11

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 - that could take some time. An alternative is using DEAP for that, it's a Python framework for evolutionary algorithm and they have NSGA-II implemented. It's quite ...


9

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 benchmarking multi-objective solvers. It covers a variety of Multiobjective linear optimization problems (multiobjective combinatorial problems, multiobjective ...


8

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 multiobjective optimization features in CPLEX V12.9.0 Optimization problems with multiple linear objective functions can be specified in CPLEX. To solve them, CPLEX ...


8

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 my colleagues looking at an interactive approach for multiobjective LPs, in which they would combine the criteria using a weighted sum, solve, show the ...


7

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) optimization instances. The repository contains instances, results, generators etc. for different MO problems and is continuously updated. The repository can be ...


7

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/10.1007/s10288-019-00429-7 I would suggest to do the followings for your problem: 1- If you have bi-linear terms in your formulation then try to linearize them ...


6

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 (possibly not all of them) fall into the following categories. Optimize a weighted combination of the objectives (as you have written). The big problem here ...


6

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 from the train station to Airport. And then you can assign 0 (or appropriate quantities, emission or time) for moving between any of them within the same city. ...


6

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 your problem case could be reformulated as a MILP/LP/QP etc. So, with the problem on hand, we're dealing a case where we cannot have a reformulation. Whatever I ...


6

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 portfolio of options is called doing a sensitivity analysis. For example, say you're an engineer designing a light-bulb. You know you want it to last a long ...


5

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 solving a minimization problem. In a mathematical programming solver, such an objective function could be easily implemented as follows. First find the solution $...


5

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. To name a few notions of optimality you might consider Pareto optimality Lexicographic optimality (as @Kuifje suggests in a comment to the question) Max-...


5

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 way of specifying the same parameters. In the prior section of the documentation titled: Multi-objective Attributes it says: These are the attributes for ...


5

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 $x_{ij} = B_{ij}+F_{ij}+T_{ij}$ for all $i,j$. This allows you to to use all standard TSP machinery (e.g. sub-tour elimination constraints) via the $x_{ij}$ variables, without having to ...


5

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 has a direct cost. If the drivers are gig workers, a relatively even distribution of idle time might be perceived as "fairer" and might contribute to driver ...


5

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 and seminars by Kaisa Miettinen and her co-authors, and their approaches seem quite interesting. On her website (http://users.jyu.fi/~miettine/engl.html#...


5

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 chain improvement, applying multi-objective optimization, specifically in where the decision-makers will need to choose between the different strategies like ...


4

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 able to generate the supported non-dominated solutions. All the unsupported non-dominated solutions cannot be found using the weighted sum approach (without adding ...


4

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 experience, the existence of such a solution is rare. There is rather a whole set of points representing possible compromises between objectives. Exploring them can be ...


4

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 int a=3; is some data definition whereas in execute { var b=2; } b is a scripting variable. In your model, I see float Q[periods]; //Inventory of the blood product at the blood center in time ...


3

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 from the target in priority order.


3

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 also Chalmet method. You can select GLPK, CPLEX or GUROBI as MIP solver (only one line to set up). vOptGeneric is implemented in Julia (https://julialang.org/) and ...


3

As basically a variant to what Rolf van Lieshout proposed, you could also add another index to your standard TSP variable: $x^t_{ij}$ where $t$ is the transport mode $t \in \{B, T, F\}$. You basically add $\sum_{t \in T}$ to most of your TSP constraints and of course need to limit the potentially chosen arcs between each city to one: $\sum_{t \in T}\sum_{i,j ...


3

Although it seems to be late to answer this question (as you need to submit a project until Friday), the following papers can be helpful in determining a solution approach to the multi-facility decision-making framework: In the paper1, the authors applied mixed integer goal programming in determining the facility location, route and flow of different ...


3

Yes we can. Branch and bound can both deal the integer variables and with the potenial non convexities of the non-linear functions. Most branch and bound methods can also handle constraints. Depending on the solver you might need provide an relaxation for the bounding part. However multi objective branch and bound methods are harder to come by, i am still ...


3

I'm not sure if this counts, since my impression is that the end users overlap the modelers, but a contact I have at The Nature Conservancy (a non-profit that works in the conservation field) confirmed to me that his group uses a multi-objective optimization model for selecting land conservation projects in which to invest. As I understand it, criteria ...


2

You can treat it as multiobjective if you treat end-to-end latency as one objective (to be minimized) and load on device 1 (which has limited capacity) as another objective (also to be minimized).


2

Model without bandwidth limitation We wish to select the most performing components to be hosted by two devices in order to have an end-to-end latency as minimum as possible. Let $ x_{i,j} $ be a Boolean variable whose value is 1 if i-th component is assigned to j-th device, 0 otherwise where $i=1,2, \cdots, 10 $ and $i=1,2$. The cpu limitation (equals to $...


2

As a student I am doing research in this field, I found Wikipedia's explanation very useful. You are right, most of the applications of MDO are in the field of design for aerospace and mechanical engineering (they may design product, not systems). In these fields, the reconciliation of different teams in the design process completely follows well-known ...


2

I think all of the above-suggested models (by You, S. Phil Kim, Rolf van Lieshout, lvenhofen) have same number of nodes and arcs, correctly representing the problem to be modeled. However, one can reduce the number of variables as well as constraints in these models by representing either of 𝐡𝑖𝑗,𝐹𝑖𝑗,𝑇𝑖𝑗 binary variables in terms of other two ...


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