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VRP benchmark instances with charging stations

Are there any benchmark instances for VRP with charging stations? I also have various delivery points with charging stations in the city(Multiple Vehicles). How can I compare my formulation?
6
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3answers
176 views

Scheduling problem data generation

I compare the strengths and weaknesses of paradigms and approaches within those paradigms for solving machine scheduling problems. The amount of real-world data I have is limited and (random) ...
10
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1answer
42 views

Benders subproblem feasible region dependent upon solution master problem

Suppose I want to solve a naturally MINLP problem of the following form: $$ \min_{x,y} \{c'x + y \mid Ax \leq b, Dx + Ey \leq f, G(x)y\leq g, x \in \mathbb{Z}, y \in \mathbb{R}^+\} $$ Here $G(x)$ ...
5
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0answers
24 views

MWIS on the 2-section of a specific uniform linear hypergraph

I have cross-posted the question from cstheory since it also very much fits the OR domain. My question concerns the maximum weight independent set (MWIS) problem on a certain (but "nice") graph. In ...
5
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1answer
83 views

Which solver solves PSD constrained convex non-linear problem

I have a problem with a vector variable $w \in \mathbb{R}^n$ and a symmetric matrix variable $V \in \mathbb{R^{n \times n}}$. I am solving a problem which is roughly like: \begin{align} \begin{array}{...
8
votes
3answers
403 views

Is there a better way to formulate this constraint?

Let $x_{r}^{j}=1\iff$ the machine schedules job $j$ using resource $r$. My constraint says that: a resource cannot be used twice, i.e., if $x_{r}^{j}=1$, then $x_{r}^{j'}=0$ for $j'\neq j$. I write ...
10
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2answers
103 views

How to exploit known solution in MILP

I have an MILP model to which I get an integer feasible solution as a result of a heuristic search. In this particular example, the initial solution turns out to be the optimal solution, which I prove ...
8
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2answers
69 views

Which MiniZinc-compatible solvers are best suited for floating decision variables and non-linear constraints?

We are working on a production scheduling problem that has both discrete ("how much to produce from good x and where") and continuous elements ("keep the workload of a production site below 0.7"), ...
5
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1answer
56 views

Maximum weight b-matching with global cardinality constraint

Suppose $A$ is an $n$-by-$n$ symmetric matrix whose entries are all nonnegative. $A_{ii} = 0$ for all $i$. We want to find an $n$-by-$n$ binary ($0/1$ valued) matrix $X$ that maximizes $$\sum_{ij} A_{...
6
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2answers
62 views

how to penalize a shortfall of a sum of absolute values

I have a model where there is a constraint on the sum of absolute values, and I would like to add a penalty on the shortfall from the constraint. More specifically: \begin{align*} \text{maximize}\ &...
4
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1answer
32 views

Inputting logical constraints into a binary programming model in Gurobi

I am very new to Gurobi and OR in general (I'm in my first class for it now), so apologies if this is a very obvious answer. For a project in that class, I am generating a flight schedule for a ...
4
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1answer
44 views

Optimize probability parameter in an optimal control problem

We have a game with infinite but countable rounds. We have one machine, that may either break down, or continue operating. For each round the machine operates, it gives cost $-1$ (so profit of $1$). ...
11
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0answers
84 views

Protein folding and protein design relation

I understand from active COVID-19 question Are there any COVID-19 (coronavirus) related optimization problems with input datasets that we can "crowd solve"? that protein folding problem is ...
12
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7answers
1k views

Does there exist an aggregation of videos on optimization?

Is there a website or otherwise maintained list of talks regarding mathematical optimization? This would be a big help for the community it seems. I'm most interested in those relating to integer ...
4
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1answer
61 views

Minimize a convex function over a sphere

Problem description Let $\mathcal{C} = \{X \in \mathbb{R}^n \mid g(X) \leq 0\}$ with $g(X)$ a convex function. Suppose I need to solve the feasibility problem, for a given $r>0$ $$ \exists ^?X \...
4
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0answers
34 views

Help with constrained or regularized optimization problem involving variable matrices and powers of matrices (or perhaps matrix logarithms)

I am attempting to solve the following optimization problem: $$ \small\min_{A,B,C} \| Y_A - AX_A \|_F + \| Y_B - BX_B \|_F + \| Y_C - CX_C \|_F + \lambda_1 \|B - A^2\|_F + \lambda_2 \|C - A^4\|_F $$ ...
3
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0answers
46 views

Integer variable optimization - decreasing execution time

I have a variable declared as follows in AMPL: ...
3
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1answer
70 views

Linear programming explanation in Algorithms by Sanjoy Dasgupta

I am reading about simplex algorithms in a textbook titled Algorithms by Dasgupta-Papadimitriou-Vairani. On each iteration, simplex has two tasks: Check whether the current vertex is ...
8
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1answer
101 views

Can Gurobi or CPLEX handle nonlinearly constrained problems?

Though my title is quite general (please feel free to edit), indeed, I wonder if the following models can be solved in Gurobi or CPLEX. Model 2 is just an alternative one to Model 1. Although we ...
-4
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0answers
36 views

Sales Impact Corona Infections [closed]

Given a company's sales per day and the number of corona infections are there good models that help us to predict the future sales increase or decrease, i.e. good model(s) showing the correlation ...
3
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0answers
52 views

Strong Duality and Slater Condition

I am studying the Duality Chapter of Convex Optimization by Boyd. Is it possible that strong duality holds for non-convex optimization? If yes, is there any specific condition? And, what is the ...
3
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1answer
48 views

Find the number of idle intervals with weights

We have one job $i$ and one machine. Let $\mathbf{x}_i=[x_{i,1},x_{i,2},\ldots,x_{i,T}]$ be a binary vector where $x_{i,t}=1\iff$ job $i$ is scheduled at time $t$. Let $u$ be a positive number. I ...
4
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1answer
76 views

Transforming a Quadratic constraint to SOCP

I have a problem similar to Markowitz portfolio optimization that I would like to transform into second-order cone programming. I have a linear objective function with a quadratic constraint (assuming ...
4
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1answer
139 views

Find the cheapest shopping cart

Given a list of items to buy on an e-commerce, generate the cheapest possible cart (which obviously includes all the items). The items can be purchased from many sellers at different prices. Sellers ...
5
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1answer
100 views

Concavity: Definition similar to sub-modularity

We know that for $b \geq a$, and some $s \geq 0$, a concave function $f$ satisfies: $f(a+s) - f(a) \geq f(b+s) - f(b)$. This is not a frequent definition of concavity, but can be found, e.g., here....
6
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2answers
1k views

IF X = 0 THEN Y = 1, IF X > 0 THEN Y => 0

I'm trying to model the following IF $tS = 0$ THEN $Y = 1$, IF $tS \gt 0$ THEN $Y \ge 0$ $tS$ is a positive real number and $Y$ is binary. I tried the following: $tS - \epsilon \ge -M Y$ but ...
9
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1answer
133 views

Operations Research Apps for everyday use

Since I am confined and I have some free time, I am looking for ideas of OR applications in everyday life. What I've seen so far are apps like solving VRP, Production planning etc. that are mostly ...
6
votes
2answers
70 views

Are there some benchmark problems for CSP Solvers?

I am building my own CSP solver with simple backtracking, AC3 filtering and variable/value ordering heuristics. It supports non binary constraints. I've done some good progress and I'd like to ...
5
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0answers
70 views

How to communicate number of integer combinations to a user

I'm working on a nifty little feature for our next release, i.e., to print the number of possible integer combinations left during branch and bound. This is really handy for the user because they ...
4
votes
1answer
105 views

Solving vehicle routing problem in java

I am trying to solve vehicle routing problem in java and I am looking for libraries for the same. I did a POC using google or-tools and it seems to be solving all my use cases. I would like to know if ...
9
votes
1answer
158 views

Compute the distance from a point inside a convex set to the boundary of the set

Problem Let $\mathcal C = \{ X \in \mathbb{R}^n \mid g(X) \leq 0\}$ where $g$ is convex, and let $X_c \in \mathcal{C}$. Is there any algorithm to compute the distance from $X_c$ to the boundary of $\...
6
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1answer
62 views

CP-SAT ortools - Is there any complete list of possible/available StringParameters for the CpSolver?

I wonder if there is any list of string parameters documented. So far, I only know max_time_in_seconds and num_search_workers. ...
3
votes
2answers
92 views

Minimizing a variable over the intersection of simplex and linear constraints

I am solving: \begin{align} \begin{array}{rll} y^* = \min & y & \\ \mathrm{s.t.} & a_i^\top x \leq y, & i=1,\ldots,m \\ & x \succeq 0,\ \mathbf{1}^\top x = 1. & \end{array} \...
4
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1answer
87 views

Constraint programming in OPL: intervals covering time slots

I am trying to model the following: There is a shop open from xx AM to yy PM. In each 30 min time slot, there have to be demand[timeSlot] = x employees present. E.g. the shop is open from 08am to ...
14
votes
2answers
1k views

Why do we need to measure the difficulty of mixed-integer programming problems?

I'm doing a project about the estimation of the difficulty of mixed-integer programming problems. The MIP instances are from MIPLIB 2017. And there are three categories of MIPs provided by MIPLIB 2017,...
5
votes
1answer
136 views

Propagate value through a graph

Here is my question where I am propagating distance through the graph, I was wondering if it is possible to do when the graph has cycles, i.e., traveling the same node multiple time then is it ...
6
votes
1answer
95 views

Cplex 12.10: How can I solve an LP relaxation?

I have an IloCplex object which contains a MILP. Is there a way to obtain the objective value of its LP relaxation, without having to rewrite the entire model as ...
3
votes
1answer
46 views

Logical operation on an array in DOCplex

Here is a simple example of logical operation in docplex taken from here. Code below works fine. ...
3
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1answer
49 views

Controlling the constraint execution sequence in docplex

I have tried to implement my question asked here with the help of Github code link. Below is the linearized version of the MTZ like constraint as per the answer given here. Constraints below assign ...
6
votes
2answers
126 views

Existence of Optimal Solution

Assume we are solving $\min\{f(x) \ | \ x \in S \}$. If $f: \mathbb{R}^n \mapsto \mathbb{R}$ is a proper closed convex function, and $S$ is a non-empty closed convex set, does this imply that the ...
7
votes
1answer
57 views

Gurobi: can you retrieve the dual solution from each node of the B&B tree using callbacks

When solving a MIP with Gurobi, one can use the cbGetNodeRel() function to extract the primal solution to the LP relaxation at each node in the branch and bound ...
5
votes
1answer
96 views

Converting if else condition to MIP constraints - validation

I have an if else condition as follows: If $g \ge 0$ then $e=1$, else $e=b$. I formulated MIP constraints using big-M as follows where I am setting $\delta=1$ if $g \ge 0$: \begin{alignat}2g &\...
5
votes
2answers
251 views

How can this relationship be modelled?

I declare an array of binary variables as $y(i), i = 1, ..., N$ I would like to model the following: If $y(i-1) + y(i) = 1$ then $y(k) = 0$ for $k < i$ and $y(m) = 1$ for $m \geq i$ To make ...
3
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1answer
95 views

Graphical illustration Excel

I have formulated a linear optimization model and solve it using the Excel Solver. How can I illustrate the slacks vs usage?
8
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2answers
528 views

Modeling and solvers

I have just started to dive into OR world on my work. Currently we are using GAMS with Gurobi but some of us have strong programming background and would like to have more programmatic approach to OR. ...
4
votes
1answer
110 views

TSP subtour elimination with multiple formulations

Referring to the question here. Given a set $S$, which we need to travel following TSP rules. I was wondering if this sub tour elimination method is good enough or not? Let $b_{i,j}$ denote edge ...
8
votes
2answers
553 views

Is there a way to view added constraints in Gurobi (Python)?

I should note that I am very new to Gurobi so apologies if this is obvious. I am working on a project for a class to maximize profit on a theoretical flight network by deciding which routes to fly at ...
3
votes
2answers
96 views

How can I direct the behaviour of a MILP Solver

I have a model involving constraints of the form $$d(i) = a \cdot W(i) + b \cdot B(i)$$ where $W(i)$ is binary and $d(i), B(i)$ are positive reals. The objective function is $\max\sum B(i)$. While ...
6
votes
2answers
88 views

Ways to strengthen QCQP relaxations

I was wondering what types of methods can be used to strengthen QCQP relaxations. Our solver has all the standard stuff, like constraint propagation, presolving, etc., but some QCQP problems seem to ...

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