hub assignment models

When solving large-scale hub assignment models (1000+ candidate hubs and 1000+ demand nodes), it is possible that parts of a cost matrix are not connected to one another. A typical workflow would be: ...
10
votes
2answers
173 views

Parallelization of an existing Adaptive Large Neighbourhood Search Heuristic

I am solving (or say, trying to find good solutions for) an arbitrary combinatorial optimization problem, think of it as a Vehicle Routing Problem with a bunch of side constraints that are not ...
13
votes
3answers
1k views

Are there any efficient algorithms to solve the longest path problem in networks with cycles?

I have a directed social network and as a preprocessing step I need to calculate the longest path lengths for each node. Longest path problem is NP-hard as far as I know but I've seen dynamic ...
1
vote
2answers
185 views

Is there any way to generate all the possible undirected graphs with unlabeled nodes?

I am looking for an efficient algorithm to generate all of the unique graphs for a given number of nodes. For small instances, the total number of graphs are as follows: n=2 G=2 n=3 G=4 n=4 G=11 ...
12
votes
2answers
244 views

Correct way to get a dual extreme ray for an infeasible LP in CPLEX / C++

We are coding a Benders decomposition using CPLEX/Concert (C++) and we are having some troubles to generate a feasibility cut because we are not sure how to get an extreme ray of the dual for a primal ...
9
votes
2answers
116 views

Does dispersion really matter?

Context: Given a counting process $\{N(t),\,t\ge 0\}$ which tracks the number of events (arrivals) by time $t$, the index of dispersion (for counts) is the variance-to-mean ratio of the cumulative ...
11
votes
3answers
179 views

Applicability of Lagrange Multipliers in the analysis of large-scale MILPs?

Qualitatively, in my experience in the solving of large scale MILPs, it is common that binary variables corresponding to "edge possibility" components are frequently chosen. Intuitively, these seem ...
7
votes
4answers
253 views

Solving MIP in Java with free software

I would like to solve mixed integer programs in Java. I need an approach that relies purely on software that is free (not only for academic use, but also for people outside academia). What would be ...
10
votes
4answers
161 views

How to linearize a constraint with a maximum of binary variables times some coefficient in the right-hand-side

I have the following constraint that I'd like to linearize: $P$ is a given set $b_p \in \{0,1\} , \forall p \in P$ a binary variable associated with each element of $P$ $c_p \in \mathbb{R}^+$, a ...
3
votes
0answers
51 views

Cellular Automata and MIP Resource Repository? [closed]

Apologies if this is not an appropriate question for the SE, however, considering that it is in beta testing it might be worthwhile. Note that "Cellular Automata" is not yet a tag, so perhaps there is ...
18
votes
3answers
185 views

Variable bounds in column generation

Consider the set covering problem \[ \begin{align} \min&\ \sum_{j=1}^nc_jx_j\\ s.t.:&\ \sum_{j=1}^na_{ij}x_j\geq 1,\quad \forall i=1,\dots,m\\ &\ 0\leq x_j \leq 1 \end{align} \] ...
13
votes
3answers
82 views

Good distribution assumptions for customer demand in a supply chain

Why do we normally assume normal distribution/Poisson distribution for customer demand in a supply chain? Are there other good distribution assumptions?
10
votes
1answer
96 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(\...
9
votes
1answer
97 views

Advantages of IBM CPLEX Studio over CPLEX in MATLAB?

This question comes from the perspective of an MSc student new to both OR and programming OR problems in a MIP framework. My research has led me down this path of needing to program an optimization ...

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