14 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 - ...
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  • 1,587
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 optimisation

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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  • 5,756
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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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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  • 241
7 votes

Benchmark problems for combinatorial multi-objective optimisation

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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  • 5,445
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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6 votes
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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 ...
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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
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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 ...
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5 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 ...
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5 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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  • 51
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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  • 5,445
5 votes
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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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  • 116
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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  • 2,052
5 votes

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 $x_{ij} = B_{ij}+F_{ij}+T_{ij}$...
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5 votes
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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 ...
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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 ...
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  • 6,114
5 votes
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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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  • 8,350
5 votes
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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 ...
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5 votes
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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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  • 5,756
4 votes
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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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  • 5,445
4 votes
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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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4 votes
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How to normalize the objective functions of multi-objective optimization for a MPC?

The reason for minimizing fuel consumption is presumably to minimize fuel cost. If you can come up with a cost rate for travel time, then you can combine the two objectives into an overall cost ...
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4 votes

Designing a multi-commodity network flow optimizer

Question 1 You could simply use the priority function as the cost function on the arcs. This way, it is for example cheaper to ship a commodity to $D_1$ from $W_2$ ($1$ unit of cost per unit of flow) ...
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4 votes
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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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  • 454
3 votes

Multi-objective function normalization

To Sune's list, I'll add goal programming, in which you set targets for your objectives (possibly more than one target for a single objective), prioritize them, then minimize unfavorable deviations ...
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3 votes

Does a pre-calculated lower bound of an MILP problem help?

My overall experience is that feeding constraints of the form $\rm objval \geq lb$ is detrimental to MIP solver performance. The main reason is the following: MIP solvers rely on branch-and-bound ...
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