Questions tagged [multi-objective-optimization]
Multi-objective optimization is an area of multiple criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Involve two or more optimization goals that are conflicting, meaning that improvement to one objective comes at the expense of another objective. The two methods for perform a multi-objetive-optimization are Pareto and scalarization.
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What are some important real life examples of multi objective optimization problem with box constraints to work on?
In the search of some of the important cutting edge many objective optimization problems to be solved using non-dominated sorting genetic algorithm (NSGA) and its variants.
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Is there a name for this variation of the generalized assignment problem?
All the input variables are positive float (x > 0). We have $M$ agents with limited amount of time $t_1,\dots,t_M$, $N$ tasks $task_1,\dots,task_N$ associated with duration $d_1,\dots, d_N$. Cost ...
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Solving a Global Optimization problem using Differential Evolutionary Algorithm using R
I need to determine the global optimum results of this objective function. I define the problem by minimizing the squared difference as represented in function $f(q_1,q_2,\alpha_1,\alpha_2)$
The ...
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Which Python package is suitable for finding the optimal non dominated set in multiobjective optimization?
I would like to know how to use pyhon or Cplex or both for finding the whole optimal pareto front for a biobjective mixed integer linear programming problem?
Thanks
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Do you have to normalize objectives when using the weighted sum approch?
Do you have to normalize objectives when using the weighted sum approch when having multiple objectives?
Actually I thought that I should do it. But now I have run several experiments with different ...
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Question about implementation method for optimization problem
Suppose we wanted to solve the following optimization problem:
$$\inf_{x \geq 0}\sup_{y \in [0, 1];\ z > 0} f(x, y, z),$$
where $f(x, y, z)$ is some objective function with a closed form that can ...
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Determining the optimize lambda in Multi-Objective Optimization
I have a convex optimization problem:
Maximize obj1
Minimize obj2
Some constraint
Now to solve this problem, I used lambda to make it one problem:
...
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Leontief utility function
For the Leontief utility function $$u_L(\lambda,y)=\min\{\lambda_1(r_1-y_1),\ldots,\lambda_m(r_m-y_m)\}$$
I would like to graphically show that, for $m=2$ and $\lambda\in\Lambda$ (for positive ...
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How to model this problem with multiple objectives?
This question is related to How to deal this L0 norm of a vector of L2 or L1 norms in objective?
I have an optimization variable denoted as ${\bf A\in\mathbb{C}^{100\times 5}}=\begin{bmatrix}{\bf a}_1&...
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Pygmo2: What is the point of evolving an archipelago in a loop if number of generations already set in algo
I want to solve a multi-objective problem with nsga2 or moead taking advantage of the parallelism available in pygmo library. I have seen a very nice example on github posted below. However I am not ...
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Need a multi-optimization environment or plugin in Anylogic
currently I am working on a model to simulate the supply chain of a group of warehouses in a country using Anylogic. Then I need to multi-optimize these outputs to get the best one based on optimizing ...
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OptaPlanner Collaboration with Anylogic
Is there a way that i can let Anylogic Collaborate with OptaPlanner?
I need to do both Simulation and Optimization for a logistic project.
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Multi-objective optimization with known variable dependencies (via a graph) -- what is this called?
Suppose that I am trying to solve a standard multi-objective optimization problem:
$$
\min_{
\begin{array}{c}
\textbf{x} \in S
\end{array}
}
\left [ f_1(\textbf{x}),f_2(\...
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Could non-supported efficient solutions in multi-objective optimization problem be an optimal solution of a parameterized single-objective problem?
Since all supported efficient solutions in a multi-objective optimization problem are actually the optimal solutions for some weighted sum scalarization single-objective optimization problem with the ...
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Multi-objective optimization for resource allocation
Say I have several portfolios of the format:
Product Name
Product Amount
Price per unit
A_1
10
2
B_1
20
6
...
...
...
Z_1
30
7
We can call this $\text{Portfolio}_{1}$.
Similarly, $\text{...
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Multicollinearity w.r.t decisions in optimal control/reinforcement learning learning/resource allocation problem
Consider the following optimization/control problem:
We aim to maximize the cumulative reward $R$ during the horizon $H$ by every day allocating a portion of total budget $B$ to our two different ...
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How can we choose the right weight to solve multi-objective problem using weighted sum method?
I have a multi-objective problem with three objectives F1, F2, and F3. the problem was formulated as a weighted sum. Now I didn't know how I can choose the right weight for my problem
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What is the default weight allocation in solving multi-objective on CPLEX?
I am currently working on a multi-objective problem where I am trying to minimize cost and time. I am using Docplex to solve it, but I did not specify any weight using the following code:
...
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Minimum cost flow problem with multiple arcs between nodes in Python / Google OR
Is it possible to work with multiple arcs between 2 nodes within Google OR?
Or are there better modeling techniques?
I want to optimize flow from supply to demand areas, where supply and demand are ...
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Is it possible to merge two objective functions using the LpSolve package in R?
I have been using the LpSolve package to solve a minimization problem in my final course work, but I need to reconcile this problem with a maximization problem. Conducting several researches, I ...
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large scale optimization with Python
I am dealing with the following optimization problem:
$$
\underset{x}{\min} q(x)
$$
subject to
$$
l_{x} \leq x \leq u_{x} \,\,\,\, \text{ and } \,\,\,\, l_{a} \leq Ax \leq u_{a}.
$$
where $q(x)$ is a ...
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How to calculate the trade-off between objectives in multi-objective optimization?
In the simple case, with only two objectives, I would like to know if it is possible to answer a question like:
How many units of objective 1 do I need to reduce, in order to improve objective 2 by ...
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Blended or hierarchical objectives if solving speed is more important
When optimizing a two objective task assignment problem, is it generally better to use blended objectives or hierarchical objectives if
the speed to obtaining a near-optimal solution is more ...
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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 ...
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How to fix unbalanced multi-commodity network flow with equal supply and demand?
I have a fairly large network with eleven commodities and arc capacities that are commodity-dependent (i.e. an arc may have a higher capacity for one commodity than another). I'm solving a protection-...
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Designing a multi-commodity network flow optimizer
I'm trying to solve multi commodity multi source network flow optimization problem using Python-PuLP. Here is how my problem looks like:
The numbers on the arcs represent the order of priority a ...
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Multiserver Queue Theory Optimization problem
I have a design optimization problem where I need to connect a customer with a server via call. The scenario is as follows:
Customer-1 is connected with $N$ servers out of a total pool of $P$ servers....
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How to use PROMETHEE multicriteria method in R
I used TOPSIS multicriteria method to select the best number of clusters out of the 34 options. As weights I used 0.5 for each criterion. The ...
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How to normalize the objective functions of multi-objective optimization for a MPC?
I have a MPC with two objective functions, one that minimises fuel consumption and one that minimises the travel time of a vessel. I want to combine these two objectives into one weighted objective, ...
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Goal Programming -- Best practice for standardizing magnitude of deviations across goals?
A certain goal program I've been working on has three goals that each operate at different scales.
Two of the goals stay between 0-10, so any deviation from the goal is generally only a couple of &...
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How to normalize the objective functions of multi-objective optimization into uniform form?
In my bi-objective model, the range of solution value for the first objective is large than the second objective. I decide to obtain a single solution by the weighted sum approach and solve it using ...
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Relationship between Hypervolume and population size, number of generations, and number of functional evaluations?
I have a multi-objective optimization with the following properties:
Objective function: two non-linear functions and one linear function
Decision variable: two real variables (Bounded)
Constraint: ...
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How to compute Generational Distance, Inverted Generational Distance, Epsilon Indicator, and Hypervolume for a Pareto front?
In order to find the quality indicators like Generational Distance, Inverted Generational Distance, Epsilon Indicator, and HyperVolume for a Pareto front I want to normalize the values of ...
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Designing Multi Floor Architectural Layouts
Architectural layouts define the position and shape of rooms in 3D space, where windows and water pipes are and as well as how humans travel between rooms (among other things). There is a lot of ...
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Are simulations a form of multi-objective optimization?
Where is the line when an approach is called multi-objective optimization? For example:
Problem
Presume I want to optimize an optimization problem, for example nurse rostering, with 2 soft constraints:...
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Do you know production deployments of multi-objective optimization?
In mathematical optimization software, defining the weight and level (hard/soft) of each of the objectives/constraints is often difficult for the business people at software development time, due to ...
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Branch and bound method for solving non-convex integer non-linear multi-objective optimization problem?
Following are the characteristics of my problem:
Objective function: two non-linear functions and one linear function
Decision variable: two integer variables ($X_1$ and $X_2$)
Constraint: three (two ...
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What methods are used to solve multi-objective optimization problem with non-linear objective functions and integer decision variables?
Case 1: NLP
When either the objective function or at least one of the constraints or both are non-linear it is a NLP. We use generalized reduced gradient or Quadratic Programming to solve NLP. However,...
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A lexicographic objective function
I am trying to solve a multi-objective vehicle routing problem, I want to implement a lexicographic objective function, I have already defined a function for each objective. if someone has an idea of ...
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How to linearize a non-convex optimization objective function?
The non-convex multi-objective optimization problem in my case is defined below:
Objective 1: Minimize $f_1(X_1,X_2)=C_0+C_1(1/X_1)+C_2(X_2/X_1)+C_3X_1+C_4X_2+C_5(X_2^2/X_1)$
Objective 2: Minimize $...
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How to interpret this problem of multicriteria decision
I am trying to optimise a cost function that consists of three parameters (A,B,C) using weighted sum approach for the selection of optimal technique out of three techniques. Parameter A unit is in ...
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Bin Packing with CP Solver
[ [0,5],
[0,4],
[1,6],
[2,4],
[3,6],
[3,2],
[4,5],
[5,5],
[6,4],
[7,3],
[8,2],
[8,3],
[9,5],
[10,3]]
...
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Does a pre-calculated lower bound of an MILP problem help?
I have an MILP model, say
$$
\begin{array}{rl}
\mbox{minimize} &f_1(x) + f_2(x)\\
\mbox{subject to} &x\in X
\end{array}
$$
which is hard to solve. And I find it simple to solve the two ...
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Which multi-objective optimization algorithm should one select?
The multi-objective optimization problem in my case is defined below:
Objective 1: Minimize $f_1(X_1,X_2)=C_1X_1+C_2X_2+C_3X_1^2+C_4X_2^2+C_5X_1^2X_2^2$
Objective 2: Minimize $f_2(X_1,X_2)=D_1X_1+...
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How define variable in CPLEX and What is diffrence between decision variables and variable in CPLEX
I want to code a problem by CPLEX, in this problem I have variables and decision variables, how define them?
In this picture you can see the variables:
which we have:
I use these codes for variables:...
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What is a good approach to deciding which jobs (from a list of HPC jobs) should be ran locally vs. on the cloud given time & cost constraints?
Cloud computing has transformed the landscape of compute operations. Of course, there are still many labs/businesses with local, large-scale compute clusters. For those businesses who keep the ...
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Multi-objective function normalization
I am trying to solve the multi-objective function of my linear program. Are there another approaches other than the weighted sum approximation?
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What are useful plots/statistics/metrics when analyzing the solution sensitivity in multi-objective optimization?
Consider an optimization problem with $n>3$ objectives.
For handling this there exists often two approaches:
a) some weighting of the objectives,
b) fix an order of objectives and then optimize ...
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Can I combine two objective functions if they have a relation between them?
I will use a meta-heuristic algorithm, to maximize the following objective functions:
Objective function 1 $=\sum\limits_{r=1}^{M} \sum\limits_{s=r+1}^{M} \sum\limits_{j=r+1}^{N} (r_{rj}w_j - r_{sj}...
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Appropriate Rotation Matrix in Nonconvex Optimization with Barrier
Let $ x \in \mathbb{R}^n_+$ be a variable such that $\sum_{i=1}^n x_i = 1$. In other words, $x$ is in a probability simplex. I am working on barrier-like functions in nonconvex optimization over such ...
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