This constraint allows more of one good to be purchased only at the sacrifice of consuming less of another good therefore, the various objectives (more consumption of each good is preferred) are in conflict with each other. For example, consumer's demand for various goods is determined by the process of maximization of the utilities derived from those goods, subject to a constraint based on how much income is available to spend on those goods and on the prices of those goods. In economics, many problems involve multiple objectives along with constraints on what combinations of those objectives are attainable. Min x ∈ X ( f 1 ( x ), f 2 ( x ), …, f k ( x ) ) is a small constant, is often defined because of numerical reasons.Įxamples of applications Economics In mathematical terms, a multi-objective optimization problem can be formulated as 9.2 Visualization in high-order multi-objective optimization problemsĪ multi-objective optimization problem is an optimization problem that involves multiple objective functions.9.1 Visualization in bi-objective problems: tradeoff curve.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).īicriteria optimization denotes the special case in which there are two objective functions. Researchers study multi-objective optimization problems from different viewpoints and, thus, there exist different solution philosophies and goals when setting and solving them. Without additional subjective preference information, there may exist a (possibly infinite) number of Pareto optimal solutions, all of which are considered equally good. 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.
In that case, the objective functions are said to be conflicting.
In practical problems, there can be more than three objectives.įor a nontrivial multi-objective optimization problem, no single solution exists that simultaneously optimizes each objective. 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. 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.
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. See also: Multiple-criteria decision analysis and Vector optimization
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