Researchers are aiming to automate very complex problems using computers, which
can be made possible only by very time-efficient algorithms. The exact
deterministic algorithms may take ages to solve combinatorial optimization problems like the
famous Traveling Salesman Problem (TSP) for larger search space, which have been proved
to be of class NP. Class NP consists of all those problems whose solutions can be found
in polynomial time on a non-deterministic Turing machine. Since such a machine is
not practically feasible, it means that an exponential algorithm can be written for an
NP-problem; also, there is no certainty as to whether a polynomial algorithm exists
or not [1]. Computing optimal solutions for many combinatorial optimization
problems are intractable, and known as NP-hard. Usually, we are pleased with good
solutions rather than having no feasible solutions at all. It has been time and again proved
in recent studies that heuristic and metaheuristic algorithms, which suggest
some approximations to the solution of optimization problems, are as good a solution
as possible for the problem instances. There are two important concepts in
metaheuristics known as intensification and diversification, which largely determine its behavior.
They are in some way contrary and complementary to each other.
The paper [2] by
Christian Blum and Andrea Roli introduced a framework, I&D frame, to put
different intensification and diversification components into relation with each other.
Some classic NP problems are TSP and Quadratic Assignment Problem (QAP), which
have been successfully solved using metaheuristics. Interested readers can refer to paper
[3], which solves TSP using Ant Colony Optimization (ACO) metaheuristics. One of
the most successful types of artificial intelligence techniques known as swarm
intelligence [4, 5, 6] solves QAP using hybrid ant colony system and Genetic Algorithm (GA)
[7]. Research on ACO algorithms has led to a number of other successful applications
to combinatorial optimization problems; the results of which indicate that it is possible
to arrive at high quality solutions in reasonable time. In addition to single solution
search algorithms such as descent local search, greedy heuristic, simulated annealing and
tabu search, there is a growing interest in population-based metaheuristics well inspired
by the behaviors of natural systems. These metaheuristics include evolutionary
algorithms, evolution strategies, genetic programming, ant colonies, scatter search and
particle swarm optimization [8]. |