11,735 research outputs found
An exact algorithm for linear optimization problem subject to max-product fuzzy relational inequalities with fuzzy constraints
Fuzzy relational inequalities with fuzzy constraints (FRI-FC) are the
generalized form of fuzzy relational inequalities (FRI) in which fuzzy
inequality replaces ordinary inequality in the constraints. Fuzzy constraints
enable us to attain optimal points (called super-optima) that are better
solutions than those resulted from the resolution of the similar problems with
ordinary inequality constraints. This paper considers the linear objective
function optimization with respect to max-product FRI-FC problems. It is proved
that there is a set of optimization problems equivalent to the primal problem.
Based on the algebraic structure of the primal problem and its equivalent
forms, some simplification operations are presented to convert the main problem
into a more simplified one. Finally, by some appropriate mathematical
manipulations, the main problem is transformed into an optimization model whose
constraints are linear. The proposed linearization method not only provides a
super-optimum (that is better solution than ordinary feasible optimal
solutions) but also finds the best super-optimum for the main problem. The
current approach is compared with our previous work and some well-known
heuristic algorithms by applying them to random test problems in different
sizes.Comment: 29 pages, 8 figures, 7 table
Modified signomial geometric programming (MSGP) and its applications
A "signomial" is a mathematical function, contains one or more independent variables. Richard J. Duffin and Elmor L. Peterson introduced the term "signomial". Signomial geometric programming (SGP) optimization technique often provides a much better mathematical result of real-world nonlinear optimization problems. In this research paper, we have proposed unconstrained and constrained signomial geometric programming (SGP) problem with positive or negative integral degree of difficulty. Here a modified form of signomial geometric programming (MSGP) has been developed and some theorems have been derived. Finally, these are illustrated by proper examples and applications
Complete solution of a constrained tropical optimization problem with application to location analysis
We present a multidimensional optimization problem that is formulated and
solved in the tropical mathematics setting. The problem consists of minimizing
a nonlinear objective function defined on vectors over an idempotent semifield
by means of a conjugate transposition operator, subject to constraints in the
form of linear vector inequalities. A complete direct solution to the problem
under fairly general assumptions is given in a compact vector form suitable for
both further analysis and practical implementation. We apply the result to
solve a multidimensional minimax single facility location problem with
Chebyshev distance and with inequality constraints imposed on the feasible
location area.Comment: 20 pages, 3 figure
Tolerance analysis approach based on the classification of uncertainty (aleatory / epistemic)
Uncertainty is ubiquitous in tolerance analysis problem. This paper deals with tolerance analysis formulation, more particularly, with the uncertainty which is necessary to take into account into the foundation of this formulation. It presents: a brief view of the uncertainty classification: Aleatory uncertainty comes from the inherent uncertain nature and phenomena, and epistemic uncertainty comes from the lack of knowledge, a formulation of the tolerance analysis problem based on this classification, its development: Aleatory uncertainty is modeled by probability distributions while epistemic uncertainty is modeled by intervals; Monte Carlo simulation is employed for probabilistic analysis while nonlinear optimization is used for interval analysis.“AHTOLA” project (ANR-11- MONU-013
A constrained tropical optimization problem: complete solution and application example
The paper focuses on a multidimensional optimization problem, which is
formulated in terms of tropical mathematics and consists in minimizing a
nonlinear objective function subject to linear inequality constraints. To solve
the problem, we follow an approach based on the introduction of an additional
unknown variable to reduce the problem to solving linear inequalities, where
the variable plays the role of a parameter. A necessary and sufficient
condition for the inequalities to hold is used to evaluate the parameter,
whereas the general solution of the inequalities is taken as a solution of the
original problem. Under fairly general assumptions, a complete direct solution
to the problem is obtained in a compact vector form. The result is applied to
solve a problem in project scheduling when an optimal schedule is given by
minimizing the flow time of activities in a project under various activity
precedence constraints. As an illustration, a numerical example of optimal
scheduling is also presented.Comment: 20 pages, accepted for publication in Contemporary Mathematic
Resolution and simplification of Dombi-fuzzy relational equations and latticized optimization programming on Dombi FREs
In this paper, we introduce a type of latticized optimization problem whose
objective function is the maximum component function and the feasible region is
defined as a system of fuzzy relational equalities (FRE) defined by the Dombi
t-norm. Dombi family of t-norms includes a parametric family of continuous
strict t-norms, whose members are increasing functions of the parameter. This
family of t-norms covers the whole spectrum of t-norms when the parameter is
changed from zero to infinity. Since the feasible solutions set of FREs is
non-convex and the finding of all minimal solutions is an NP-hard problem,
designing an efficient solution procedure for solving such problems is not a
trivial job. Some necessary and sufficient conditions are derived to determine
the feasibility of the problem. The feasible solution set is characterized in
terms of a finite number of closed convex cells. An algorithm is presented for
solving this nonlinear problem. It is proved that the algorithm can find the
exact optimal solution and an example is presented to illustrate the proposed
algorithm.Comment: arXiv admin note: text overlap with arXiv:2206.09716,
arXiv:2207.0637
- …