ACO with Intuitionistic Fuzzy Pheromone Updating Applied on Multiple-Constraint Knapsack Problem

Abstract

Some of industrial and real life problems are difficult to be solved by traditional methods, because they need exponential number of calculations. As an example, we can mention decision-making problems. They can be defined as optimization problems. Ant Colony Optimization (ACO) is between the best methods, that solves combinatorial optimization problems. The method mimics behavior of the ants in the nature, when they look for a food. One of the algorithm parameters is called pheromone, and it is updated every iteration according quality of the achieved solutions. The intuitionistic fuzzy (propositional) logic was introduced as an extension of Zadeh’s fuzzy logic. In it, each proposition is estimated by two values: degree of validity and degree of non-validity. In this paper, we propose two variants of intuitionistic fuzzy pheromone updating. We apply our ideas on Multiple-Constraint Knapsack Problem (MKP) and compare achieved results with traditional ACO.

An Elliptic Intuitionistic Fuzzy Portfolio Selection Problem based on Knapsack Problem

“…A dynamic programming strategy has been provided in [9], [38], [39] for solving FKP. In the work [14], an approach for ant colonies to optimize the Multiple-Constraint Knapsack Problem utilizing intuitionistic fuzzy (IF) pheromone updating is described. The idea of the E-IFKP and its usage for the portfolio selection problem according to three scenarios give this work its novelty.…”