In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated where the feasible region is formed as the intersection of two inequality fuzzy systems and Yager family of t-norms is considered as fuzzy composition. Yager family of t-norms is a parametric family of continuous nilpotent t-norms which is also one of the most frequently appli...

In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated where the feasible region is formed as the intersection of two inequality fuzzy systems and Dombi family of t-norms is considered as fuzzy composition. Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increasing functions of ...

Recall that a linear program defines a polyhedron. For simplicity, let us assume here that this polyhedron is nonempty (i.e., the LP is feasible) and bounded (namely, it is a polytope). Then we know that the optimal value of the LP is attained at a vertex of the polytope (equivalently, at a basic feasible solution to the LP). We say that two vertices of a polytope are adjacent if they are conne...

In the last chapter, we introduced the concept of a basis of a linear program (P) Minimize Z = c T x s.t. Recall that a basis of (P) is a subset B ⊆ {1, 2,. .. , n} of the variables. We also introduced the concepts of a basic solution x B of (P), and a dual basic solution y B associated with B and the dual (D) of (P). We finished by proving Lemma 1 Let B be an arbitrary basis for (P). If B is a...

The adsorption ability of Dowex Optipore L493 resin modified with Aliquat 336 (MR), activated carbon modified with Aliquat 336 (MAC) and sawdust modified with Aliquat 336 (MS) for removal of Cr(VI) from aqueous solution in batch system was investigated. The effects of operational parameters such as adsorbent dosage, initial concentration of Cr(VI) ions, pH, temperature and contact time were stu...

This paper is a survey of greedy randomized adaptive search procedures (GRASP). GRASP is a multi-start or iterative procedure where each GRASP iteration consists of a construction phase, where a feasible solution is constructed, followed by a local search procedure that finds a locally optimal solution. The construction phase of GRASP is essentially a randomized greedy algorithm. Repeated appli...

We discuss a finite method of feasible directions for linear programs. The method begins with a BFS (basic feasible solution) and constructs a profitable direction by combining the updated columns of several nonbasic variables eligible to enter. Moving in this direction as far as possible, while retaining feasibility, leads to a point which is not in general a basic solution of the original pro...

Background and purpose: Textile industries are among the most polluting industries regarding the volume and the complexity of treatment of its effluents discharge. This study investigated the efficiency of electrocoagulation process using aluminum electrodes in basic red 18 dye removal from aqueous solutions. Materials and Methods: This study was performed in a bipolar batch reactor with ...

A new two-phase method for solving the multi-parametric linear complementarity problem (mpLCP) with sufficient matrices is presented. In the first phase an initial feasible solution to mpLCP which satisfies certain criteria is determined. In the second phase the set of feasible parameters is partitioned into polyhedral regions such that the solution of the mpLCP, as a function of the parameters...