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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 ...


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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 ...


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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 ...


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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 ...


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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 ...


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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. ...


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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 ...


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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 ...


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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 ...


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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 ...


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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 ...


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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 ...


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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 ...


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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 ...


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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 ...


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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 𝐵𝑖𝑗,𝐹𝑖𝑗,𝑇𝑖𝑗 binary variables in terms of other two ...


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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).


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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 $...


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This is a clustering problem, i.e., you want split your services into two clusters, each of which will run on a different device. The way you would do this with RL is to use the goals an objective that includes weighted constraints. This of course assumes you have the right data/setup to train the algorithm. After enough training, your system will be able to ...


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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 ...


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