Questions tagged [combinatorial-optimization]

For questions about optimization over a discrete solution space.

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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, Ramsey numbers, factoring numbers, the ...
Nike Dattani's user avatar
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15 votes
2 answers
2k 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)....
rasul's user avatar
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1 vote
2 answers
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weight choice in multi-objective weighted sum

I have a combinatorial optimization problem where there are three objectives F1, F2, and F3 to be minimized. The problem was formulated as a weighted sum where F=alphaF1+betaF2+gamma*F3. My question ...
MAJID majid's user avatar
31 votes
5 answers
5k 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 ...
prubin's user avatar
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15 votes
4 answers
881 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 ...
Daniel Duque's user avatar
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12 votes
1 answer
445 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 ...
Dimitris Boukosis's user avatar
11 votes
2 answers
1k 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 ...
cdrootsudormstardashr's user avatar
10 votes
2 answers
191 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 ...
sedge's user avatar
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10 votes
2 answers
397 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
3 answers
535 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. ...
Slim Shady's user avatar
8 votes
2 answers
545 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\\...
KGM's user avatar
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8 votes
1 answer
447 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 ...
ooo's user avatar
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8 votes
1 answer
168 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). ...
Brendan Hill's user avatar
7 votes
1 answer
842 views

Minimum vertex cover and linear programming

Suppose we have a graph G. Consider the minimum vertex cover problem of G formulated as a linear programming problem, that is for each vertex $v_{i}$ we have the variable $x_{i}$, for each edge $v_{i}...
Mario Giambarioli's user avatar
7 votes
2 answers
486 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 ...
KGM's user avatar
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7 votes
3 answers
2k views

Solving Logic puzzles through optimization

I have the following "logic puzzle" (I think this is considered as a "scheduling problem"): In this problem, there are 5 basketball players - provided some clues about their ...
stats_noob's user avatar
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6 votes
2 answers
581 views

Branch and Price Algorithm

Can branch and price be a good solution approach for a routing problem with min-max objective function? For example, minimizing the max length of any vehicle route in a VRP. In the literature, I haven'...
Bhr's user avatar
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6 votes
1 answer
509 views

Column Generation algorithm for vehicle routing problem

I want to solve a VRP with a column generation algorithm. The objective of the problem is makespan minimization. In more detail, I want to minimize the arrival time of the last vehicle in the depot. I ...
Bhr's user avatar
  • 455
5 votes
2 answers
542 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 conditional: If $A\le B$ then $Y=1$ otherwise $Y=0$ where $A, B$ are reals and $Y$ is binary. I can model as follows: $Y \cdot A \le B$...
Clement's user avatar
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5 votes
2 answers
682 views

Where can I find resources to learn mathematical modelling for real life operation research problems like combinatorial optimization?

I find it hard to form math models for real life operations research problems, how can I learn this? Any books, tutorials available?
21vs's user avatar
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4 votes
1 answer
261 views

Column Generation algorithm

I want to solve a VRP with a column generation algorithm. The objective of the problem is makespan minimization. but there is a point in calculating the arrival time of the vehicle in each node. the ...
Bhr's user avatar
  • 455
3 votes
1 answer
672 views

Discrete problems versus Combinatorial problems

I have seen one explanation about the difference between discrete and combinatorial optimization problems in such a way that "all combinatorial optimization problems are also discrete ...
YcK's user avatar
  • 79
3 votes
0 answers
115 views

Hard time in understanding OR Research or Paper [closed]

I'm from soft-engineering background and really having a hard time when reading and understanding the formulation from a research or published paper. For example, when looking at a container loading ...
overboxed's user avatar
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3 votes
0 answers
121 views

Mathematical model complexity Vs Time Complexity of the model

As far as I know, when we talk about the term of complexity, it referred to the time complexity of the model in which how long does it take to solve a specific mathematical program by a specific ...
A.Omidi's user avatar
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2 votes
2 answers
464 views

implementation of heuristics using C++ to solve operations research problems

can anyone suggest some good books with the implementation of heuristics and matheuristics using C++ to solve operations research problems especially routing problems such as TSP and VRP. also, I need ...
Bhr's user avatar
  • 455
1 vote
2 answers
113 views

Priotization rules for variable allocation in linear programming

I’m working on an optimization problem and need help with correctly prioritizing the allocation of certain variables in a constraint. The rules are: Only one of the variables $y_{t}$, $zn_{t}$ and $...
Lemma's user avatar
  • 23
1 vote
2 answers
494 views

Subtour elimination in SDVRP

I have the model below, based on this paper. It's a vehicle routing problem with split deliveries, i.e the locations/customers can be visited by multiple vehicles that share the demand at that vehicle....
Parseval's user avatar
  • 207