Modified Quick Convergent Inflow Algorithm for Solving Linear Programming Problems

Abstract

A Modified Quick Convergent Inflow Algorithm (MQCIA) for Solving Linear Programming problems, based on variance of predicted response, is presented. The method adds a point of maximum variance to an initial design thus leading to a maximizer of the response function in a maximization problem. Similarly, a point of minimum variance is added to an initial design thus leading to a minimizer of the response function in a minimization problem. Effectiveness of the method has been demonstrated and the results show that by improving an existing experimental design, the optimizer of the response function is approached. Analytical justification for the MQCIA has also been established.

Comparative Study of the Quick Convergent Inflow Algorithm (QCIA) and the Modified Quick Convergent Inflow Algorithm (MQCIA)

“…The success of the Modified Quick Convergent Inflow Algorithm (MQCIA) of Iwundu and Ebong (2014) lies fundamentally on the fact that by improving an experimental design, the optimizer of a response function is approached. Many techniques are suggested on the subject of designing experiments, on how to improve an existing experimental design.…”

“…If Yes, the optimizer of the objective function is (Iwundu and Ebong; The sequential steps that make up the Modified Quick Convergent Inflow Algorithm are;…”

“…However, in some few years now, experimental design techniques have been employed as alternative methods in solving linear programming problems. These methods, usually based on sequential algorithms, include Maximum Norm Exchange Algorithm of Umoren (1999), Quadratic Exchange Algorithm of Umoren (2002), Quick Convergent Inflow Algorithm of Odiakosa and Iwundu (2013), Modified Quick Convergent Inflow Algorithm of Iwundu and Ebong (2014), etc. Umoren (1999) and Umoren (2002) applied the optimal design principles in solving constrained optimization problems.…”

Rules for Identifying the Initial Design Points for Use in the Quick Convergent Inflow Algorithm

“…As a further observation on the QCIA, Iwundu and Ebong (2014) noted that problem occurs with the QCIA when the point reached by the line equation does not satisfy the linear inequality constraints and hence cannot be used as an admissible point of the experimental design. At this instance, the QCIA cannot successfully converge at the required optimum.…”

“…Other works that apply experimental design principles for solving optimization problems include Umoren and Etukudo (2010), Osita and Iwundu (2013), Ekezie and Nzenwa (2013), Chigbu and Ukaegbu (2013), Ekezie etal. (2013), Iwundu and Hezekiah (2014), Iwundu and Ebong (2014) and Iwundu and Ndiyo (2015). p-parameter model.…”