Pareto efficiency

No one can be made better without making someone worse off (Pareto efficient). 

Pareto efficiency, also known as Pareto optimality, is named after an Italian economist, Vilfredo Pareto (1848-1923). The definition of a Pareto efficient economic system is that no re-allocation of given goods can be made without making at least one individual worse off (there is no way to make any person better off without hurting anybody else). Pareto improvement from a non-efficient system is achieved when a change to a different allocation makes at least one individual better off without making any other individual worse off [Varian 47],... 

Developed by economist, Vilfredo Pareto, in the nineteenth century, this provides a means to evaluate the desirability of alternate economic and social states, and of change from one to another. It recognises that in order for a maximum welfare position to be reached then the benefits of some should not increase to the detriment of others. In these terms, Pareto efficiency can only be achieved when it is no longer possible to make anyone better off without an adverse impact on someone else. From a practical perspective, this is a very strict criterion, and hence, has limited use. Even if it were possible for the beneficiary of a transaction to fully compensate those who were losing out, such compensation would never be paid. Analysis of the customer-product relationship can be organised through a Pareto matrix (Figure 2.14). From this observation, it follows that 20% of products will account for 80% of sales. 

Moreover, if no feasible solution dk)) exists that dominates solution v(dy), then v(d,) is classified as a non-dominated or Pareto optimal solution. More simply, bj e is a Pareto optimal solution if there exists no feasible vector bk which could decrease some criterion without causing a simultaneous increase in at least one other criterion [26].The collection of all Pareto optimal solution are know as the Pareto optimal set or Pareto efficient set. Instead, the corresponding objective vectors are described as the Pareto front or Trade-off surface. 

Efficient outcomes make at least one person better off and no one worse off as the result of choice. Choices that make some better off without making others worse off are described as having gains from trade and are labeled Pareto optimal or just optimal. Neoclassical economic theory argues that, under most circumstances, a system of property rights and markets produces these efficient outcomes. But this system is efficient only if aU the effects of choices are included in market prices. If prices do not incorporate aU these effects, such situations are described as inefficient or market failures. 

Assign efficiency value to solutions based on Pareto-rank While Not Stop Condition ... 

Secondary population update. Efficiency scores are initially used to update the Pareto-archive. The current Pareto-archive is erased and a subset of the current working population that favours individuals with high efficiency score, i.e. low domination rank and high chromosome graph diversity, takes its place. Note that the size of the secondary population selected is limited by a user-supplied parameter. The secondary population mechanism has been designed specifically to preserve good solutions, non-dominated or dominated but substantially structurally unique, from all... 

There are two notions of efficiency that are easily confused. Changes that make everybody better off are called Pareto improvements, after the Italian economist Pareto. A state in which nobody can be made better off without someone else being made worse off is called Pareto optimal. A Pareto impnive-ment may be a move to a Pareto-optimal state, but need not be so if there is room for further Pareto improvement. A move to a Pareto-optimal state may be a Pareto improvement, but need not be so if someone is made worse off. as in the move from C to A. 

Welfare theory A macroeconomic discipline theory, dealing with the most efficient allocation of resources in an economy. An important aspect of welfare fheory is the so-called Pareto criterion. 

It seems reasonable that planners in North American democracies need not respect individual beliefs about future possibilities in the same manner as they respect individual tastes. Tastes may be refined or vulgar still, it may be held that a person s tastes must be respected. Beliefs, however, can be wrong and it may be very costly to correct them. In these circumstances, a planner might make decisions about Q-goods on this basis of his expectations of the individual s ex post utility level. Existence value would then be the planner s perception of differences in the individual s ex post utility level, where the planner s ex ante beliefs have been substituted for the individual s. The usual economic efficiency (Pareto optimality) conditions would still apply. The danger of paternalism in which the planner substitutes his own tastes for those of the individual is acknowledged. In addition, account would have to be taken of the accuracy and precision of the planner s knowledge of world states and the individual s tastes. 

A Priori Methods (e.g., value function, lexicographic and goal programming methods) These have been studied and applied for a few decades. Their recent applications in chemical engineering are limited. These methods require preferences in advance from the DM, who may find it difficult to specify preferences with no/limited knowledge on the optimal objective values. They will provide one Pareto-optimal solution consistent with the given preferences, and so may be considered as efficient. 

Interactive Methods (e.g., interactive surrogate worth tradeoff and NIMBUS methods) Decision maker plays an active role during the solution by interactive methods, which are promising for problems with many objectives. Since they find one or a few optimal solutions meeting the preferences of the DM and not many other solutions, one may consider them as computationally efficient. Time and effort from the DM are continually required, which may not always be practicable. The full range of Pareto optimal solutions may not be available. 

Industrial cyclone separator Two problems maximization of overall collection efficiency while minimizing (a) pressure drop and (b) cost. NSGA Pareto-optimal solutions of the two problems are similar although their ranges are different Ravi et al. (2000)... 

Cyclic adsorption processes Two examples (a) thermal swing adsorption -maximization of total adsorption efficiency and minimization of consumption rate of regeneration energy, and (b) rapid pressure swing adsorption -maximization of both purity and recovery of the desired product for RPSA. Modified Sum of Weighted Objective Function (SWOF) method Modified SWOF method is superior to the conventional SWOF as it was able to find the non-convex part of the Pareto-optimal set. Ko and Moon (2002)... 

Wilson, B., Cappelleri, D., Simpson, T. W. and Frecker, M. (2001). Efficient Pareto frontier exploration using surrogate approximations, Optim,ization and Engineering 2, 1, pp. 31-50. 

For multi-objective optimization, theoretical background has been laid, e.g., in Edgeworth (1881) Koopmans (1951) Kuhn and Tucker (1951) Pareto (1896, 1906). Typically, there is no unique optimal solution but a set of mathematically incomparable solutions can be identified. An objective vector can be regarded as optimal if none of its components (i.e., objective values) can be improved without deterioration to at least one of the other objectives. To be more specific, a decision vector x S and the corresponding objective vector f(x ) are called Pareto optimal if there does not exist another x G S such that / (x) < /j(x ) for alH = 1,..., A and /j(x) < /j(x ) for at least one index j. In the MCDM literature, widely used synonyms of Pareto optimal solutions are nondominated, efficient, noninferior or Edgeworth-Pareto optimal solutions. 

The methodology proposed in this chapter, is based on the determination of the Pareto Optimal set of solutions for multi-objective emergency response decision-making around chemical plants. Given the size of the decision space, the efficient set of solutions cannot be... 

Otherwise, the maximal number of efficient configurations to be found equals the population size in each iteration. This loss of non-dominated configurations is called Pareto drift and the improved algorithm is called NSGA-IIa, see Goel et al. (2007). 

Let Xi denote the ith configuration of the determined sample of the Pareto-front and yi the associated performance measures such that = J7(xj) where II -) represents the simulation model. Hence, the set of Zi = (Xi,y ) constitutes a sub-sample of the set of efficient constellation Z 6 c Z H Based on the range and the relations among the y-components a Pareto-front meta-model (4.22) is estimated which can be used to describe the set of efficient constellations Z H more precisely. 

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