Abstract: The Traveling salesman problem (TSP) is NP-hard in combinatorial optimization. The research shows the algorithms for TSP on the sparse graphs have the shorter computation time than those for TSP according to the complete graphs. We present an improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals. The iterative algorithm is enhanced by adjusting two parameters of the algorithm. The computation time of the algorithm is O(CNmaxn2) where C is the iterations, Nmax is the maximum number of frequency quadrilaterals containing each edge and n is the scale of TSP. The experimental results showed the computed sparse graphs generally have less than 5n edges for most of these Euclidean instances. Moreover, the maximum degree and minimum degree of the vertices in the sparse graphs do not have much difference. Thus, the computation time of the methods to resolve the TSP on these sparse graphs will be greatly reduced.
Abstract: Ant Colony Optimization (ACO) is a promising
modern approach to the unused combinatorial optimization. Here
ACO is applied to finding the shortest during communication link
failure. In this paper, the performances of the prim’s and ACO
algorithm are made. By comparing the time complexity and program
execution time as set of parameters, we demonstrate the pleasant
performance of ACO in finding excellent solution to finding shortest
path during communication link failure.
Abstract: A new Meta heuristic approach called "Randomized gravitational emulation search algorithm (RGES)" for solving large size set covering problems has been designed. This algorithm is found upon introducing randomization concept along with the two of the four primary parameters -velocity- and -gravity- in physics. A new heuristic operator is introduced in the domain of RGES to maintain feasibility specifically for the set covering problem to yield best solutions. The performance of this algorithm has been evaluated on a large set of benchmark problems from OR-library. Computational results showed that the randomized gravitational emulation search algorithm - based heuristic is capable of producing high quality solutions. The performance of this heuristic when compared with other existing heuristic algorithms is found to be excellent in terms of solution quality.
Abstract: The job shop scheduling problem (JSSP) is a
notoriously difficult problem in combinatorial optimization. This
paper presents a hybrid artificial immune system for the JSSP with the
objective of minimizing makespan. The proposed approach combines
the artificial immune system, which has a powerful global exploration
capability, with the local search method, which can exploit the optimal
antibody. The antibody coding scheme is based on the operation based
representation. The decoding procedure limits the search space to the
set of full active schedules. In each generation, a local search heuristic
based on the neighborhood structure proposed by Nowicki and
Smutnicki is applied to improve the solutions. The approach is tested
on 43 benchmark problems taken from the literature and compared
with other approaches. The computation results validate the
effectiveness of the proposed algorithm.
Abstract: A new Meta heuristic approach called "Randomized gravitational emulation search algorithm (RGES)" for solving vertex covering problems has been designed. This algorithm is found upon introducing randomization concept along with the two of the four primary parameters -velocity- and -gravity- in physics. A new heuristic operator is introduced in the domain of RGES to maintain feasibility specifically for the vertex covering problem to yield best solutions. The performance of this algorithm has been evaluated on a large set of benchmark problems from OR-library. Computational results showed that the randomized gravitational emulation search algorithm - based heuristic is capable of producing high quality solutions. The performance of this heuristic when compared with other existing heuristic algorithms is found to be excellent in terms of solution quality.
Abstract: The weight constrained shortest path problem
(WCSPP) is one of most several known basic problems in
combinatorial optimization. Because of its importance in many areas
of applications such as computer science, engineering and operations
research, many researchers have extensively studied the WCSPP.
This paper mainly concentrates on the reduction of total search space
for finding WCSP using some existing Genetic Algorithm (GA). For
this purpose, some controlled schemes of genetic operators are
adopted on list chromosome representation. This approach gives a
near optimum solution with smaller elapsed generation than classical
GA technique. From further analysis on the matter, a new
generalized schema theorem is also developed from the philosophy
of Holland-s theorem.
Abstract: The vehicle routing problem (VRP) is a famous combinatorial optimization problem. Because of its well-known difficulty, metaheuristics are the most appropriate methods to tackle large and realistic instances. The goal of this paper is to highlight the key ideas for designing VRP metaheuristics according to the following criteria: efficiency, speed, robustness, and ability to take advantage of the problem structure. Such elements can obviously be used to build solution methods for other combinatorial optimization problems, at least in the deterministic field.