Filomat 2022 Volume 36, Issue 7, Pages: 2237-2267
https://doi.org/10.2298/FIL2207237S
Full text ( 512 KB)
Iterative algorithms for determining optimal solution set of interval linear fractional programming problem
Salary Pour Sharif Abad Fatemeh (Mathematics Faculty, University of Sistan and Baluchestan, Zahedan, Iran), fatehsalari63@yahoo.com
Allahdadi Mehdi (Mathematics Faculty, University of Sistan and Baluchestan, Zahedan, Iran), m_allahdadi@math.usb.ac.ir
Nehi Hasan Mishmast (Mathematics Faculty, University of Sistan and Baluchestan, Zahedan, Iran), hmnehi@hamoon.usb.ac.ir
Determining the optimal solution (OS) set of interval linear fractional
programming (ILFP) models is generally an NP-hard problem. Few methods have
been proposed in this field which have only been able to obtain the optimal
value of the objective function. Thus, there is a need for an appropriate
method to determine the OS set of the ILFP model. In this paper, we
introduce three algorithms to obtain the OS of ILFP. In the first and second
algorithms, using the definition of strong and weak feasible solutions, the
objective function of ILFP has been transformed to a linear objective
function on the largest feasible region (LFR) and we obtain the OS of ILFP.
These two algorithms, only introduce one point as the feasible OS. Since
ILFP is an interval model, we seek an algorithm, where for the first time a
solution set is obtained as the OS set by solving two sub-models. Hence, we
transform the ILFP model into two pessimistic and optimistic sub-models, as
one is in the smallest feasible region (SFR) and the other on the LFR. We
add constraints to the optimistic model to ensure that the OS set is
feasible. Then, we introduce pessimistic and modified optimistic model
(PMOM) algorithm. In this algorithm, each PMOM is solved separately. The OSs
obtained from these two models give the OS set so that this OS set is
feasible. Note that the union of feasible OSs obtained from the proposed
algorithms will be a more complete feasible OS set.
Keywords: Optimal solution set, Interval linear fractional programming, Uncertainty, Feasibility
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