Innovative Computing Methods and Their Applications to Engineering Problems

Combinatorial optimization problems are very commonly seen in scientific research and practical applications. Traveling Salesman Problem (TSP) is one nonpolynomial-hard combinatorial optimization problem. It can be describe as follows: a salesman, who has to visit clients in different cities, wants to find the shortest path starting from his home city, visiting every city exactly once and ending back at the starting point. There are exact algorithms, such as cutting-plane or facet-finding, are very complex and demanding of computing power to solve TSPs. There here, however, metaheuristics based on evolutionary algorithms that are useful to finding solutions for a much wider range of optimization problems including the TSP. Differential Evolution (DE) is a relatively simple evolutionary algorithm, which is an effective adaptive approach to global optimization over continuous search spaces. Furthermore, DE has emerged as one of the fast, robust, and efficient global search heuristics of current interest. DE shares similarities with other evolutionary algorithms, it differs significantly in the sense that distance and direction information from the current population is used to guide the search process. Since its invention, DE has been applied with success on many numerical optimization problems outperforming other more popular metaheuristics such as the genetic algorithms. Recently, some researchers extended with success the application of DE to combinatorial optimization problems with discrete decision variables. In this paper, the following discrete DE approaches for the TSP are proposed and evaluated: i) DE approach without local search, ii) DE with local search based on Lin-Kernighan-Heulsgaun (LKH) method, and iii) DE with local search based on Variable Neighborhood Search (VNS) and together with LKH method. Numerical study is carried out using the TSPLIB of test TSP problems. In this context, the computational results are compared with the other results in the recent TSP literature. The obtained results show that LKH method is the best method to reach optimal results for TSPLIB benchmarks, but for largest problems, the DE+VNS improve the quality of obtained results.

The objective of this chapter is to develop and solve the reliability optimization problems of series-parallel, parallel-series and complicated system considering the reliability of each component as interval valued number. For optimization of system reliability and system cost separately under resource constraints, the corresponding problems have been formulated as constrained integer/mixed integer programming problems with interval objectives with the help of interval arithmetic and interval order relations. Then the problems have been converted into unconstrained optimization problems by two different penalty function techniques. To solve these problems, two different real coded genetic algorithms (GAs) for interval valued fitness function with tournament selection, whole arithmetical crossover and non-uniform mutation for floating point variables, uniform crossover and uniform mutation for integer variables and elitism with size one have been developed. To illustrate the models, some numerical examples have been solved and the results have been compared. As a special case, taking lower and upper bounds of the interval valued reliabilities of component as same the corresponding problems have been solved and the results have been compared with the results available in the existing literature. Finally, to study the stability of the proposed GAs with respect to the different GA parameters (like, population size, crossover and mutation rates), sensitivity analyses have been shown graphically.

In this chapter, we take advantage of particle swarm optimization to build fuzzy systems automatically for different kinds of problems by simply providing the objective function and the problem variables. Particle swarm optimization (PSO) is a technique used in complex problems, including multi-objective problems. Fuzzy systems are currently used in many kinds of applications, such as control, for their effectiveness and efficiency. However, these characteristics depend primarily on the model yield by human experts, which may or may not be optimized for the problem. To avoid dealing with inconsistent during the fuzzy systems generation, we used some known techniques, such as the WM method, to help evolving meaningful rules and clustering concepts to generate membership functions. Tests using three three-dimensional functions have been carried out and show that the evolutionary process is promising.

Wind energy is an important source of renewable energy, and reliability is a critical issue for operating wind energy systems. The Canadian wind energy industry has been growing very rapidly. The installed wind energy capacity in Canada in 2008 was approximately 2,000 mega watts (MW), which is less than one percent of the total electricity. It is believed that wind energy will satisfy 20% of Canada’s electricity demand by 2025, by adding 55,000MW of new generating capacity [1]. Operation and maintenance costs account for 25-30% of the wind energy generation cost. Currently, the wind turbine manufacturers and operators are gradually changing the maintenance strategy from time-based preventive maintenance to condition based maintenance (CBM) [2-5]. In this article, we review the current research status of maintenance of wind turbine systems, and discuss the applications of artificial neural networks (ANN) based health prediction tools in this field. A CBM method based on ANN health condition prediction is presented.

Economic dispatch is an important problem in power systems. This chapter presents how a method of stochastic optimization, a metaheuristic known as CLONALG (CLONal selection ALGorithm), can be applied to the economic dispatch problem. The objective function used in the optimization is based on Karush-Kuhn-Tucker conditions, thus, guaranteeing a convergence to the global optimum. Examples and results are presented showing the method is capable of finding the optimum solution while respecting power generation limits.

Several approaches for solving multi-objective optimization problems entail a form of scalarization of the objectives. This chapter proposes a study of different dynamic objectives aggregation methods in the context of evolutionary algorithms. These methods are mainly based on both weighted sum aggregations and curvature variations. Since the incorporation of chaotic rules or behaviour in population-based optimization algorithms has been shown to possibly enhance their searching ability, this study proposes to introduce and evaluate also some chaotic rules in the dynamic weights generation process. A comparison analysis is presented on the basis of a campaign of computational experiments on a set of benchmark problems from the literature.

Network-on-chip (NoC) are considered the next generation of communication infrastructure, which will be omnipresent in most of industry, office and personal electronic systems. In the platform-based methodology, an application is implemented by a set of collaborating intellectual properties (IPs) blocks. In this paper, we use multi-objective evolutionary optimization to address the problem of mapping topologically pre-selected sets IPs, which constitute the set of optimal solutions that were found for the IP assignment problem, on the tiles of a mesh-based NoC. The IP mapping optimization is driven by the area occupied, execution time and power consumption.

In our society, various combinatorial optimization problems exist and we must often solve them, for e.g. scheduling, delivery planning, circuit design, and computer wiring. Then, one of the important issues in science and engineering is how to develop effective algorithms for solving these combinatorial problems.