Multi-objective optimization - Revision history

Ngs111: /* A posteriori methods */ Fixed grammar

2025-06-10T14:50:30Z

A posteriori methods: Fixed grammar

← Previous revision		Revision as of 14:50, 10 June 2025
Line 202:		Line 202:
	== A posteriori methods ==		== A posteriori methods ==
	A posteriori methods aim at producing all the Pareto optimal solutions or a representative subset of the Pareto optimal solutions. Most a posteriori methods fall into either one of the following three classes:		A posteriori methods aim at producing all the Pareto optimal solutions or a representative subset of the Pareto optimal solutions. Most a posteriori methods fall into either one of the following three classes:
	* [[Mathematical programming]]-based a posteriori methods where an algorithm is ~~repeated~~ ~~and~~ each run ~~of the algorithm produces~~ one Pareto optimal solution;		* [[Mathematical programming]]-based a posteriori methods where an algorithm is run repeatedly, each run producing one Pareto optimal solution;
	* [[Evolutionary algorithm]]s where one run of the algorithm produces a set of Pareto optimal solutions;		* [[Evolutionary algorithm]]s where one run of the algorithm produces a set of Pareto optimal solutions;
	* [[Deep learning]] methods where a model is first trained on a subset of solutions and then queried to provide other solutions on the Pareto front.		* [[Deep learning]] methods where a model is first trained on a subset of solutions and then queried to provide other solutions on the Pareto front.

Maxeto0910: /* Scalarizing */ period after sentence

2025-05-30T18:30:42Z

Scalarizing: period after sentence

← Previous revision		Revision as of 18:30, 30 May 2025
Line 140:		Line 140:

	=== Scalarizing ===		=== Scalarizing ===
	[[File:NonConvex.gif\|thumb\|Linear scalarization approach is an easy method used to solve multi-objective optimization problem. It consists in aggregating the different optimization functions in a single function. However, this method only allows to find the supported solutions of the problem (i.e. points on the convex hull of the objective set). This animation shows that when the outcome set is not convex, not all efficient solutions can be found]]		[[File:NonConvex.gif\|thumb\|Linear scalarization approach is an easy method used to solve multi-objective optimization problem. It consists in aggregating the different optimization functions in a single function. However, this method only allows to find the supported solutions of the problem (i.e. points on the convex hull of the objective set). This animation shows that when the outcome set is not convex, not all efficient solutions can be found.]]

	Scalarizing a multi-objective optimization problem is an a priori method, which means formulating a single-objective optimization problem such that optimal solutions to the single-objective optimization problem are Pareto optimal solutions to the multi-objective optimization problem.<ref name="HwangMasud1979" /> In addition, it is often required that every Pareto optimal solution can be reached with some parameters of the scalarization.<ref name="HwangMasud1979" /> With different parameters for the scalarization, different Pareto optimal solutions are produced. A general formulation for a scalarization of a multi-objective optimization problem is		Scalarizing a multi-objective optimization problem is an a priori method, which means formulating a single-objective optimization problem such that optimal solutions to the single-objective optimization problem are Pareto optimal solutions to the multi-objective optimization problem.<ref name="HwangMasud1979" /> In addition, it is often required that every Pareto optimal solution can be reached with some parameters of the scalarization.<ref name="HwangMasud1979" /> With different parameters for the scalarization, different Pareto optimal solutions are produced. A general formulation for a scalarization of a multi-objective optimization problem is

User-duck: Cite CE to eliminate errors and warnings, some cosmetic.

2025-03-12T03:59:27Z

Cite CE to eliminate errors and warnings, some cosmetic.

Show changes

MrOllie: Reverted 1 edit by Zyzc75 (talk): Rv duplication

2025-03-12T03:38:38Z

Reverted 1 edit by Zyzc75 (talk): Rv duplication

Show changes

Zyzc75: /* No-preference methods */

2025-03-12T03:37:33Z

No-preference methods

Show changes

MrOllie: Reverted 1 edit by Zyzc75 (talk) to last revision by Antured

2025-03-12T02:47:57Z

Reverted 1 edit by Zyzc75 (talk) to last revision by Antured

Can't load revision 1280038730

Zyzc75: /* Solution */

2025-03-12T02:42:57Z

Solution

Can't load revision 1280038190

Antured: Restored revision 1280005389 by Moneytrees (talk): Possible copyright violation

2025-03-12T02:31:58Z

Restored revision 1280005389 by Moneytrees (talk): Possible copyright violation

Can't load revision 1280037093

Zyzc75: /* Examples of applications */

2025-03-12T01:32:40Z

Examples of applications

Can't load revision 1280031136

Zyzc75: /* Introduction */

2025-03-12T01:31:20Z

Introduction

Can't load revision 1280031019