Multi-Objective Optimization Task
A Multi-Objective Optimization Task is an optimization task applied to a vector of objective functions.
- AKA: Multi-Criteria Optimization, Vector Optimization, Multi-Objective Programming, Multi-Attribute Optimization, Pareto Optimization.
- Context:
- It can be solved by a Multi-Objective Optimization System (that implements a Multi-Objective Optimization Algorithm).
- Example(s):
- Evolutionary Multiobjective Optimization (EMO).
- Normal Boundary Intersection (NBI)
- Successive Pareto Optimization (SPO).
- Directed Search Domain (DSD)
- NSGA-II
- PGEN (Pareto surface generation for convex multi-objective instances)
- IOSO (Indirect Optimization on the basis of Self-Organization)
- SMS-EMOA (S-metric selection evolutionary multi-objective algorithm)[48]
- Reactive Search Optimization.
- Multi-Objective Particle Swarm Optimization.
- See: Multiple Classifier System, Loss Function, Multiple-Instance Learning, Multiple-Instance Classification, Multiple Criteria Decision Making, Multidisciplinary Design Optimization, Pareto Efficiency, Goal Programming, Concurrent Programming, Multi-Criteria Decision Analysis, Interactive Decision Map, Utility Function.
References
2018
- (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Multi-objective_optimization Retrieved:2018-6-26.
- Multi-objective optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, multiattribute optimization or Pareto 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. Multi-objective optimization has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives. Minimizing cost while maximizing comfort while buying a car, and maximizing performance whilst minimizing fuel consumption and emission of pollutants of a vehicle are examples of multi-objective optimization problems involving two and three objectives, respectively. In practical problems, there can be more than three objectives.
For a nontrivial multi-objective optimization problem, no single solution exists that simultaneously optimizes each objective. In that case, the objective functions are said to be conflicting, and there exists a (possibly infinite) number of Pareto optimal solutions. A solution is called nondominated, Pareto optimal, Pareto efficient or noninferior, if none of the objective functions can be improved in value without degrading some of the other objective values. Without additional subjective preference information, all Pareto optimal solutions are considered equally good (as vectors cannot be ordered completely). Researchers study multi-objective optimization problems from different viewpoints and, thus, there exist different solution philosophies and goals when setting and solving them. The goal may be to find a representative set of Pareto optimal solutions, and/or quantify the trade-offs in satisfying the different objectives, and/or finding a single solution that satisfies the subjective preferences of a human decision maker (DM).
- Multi-objective optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, multiattribute optimization or Pareto 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. Multi-objective optimization has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives. Minimizing cost while maximizing comfort while buying a car, and maximizing performance whilst minimizing fuel consumption and emission of pollutants of a vehicle are examples of multi-objective optimization problems involving two and three objectives, respectively. In practical problems, there can be more than three objectives.
2012
- (Rodriguez et al., 2012) ⇒ Mario Rodriguez, Christian Posse, and Ethan Zhang. (2012). “Multiple Objective Optimization in Recommender Systems.” In: Proceedings of the sixth ACM conference on Recommender systems. ISBN:978-1-4503-1270-7 doi:10.1145/2365952.2365961
2011
- (Sammut & Webb, 2011) ⇒ Claude Sammut, and Geoffrey I. Webb. (2011). “Multi-Objective Optimization.” In: (Sammut & Webb, 2011) p.710
- QUOTE: Definition - Multi-criteria optimization is concerned with the optimization of a vector of objectives, which can be the subject of a number of constraints or bounds. The goal of multi-objective optimization is usually to find or to approximate the set of Pareto-optimal solutions. A solution is Pareto-optimal if it cannot be improved in one objective without getting worse in another one.
2004
- (Marler & Arora, 2004) ⇒ Marler, R. T., & Arora, J. S. (2004). Survey of multi-objective optimization methods for engineering. Structural and multidisciplinary optimization, 26(6), 369-395, DOI:10.1007/s00158-003-0368-6.
- ABSTRACT: A survey of current continuous nonlinear multi-objective optimization (MOO) concepts and methods is presented. It consolidates and relates seemingly different terminology and methods. The methods are divided into three major categories: methods with a priori articulation of preferences, methods with a posteriori articulation of preferences, and methods with no articulation of preferences. Genetic algorithms are surveyed as well. Commentary is provided on three fronts, concerning the advantages and pitfalls of individual methods, the different classes of methods, and the field of MOO as a whole. The Characteristics of the most significant methods are summarized. Conclusions are drawn that reflect often-neglected ideas and applicability to engineering problems. It is found that no single approach is superior. Rather, the selection of a specific method depends on the type of information that is provided in the problem, the user’s preferences, the solution requirements, and the availability of software.