Questions tagged [combinatorial-optimization]
For questions about optimization over a discrete solution space.
43
questions
5
votes
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
votes
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
$$\sum_{ij} A_{...
4
votes
1answer
50 views
How to model $A_i=B_i$ for only one $i$
I would like to model the following:
Only one of the following equalities can hold.
$$(A_1 = B_1)\quad\text{OR}\quad(A_2 = B_2)\quad\text{OR}\quad\dots\quad\text{OR}\quad(A_k = B_k)$$
I can ...
4
votes
2answers
133 views
How to model If $A \le B$ then $Y = 1$, otherwise $Y = 0$
Somehow I don't get it right.
I would like to model the following:
If $a\le B$ then $Y=1$ otherwise $Y=0$ where $A, B$ are reals and $Y$ is binary.
I can model as follows:
$Y \cdot A \le B$ and ...
12
votes
2answers
190 views
Restoring a list from differences
Given a list of (absolute valued) pair differences ordered and with duplicates removed, how can we recover/reconstruct the list that generated these differences? We do not know anything about the ...
10
votes
2answers
303 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.
9
votes
1answer
99 views
Equivalence of formulations
I have a simple model such as:
\begin{align}\max&\quad z=X_1+X_2+X_3+X_4\\\text{s.t.}&\quad y_1+y_2+y_3+y_4=2\\&\quad X_1 \leq y_1\\&\quad X_2 \leq y_1+y_2\\&\quad X_3 \leq y_2+...
17
votes
3answers
484 views
What's the current status of the Vehicle Routing Problem in the logistics industry?
After a bit of reading I think I've been able to conclude that state-of-the-art VRP can get solutions for 100~500 stops.
My question is around how this actually affects logistics (like Amazon for ...
8
votes
3answers
416 views
Equipment replacement problem
I have a question on the Equipment Replacement Problem, where the following is taken (with some syntactic modifications) from IB2070 Mathematical Programming II (MP2), Warwick Business School.
...
7
votes
1answer
99 views
How to convert 3D bin packing problem to 2D bin packing approximation?
I'm trying to approximately solve a 3D container loading problem. Is it possible to use 2D bin packing algorithms? If so, how do we make the transformation? What are the conditions needed to make the ...
12
votes
1answer
184 views
Two-stage $k$-means clustering
The problem I am facing is clustering problem, needed for a Vehicular Routing Problem (VRP) I'm tackling. It is a heterogeneous VRP with Time Window (TW) and a capacity utilization constraint, i.e. a ...
8
votes
2answers
382 views
Is there a greedy heuristic approach to the MILP problem?
I have the following optimization problem which is an MILP. I can solve it with an MILP solver.
\begin{alignat}{1}\max_{x_n,t}\,&\quad t\quad\\\text{s.t.}&\quad\sum_{n=1}^{N} x_n \,&= M\\...
9
votes
3answers
686 views
Modeling the Choose function
In statistics, one often encounters the choose function ${x \choose y}$ which encodes the number of ways of choosing $y$ items from a set of $x$ items. How would one go about modeling a choose ...
9
votes
2answers
148 views
How to formulate a MIP that can minimize the costs with a combination of subsets given a set?
I am trying to solve the following problem. I have a set $\{1,2,3\}$, which gives the following subsets with its costs:
$\{1\}=8$, $\{2\}=9$, $\{3\}=7$, $\{1,2\}=9$, $\{1,3\}=18$, $\{2,3\}=15$ and $\{...
14
votes
1answer
366 views
Duality in mixed integer linear programs
I know that the standard duality theory for the linear programming problem does not hold for mixed integer linear programming problems. I was wondering why an integer program does not have a dual ...
10
votes
2answers
163 views
Optimal set order to maximize stochastic reward
You have a ticket allowing you to visit up to $n$ of $M$ carnival booths offering games of chance. At each booth you have probability $p_{i}$ of winning a reward with average value $r_{i}$. Each booth ...
10
votes
2answers
72 views
Heuristic methods for optimising complex black box function over permutations/ranks?
Suppose I have a set $S=\{1,2,\dots,500\}$ and some function $f(\sigma)$ from the permutations $\operatorname{Perm}(S) \rightarrow \mathbb{R}$ to be minimized.
The function is complex (simulation ...
17
votes
3answers
561 views
Variable fixing based on a good feasible solution
Suppose you have a combinatorial optimization problem that is formulated as a mixed integer linear program (minimization). The problem size is denoted $n$ and the expected $n$ is around $100$. The ...
9
votes
2answers
177 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 ...
9
votes
2answers
121 views
CVRP With Unconstrained Fleet Size: Upper Bound on Optimal Fleet Size
Given a CVRP where the number of trucks is not constrained, is there an upper bound on the number of trucks used in an optimal solution in terms of number of customers, some distances, capacities, and ...
6
votes
0answers
69 views
What are the top three applications (in terms of number of citations) of the “reverse search” algorithm of David Avis?
I can see that this algorithm is quite popular, and that one of the original papers now has 820 citations on Google Scholar. However, what are the most highly cited applications of it?
If in Google ...
14
votes
2answers
612 views
State-of-the-art algorithms for solving linear programs
Průša and Werner (2019) show that the general linear programming problem reduces in nearly linear time to the LP relaxations of many classical NP-hard problems (assuming sparse encoding of instances)....
9
votes
1answer
110 views
How to get solver time from CPLEX when using the NEOS server through Pyomo?
I've been using CPLEX on the NEOS server, via Pyomo, to solve a binary program I'm working on.
NEOS is amazing, but the documentation is somewhat lacking on the Pyomo side, so I haven't been able to ...
13
votes
7answers
816 views
What are the examples (applications) of the MIPs in which the objective function has nonzero coefficients for only continuous variables?
I'm specifically looking for real applications of the following form of MIP:
$$\max\,Cx$$
subject to:
\begin{align}Ax +By &= D\\Ax &= E\\By &= F\\ x &\ge 0\\ y &\in \mathbb{...
8
votes
1answer
90 views
What class of scheduling problem models jobs which require multiple machines simultaneously?
In the Flow/Job Shop problems, and other related scheduling problems, a common assumption is that at any given time, a particular job will be being processed on at most one machine (usually... none).
...
6
votes
2answers
257 views
How to modify EMSR when capacity for each fare class is different
In the normal EMSRa and EMSRb (Expected Marginal Seat Revenue) algorithms, each fare class is utilizes exactly 1 unit of capacity (for example, one seat on a plane).
But I have a similar problem for ...
14
votes
3answers
2k views
A variant of the Multiple Traveling Salesman Problem
I am trying to find a reference (or a reformulation) of a variant of the multiple Traveling Salesman Problem, where multiple agents need to visit each vertex in a graph with minimal cost.
Most of the ...
8
votes
1answer
384 views
Finding minimum time for vehicle to reach to its destination
Given a set of Vehicles with source and destination I need to find the minimum time of travel for all the vehicles, there are also some charging stations and its necessary for vehicles to charge 1 ...
7
votes
1answer
129 views
How to interpret the random solution pick by Lévy flight on cuckoo search
I am working on an implementation of Cuckoo Search for a set covering problem. After reading some papers I cannot understand how choosing a random solution (new cuckoo) works. What I see is that ...
7
votes
1answer
233 views
How to reformulate (linearize/convexify) a budgeted assignment problem?
I have a scheduling problem at hand. In my system, there is a service station with $M$ service outlets, therefore, the service station can serve $M$ users at a time. But, there are $N$ users $N>M$ ...
12
votes
2answers
114 views
Benchmark problems for combinatorial multi-objective optimisation
Does anyone know of any good benchmark problems for combinatorial multi-objective optimisation? Something where pareto frontiers are known for example would be very useful.
25
votes
5answers
2k views
Optimization terminology: “Exact” v. “Approximate”
In optimization literature, I frequently see solution methods termed "exact" or "approximate". (I use the term "method" here because I suspect exactness, or its lack, is a function of both algorithm ...
7
votes
2answers
319 views
How can I linearize or convexify this binary quadratic optimization problem?
I have an optimization problem as below. I am having a hard time with the last constraint.
$\max \eta$
subject to
${\bf U}(:,m)^T{\bf A}{\bf U}(:,m)=0,m=1,2,\cdots,M$
here
$\bf{A}$ is a Binary ...
15
votes
4answers
588 views
Optimization models for portfolio optimization
What are the mainstream models for portfolio optimization? We have Markowitz mean-variance model and CVaR-based models (e.g., max return subject to a CVaR constraint). What else is out there in terms ...
11
votes
2answers
446 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.
...
16
votes
2answers
375 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 ...
16
votes
3answers
923 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 accommodated using the least amount of bins. Each object $x_i$ has a volume ...
5
votes
0answers
96 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 ...
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 ...
10
votes
1answer
123 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(\...
10
votes
1answer
98 views
Relationship between the Assignment Problem and the Stable Marriage Problem
Suppose I'm solving a minimum-weight matching problem in a bipartite graph with sets $\mathcal{I}$ and $\mathcal{J}$, where $w_{ij}$ denotes the weight of matching item $i$ to $j$. I can model the ...
18
votes
1answer
170 views
Combinatorial Optimization: Metaheuristics, CP, IP — “versus” or “and”?
"Recently" someone asked on Twitter whether "people still use genetic algorithms for integer programs". The "majority answer", i.e., 1 out of 1, was: "Yes" .
So, my follow-up question is: With all ...
29
votes
2answers
281 views
When are Decision Diagrams the right way to model and solve a problem?
Decision Diagrams are a relatively new approach to solving difficult combinatorial optimization problems. See http://www.andrew.cmu.edu/user/vanhoeve/mdd/ for some information on this approach. Are ...
