TY - JOUR ID - 71057 TI - The Quasi-Normal Direction (QND) Method: An Efficient Method for Finding the Pareto Frontier in Multi-Objective Optimization Problems JO - Interdisciplinary Journal of Management Studies (Formerly known as Iranian Journal of Management Studies) JA - IJMS LA - en SN - AU - Ghane Kanafi, Armin AD - Department of Mathematical sciences, Islamic Azad University, Lahijan Branch Y1 - 2019 PY - 2019 VL - 12 IS - 3 SP - 379 EP - 404 KW - Multi-criteria optimization problems KW - Pareto surface KW - Non-convex and Nonlinear optimization KW - Health care management problem KW - Scalarization techniques DO - 10.22059/ijms.2019.255551.673089 N2 - In managerial and economic applications, there appear problems in which the goal is to simultaneously optimize several criteria functions (CFs). However, since the CFs are in conflict with each other in such cases, there is not a feasible point available at which all CFs could be optimized simultaneously. Thus, in such cases, a set of points, referred to as 'non-dominate' points (NDPs), will be encountered that are ineffective in relation to each other. In order to find such NDPs, many methods including the scalarization techniques have been proposed, each with their advantages and disadvantages. A comprehensive approach with scalarization perspective is the PS method of Pascoletti and Serafini. The PS method uses the two parameters of  as the starting point and  as the direction of motion to find the NDPs on the 'non-dominate' frontier (NDF). In bi-objective cases, the point  is selected on a special line, and changing point on this line leads to finding all the NDPs. Generalization of this approach is very difficult to three- or more-criteria optimization problems because any closed pointed cone in a three- or more-dimensional space is not like a two-dimensional space of a polygonal cone. Moreover, even for multifaceted cones, the method cannot be generalized, and inevitably weaker constraints must be used in the assumptions of the method. In order to overcome such problems of the PS method, instead of a hyperplane (two-dimensional line), a hypersphere is applied in the current paper, and the parameter  is changed over its boundary. The generalization of the new method for more than two criteria problems is simply carried out, and the examples, provided along with their comparisons with methods such as mNBI and NC, ensure the efficiency of the method. A case study in the realm of health care management (HCM) including two conflicting CFs with special constraints is also presented as an exemplar application of the proposed method. UR - https://ijms.ut.ac.ir/article_71057.html L1 - https://ijms.ut.ac.ir/article_71057_c2ff1829d20f01971d447e9dd4c701f5.pdf ER -