The Measure of Pareto Optima : Applications to Multi -
نویسنده
چکیده
This article describes a set function that maps a set of Pareto optimal points to a scalar. A proof is presented that shows that the maximization of this scalar value constitutes the necessary and sufficient condition for the function’s arguments to be maximally diverse Pareto optimal solutions of a discrete, multi-objective, optimization problem. This scalar quantity, a hypervolume based on a Lebesgue measure, is therefore the best metric to assess the quality of multiobjective optimization algorithms. Moreover, it can be used as the objective function in simulated annealing (SA) to induce convergence in probability to the Pareto optima. An efficient algorithm for calculating this scalar and analysis of its complexity is presented.
منابع مشابه
The Measure of Pareto Optima : Applications to Multi - objective Metaheuristics
This article describes a set function that maps a set of Pareto optimal points to a scalar. A proof is presented that shows that the maximization of this scalar value constitutes the necessary and sufficient condition for the function’s arguments to be maximally diverse Pareto optimal solutions of a discrete, multi-objective, optimization problem. This scalar quantity, a hypervolume based on a ...
متن کاملModel and Solution Approach for Multi objective-multi commodity Capacitated Arc Routing Problem with Fuzzy Demand
The capacitated arc routing problem (CARP) is one of the most important routing problems with many applications in real world situations. In some real applications such as urban waste collection and etc., decision makers have to consider more than one objective and investigate the problem under uncertain situations where required edges have demand for more than one type of commodity. So, in thi...
متن کاملMOEICA: Enhanced multi-objective optimization based on imperialist competitive algorithm
In this paper, a multi-objective enhanced imperialist competitive algorithm (MOEICA) is presented. The main structures of the original ICA are employed while some novel approaches are also developed. Other than the non-dominated sorting and crowding distance methods which are used as the main tools for comparing and ranking solutions, an auxiliary comparison approach called fuzzy possession is ...
متن کاملWinner Determination in Combinatorial Auctions using Hybrid Ant Colony Optimization and Multi-Neighborhood Local Search
A combinatorial auction is an auction where the bidders have the choice to bid on bundles of items. The WDP in combinatorial auctions is the problem of finding winning bids that maximize the auctioneer’s revenue under the constraint that each item can be allocated to at most one bidder. The WDP is known as an NP-hard problem with practical applications like electronic commerce, production manag...
متن کاملPareto-based Multi-criteria Evolutionary Algorithm for Parallel Machines Scheduling Problem with Sequence-dependent Setup Times
This paper addresses an unrelated multi-machine scheduling problem with sequence-dependent setup time, release date and processing set restriction to minimize the sum of weighted earliness/tardiness penalties and the sum of completion times, which is known to be NP-hard. A Mixed Integer Programming (MIP) model is proposed to formulate the considered multi-criteria problem. Also, to solve the mo...
متن کامل