17
votes
Accepted
Which Python package is suitable for multiobjective optimization
If you use packages like PyOMO, PuLP or pyOpt, you'd have to implement all the operations for multiobjective optimization - e.g. to find nondominated solutions or the different mutation operators - ...
- 1,687
10
votes
Which Python package is suitable for multiobjective optimization
If @dbasson 's excellent answer is not what you're looking for, may I suggest the possibility of using multiobjective optimization capabilities in CPLEX or Gurobi (under Python)?
CPLEX
New ...
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9
votes
Benchmark problems for combinatorial multi-objective optimization
vOptLib: Library of numerical instances for MultiObjective Linear Optimization problems
From the site:
vOptLib (short for vector optimization library) is a collection
problem instances for ...
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9
votes
Accepted
Are simulations a form of multi-objective optimization?
There's a fair sized body of research in interactive multiobjective optimization, and while I'm not familiar with most of it, I think this would fit right in. Decades ago, I (vaguely) remember two of ...
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9
votes
Accepted
Determining the optimize lambda in Multi-Objective Optimization
There is no mathematical way to derive (or justify) a value for $\lambda$. The justification has to be made in the context of a specific problem and a specific (reasonably credible) decision maker. ...
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8
votes
Are simulations a form of multi-objective optimization?
tl;dr– The term you're looking for is sensitivity analysis.
Would you still call this approach multi-objective solving? What does the literature say?
Trying different possible parameters to form a ...
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8
votes
Determining the optimize lambda in Multi-Objective Optimization
Another approach could be generating the Pareto Frontier, solving the problem several times for different values of lambda, using a Weighted sum algorithm (see this or this).
7
votes
Benchmark problems for combinatorial multi-objective optimization
There is also the MOrepo maintained by Lars Relund Nielsen. MOrepo describe itself as:
This repository is a response to the needs of researchers from the MCDM society to access multi-objective (MO) ...
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7
votes
Software for multi-objective optimization
You may be interested in the following paper because it uses chance-constrained programming and bi-objective optimization together in a transportation application:
https://link.springer.com/article/...
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7
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Determining the optimize lambda in Multi-Objective Optimization
In addition to the above answers, there's good deal of discussion here. One of the experts logically breaks down some key questions like avoiding dominating solution by sticking to single combination ...
- 3,553
6
votes
Accepted
Which method to use to solve this multi-objective conflicting objectives
There is a rich literature on reconciling multiple objectives (which I will not attempt to repeat in its entirety here, although what follows is long-winded enough to appear to do so). The ones I know ...
- 40.9k
6
votes
How to model a TSP where the salesman can choose between flight, train and bus for every single connection?
You can create three nodes for one city.
In other words,
You create a bus station, train station, airport in one city.
If you arrive in city A with a train but leave with a plane, you have to move ...
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6
votes
Which Python package is suitable for multiobjective optimization
The vOptGeneric (https://github.com/vOptSolver/vOptGeneric.jl) package of the vOptSolver includes the primitives for solving 2-objectives IP with weighted sum method, epsilon-constraint method and ...
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6
votes
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A lexicographic objective function
Let $f(x)=(f_1(x),f_2(x),\dots,f_n(x))$ be a lexicographic objective function, where $f_1(x)$ is more important than $f_2(x)$ which in turn is more important than $f_3(x)$, etc. I'll assume you are ...
- 3,491
6
votes
Accepted
What methods are used to solve multi-objective optimization problem with non-linear objective functions and integer decision variables?
Disclaimer: One might want to look for a reformulation or a special structure to apply mathematical tools to find optimal in the feasible set. I am assuming you're already past the possibility that ...
- 404
6
votes
Accepted
How to calculate the trade-off between objectives in multi-objective optimization?
Understanding the Pareto frontier
In your question, you say that "we have the Pareto frontier." This makes your question difficult to parse, because the object that represents the tradeoff ...
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6
votes
Can I tell a MILP solver to prefer solutions with fewer fractions?
Introduce integer variable $y_i$, continuous variable $f_i\in[0,1]$, and binary variable $z_i$ to indicate whether $f_i>0$. Now minimize $\sum_i z_i$ subject to
\begin{align}
x_i&=y_i+f_i \\
...
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5
votes
Multi-objective function normalization
Yes. There are plenty of other approaches to handle multiple objectives. First of all, you need to figure out, what you consider an optimal solution (set) to your multi objective optimization problem. ...
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5
votes
Accepted
How to resolve this issue in multi-objective optimization?
If there is a solution that maximizes all the objectives at once, then your choice of objective function is satisfying because this solution will be optimal for the weighted sum. However, from ...
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5
votes
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Are there any benefits to using Gurobi's built-in "blended" multi-objective functionality?
Q: It seems to me, based on the documentation available, that specifying "blended" objectives is no different from the manual weighted-sum approach? ...
It's two different explanations of the same ...
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5
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How to model a TSP where the salesman can choose between flight, train and bus for every single connection?
I suggest to start with the classical TSP formulation using $x_{ij}$ variables that are 1 if you go to city $j$ directly after city $i$ and then add the constraints that $x_{ij} = B_{ij}+F_{ij}+T_{ij}$...
- 2,335
5
votes
Accepted
Defining and comparing utilization rates for delivery service
One possibility is to look at idle time (time a driver spends waiting for the next order). If the drivers are on your payroll (as opposed to working on commission, i.e., doing "gig" work), idle time ...
- 40.9k
5
votes
Do you know production deployments of multi-objective optimization?
Not a direct answer, but I think that "interactive multiobjective optimization" has shown that it can overcome the obstacle of expontially man Pareto optimal solutions. I have attended talks ...
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5
votes
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Do you know production deployments of multi-objective optimization?
I am not aware of the timetabling, but if you mean by production is something like supply chain optimization, the answer would be actually yes.
As the optimization methods are widely used in supply ...
- 9,456
5
votes
Accepted
large scale optimization with Python
Quadratic programming solvers in Python with a unified API (here) includes most of the quadratic programming solvers such as CVXOPT (can take advantage of sparsity), Gurobi, MOSEK, OSQP, etc.
The ...
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5
votes
Accepted
Is it possible to merge two objective functions using the LpSolve package in R?
There are a variety of ways to deal with multiple objectives, so the answer is "it depends".
Probably the most common approach is to optimize a weighted sum or difference of the individual ...
- 40.9k
5
votes
Accepted
What is the default weight allocation in solving multi-objective on CPLEX?
Weights are defined by you to tell CPLEX how objectives with the same priorities are blended together. If you don't define weights, by default they are all assumed to be equal to 1.
Let's assume in ...
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4
votes
Accepted
Does the weighted sum approach find all pareto-optimal solutions in MILP
No. You cannot be sure to find all Pareto optimal solutions to a MILP using the weighted sum approach. You are not even guaranteed to find all non-dominated outcomes.
You are only guaranteed to be ...
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4
votes
Accepted
How define variable in CPLEX and What is diffrence between decision variables and variable in CPLEX
as can be read in OPL CPLEX documentation, A decision variable is an unknown in an optimization problem.
For instance
dvar int x in 0..10;
is a decision variable
<...
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4
votes
How to normalize the objective functions of multi-objective optimization into uniform form?
You should scale the objective functions so that they have similar size values and then weight them. (The scaling factors effectively become part of the weights.) If your metaheuristics are fast, it ...
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