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Multi-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute 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.
Formally, a state is Pareto-optimal if there is no alternative state where at least one participant's well-being is higher, and nobody else's well-being is lower. If there is a state change that satisfies this condition, the new state is called a "Pareto improvement". When no Pareto improvements are possible, the state is a "Pareto optimum".
In multi-objective optimization, the Pareto front (also called Pareto frontier or Pareto curve) is the set of all Pareto efficient solutions. [1] The concept is widely used in engineering. [2]: 111–148 It allows the designer to restrict attention to the set of efficient choices, and to make tradeoffs within this set, rather than considering ...
In this example a company should prefer product B's risk and payoffs under realistic risk preference coefficients. Multiple-criteria decision-making (MCDM) or multiple-criteria decision analysis (MCDA) is a sub-discipline of operations research that explicitly evaluates multiple conflicting criteria in decision making (both in daily life and in settings such as business, government and medicine).
An allocation is possibly Pareto-optimal (PPE) if it is Pareto-optimal according to at least one responsive bundle-ranking consistent with the item-ranking. The following results are known: Bouveret, Endriss and Lang [2] assume that all agents have strict preferences.
Fundamental theorems of welfare economics. There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information, and in perfect competition, will be Pareto optimal (in the sense that no further exchange would make one person better off without making another ...
The Interactive Decision Maps technique of multi-objective optimization is based on approximating the Edgeworth -Pareto Hull (EPH) of the feasible objective set, that is, the feasible objective set broadened by the objective points dominated by it. Alternatively, this set is known as Free Disposal Hull. It is important that the EPH has the same ...
Kaldor–Hicks efficiency. A Kaldor–Hicks improvement, named for Nicholas Kaldor and John Hicks, is an economic re-allocation of resources among people that captures some of the intuitive appeal of a Pareto improvement, but has less stringent criteria and is hence applicable to more circumstances. A re-allocation is a Kaldor–Hicks ...
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