Volume 8, Issue 7, July 2016

 

 

 

Optimizing Multiset Metagrammars. Formal Definitions

Pages: 106-114 (9) | [Full Text] PDF (1015 KB)
I Sheremet, I Zhukov
Financial University under the Government of Russian Federation, Moscow, Russian Federation
National Research Nuclear University Moscow Engineering Physical Institute, Moscow, Russian Federation

Abstract -
A multiset-based approach to optimization problems formalizing and solving is considered. Optimizing multiset metagrammars (OMMG) are described as specific knowledge representation model developed precisely for this purposes. OMMG provide convergence of classical optimization theory and modern knowledge engineering combining the best features of mathematical and logical programming. Paper is dedicated to the formal definition of OMMG syntax and semantics as well as to the multigrammaticĐ°l representation of the most well-known classical optimization problems.
 
Index Terms - Multisets, Multiset grammars and metagrammars, Optimizing multiset metagrammars, Multigrammatical represent-ation of optimization problems, Unconventional programming paradigms, Knowledge representation, Mathematical program-ing, Logical programming

Citation - I Sheremet, I Zhukov. "Optimizing Multiset Metagrammars. Formal Definitions." International Journal of Computer Engineering and Information Technology 8, no. 7 (2016): 106-114.

 

Optimizing Multiset Metagrammars. Multigrammatical Representation of Classical Optimization Problems

Pages: 115-124 (10) | [Full Text] PDF (917 KB)
I Sheremet, I Zhukov
Financial University under the Government of Russian Federation, Moscow, Russian Federation
National Research Nuclear University Moscow Engineering Physical Institute, Moscow, Russian Federation

Abstract -
Optimizing multiset metagrammars (OMMG) are specific knowledge representation model developed for problem solving in the areas of systems analysis and optimization. Formal definitions of OMMG syntax and semantics were considered in previous paper. Presented material is dedicated to OMMG application to the most well-known classical optimization problems. Techniques of multigrammatical representation of the following problems is considered: shortest path, travelling salesman, maximal flow, optimal assignments, optimal pair matching, transportation, integer linear programming.
 
Index Terms - Multisets, Optimizing multiset metagrammars, Optimization problems, Integer linear programming

Citation - I Sheremet, I Zhukov. "Optimizing Multiset Metagrammars. Multigrammatical Representation of Classical Optimization Problems." International Journal of Computer Engineering and Information Technology 8, no. 7 (2016): 115-124.

 

The Conventional, the Theory of Constraints, and the Linear Programming: Three Approaches to the Optimum Production Mix: A Comparative Study

Pages: 125-140 (16) | [Full Text] PDF (742 KB)
A Altumi, AH AL-yaseer
BSc, MSc, PhD, Associate Professor, Faculity of Engineering, Mechanical & Industrial Engineering Dept., University of Tripoli
BSc, MSc, MBA, PG. D., Ph.D, Lecturer, Libyan Academy (seconded to Housing & Infrastructure Board)

Abstract -
This paper contains research work about three approaches to the optimum production mix problem (OPM); Conventional, theory of constraints (TOC), and Linear programming (LP). The research has two aims, first to develop a solid and clear heuristic describes the conventional and the TOC steps towards OPM. The second is to examine the common belief about the superiority of TOC over the conventional approach.This study is based on a comparative methodology where the three approaches were applied to a numerical case study and the obtained solutions were compared in terms of which provide the OPM in the form of the highest contribution margin.As a searching tool for OPM, The Conventional approach is equivalent to TOC and LP in case of a single-constraint system and superior to TOC in situations of single-constraint system with one local constraint.This paper provided complete and clear heuristics for the conventional and TOC approaches o OPM. And demonstrated that there are situations where the conventional approach is more efficient than the TOC, unlike what is commonly found in the literature.
 
Index Terms - Optimum Production Mix Problem (OPM), Theory of Constraints (TOC), Linear Programming (LP)

Citation - A Altumi, AH AL-yaseer. "The Conventional, the Theory of Constraints, and the Linear Programming: Three Approaches to the Optimum Production Mix: A Comparative Study." International Journal of Computer Engineering and Information Technology 8, no. 7 (2016): 125-140.