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4
votes
1answer
54 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 $1$). ...
12
votes
0answers
117 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 ...
16
votes
7answers
2k 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
votes
1answer
79 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
votes
0answers
39 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
votes
0answers
59 views

Integer variable optimization - decreasing execution time

I have a variable declared as follows in AMPL: ...
3
votes
1answer
84 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 optimal (and if ...
8
votes
1answer
144 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 ...
3
votes
0answers
57 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 ...
4
votes
1answer
53 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
votes
1answer
112 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 ...
5
votes
1answer
149 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
votes
1answer
102 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
votes
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
votes
1answer
146 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
84 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
votes
0answers
75 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
149 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
184 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
votes
1answer
136 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
109 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
votes
1answer
93 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
144 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
2answers
205 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
68 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
votes
1answer
85 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
133 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
66 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
117 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
256 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
votes
1answer
98 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?
9
votes
2answers
590 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
129 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
594 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
97 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 ...
7
votes
3answers
157 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 ...
3
votes
1answer
102 views

Optimal way to ensure optional intervals are consecutive in OR-Tools

I am trying to solve a scheduling problem in OR-Tools. There are lots of "events" that need to be scheduled to "blocks" (essentially half-days). I am naturally using optional intervals for the events. ...
3
votes
0answers
56 views

Pyomo CBC 1.#j error

I am using to solve my model Pyomo/CBC combination. But rarely, CBC Gap shows 1.#j and pyomo generate an error. Hence, it doesn't get solution. How can I solve this problem? Screen output: ...
3
votes
1answer
53 views

How to set combined stop condition in AMPL/CPLEX?

I would like to set a stop condition combined of a timelimit and a relative MIP gap. So I would like AMPL/CPLEX to look for the solution of my LP for an hour and if there isn't a solution stop if or ...
-4
votes
2answers
85 views

How can I model this binary logic?

I am looking for a constraint to express the following: IF W1 = 0 AND W2 = 0 THEN Y = 0 IF W1 = 0 AND W2 = 1 THEN Y = 1 IF W1 = 1 AND W2 = 0 THEN Y = 0 IF W1 = 1 AND W2 = 1 THEN Y <= 1 ...
42
votes
10answers
6k views

Are there any COVID-19 (coronavirus) related optimization problems with input datasets that we can “crowd solve”?

Is anyone aware of a medicine/vaccine related challenges with a good problem definition and some available input datasets, ideally related to COVID-19? What kind of constraint solving challenges would ...
6
votes
2answers
197 views

How can this be expressed as a MILP constraint?

I am looking for a constraint to express the following: IF W1 = 0 AND W2 = 0 THEN Y = 1 IF W1 = 0 AND W2 = 1 THEN Y = 1 IF W1 = 1 AND W2 = 0 THEN Y = 0 IF W1 = 1 AND W2 = 1 THEN Y <= 1 ...
4
votes
1answer
148 views

Cutting-planes application procedure for a specific problem

Sort of following up with this question. I reformulated another model to make it convex and possibly solve it with some cut generation method. I would like to double-check whether I am doing it ...
3
votes
1answer
81 views

Linear programming sensitivity analysis using Matlab

I have a linear program in the MPS file format listing all the rows, columns, right-hand sides, etc. I can read that in Matlab and solve it using linprog. However, it seems there is no easy way to do ...
8
votes
1answer
270 views

if-else condition for the objective variable using big M notation

Let $0\leq \beta\leq 1$ be an objective variable. The size of $\beta$ is $N\!\times\!N$. Now, how can I impose the following? if $\beta_{i,j}>0$ then $\beta_{j,i}=0$ Big M notation can be ...
5
votes
1answer
172 views

How to represent multiple elements of the same set correctly?

In a mathematical model, I have a set $J$ of distinct jobs, and a constraint dealing with pairs of elements from the job set. Which of the following is the most accurate way to address two jobs $j$ ...
4
votes
1answer
68 views

Dealing with a non-convex problem

I have the following objective function. The variables: $h_p$, $e_{trs}\left(h_p\right), w_{trs}\left(h_p\right)$ are all non-negative continuous. $T,R,S,\pi_{trs}$ are polynomially-sized sets. All ...
5
votes
1answer
215 views

Solution time out for VRPTW in or-tools

I am experimenting around with or-tools and somehow I can't get a solution for the VRPTW problem for any of the instances I have tested from Gehring & Homberger ...
6
votes
1answer
137 views

TSP subtour elimination by assigning distance traveled

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 from $i$ to $j$ is taken or not and $...

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