Research On Heuristic Algorithms And Their Applications

Heuristic algorithms and their applications have obtained widespread attention in recent years and they have been applied in many practical fields. Some of them and their applications are studied including differential evolution algorithm, harmony search algorithm and particle swarm optimization algorithm. And the main work is as follows.(1) In order to improve the performance of the PSO algorithms, a global particle swarm optimization (GPSO) algorithm is proposed. The GPSO introduces a new inertia weight, and it is defined as the product of an exponential type function and a random number, which is beneficial to keep the global and local searching capabilities of the proposed algorithm. On the other hand, the GPSO adds small disturbance to the global optimal solution, which can effectively avoid the premature problems in the convergence of the GPSO algorithm. Three particle swarm optimization algorithms are used to solve six unconstrained optimization problems. The simulation results demonstrate that the GPSO has faster convergence rate and stronger capability of escaping from the local optimum when compared with the other two existing particle swarm optimization algorithms.(2) Based on the analysis of the classic differential evolution algorithm, an improved adaptive differential evolution algorithm with variables extended is proposed. In this algorithm, the mutation rate is taken as a component of the solution space, varying with the evolving of the algorithm, so that the parameters of the algorithm can be adapted well to meet the requirements of each stage in the evolution, thereby improving the performance of the algorithm. Besides, a new mutation scheme is proposed which can better balance the global search and local search.(3) The system reliability problem is described and three typical systems and their mathematical models are introduced. The constrained mathematical model is converted to an unconstrained one through the treatment of the discrete variables and constraints. The variable extended adaptive differential evolution algorithm proposed in the previous section is applied to solve the system reliability problems. Experiments on three typical systems and comparison with other two differential evolution algorithms including DE and JADE are performed. The result shows that the proposed algorithm has better optimization ability and can satisfy the need of solving the system reliability optimization problems.(4) From the view of engineering practice, the concept of practicably point is led to an optimization problem in this paper. In certain situations, it should not only consider the objective function of the global extreme points, but also the neighborhood characteristics of them are concerned. Practicably optimal point is essentially the global optimal point with a neighborhood constraint which is difficult to deal with traditional methods, so an approximate method based on neighborhood sampling is proposed to handle this constraint. A new quick search algorithm based on particle swarm optimization algorithm is introduced to find the practicably optimal points according to different requirements. The experiment verifies the feasibility of the concept and solving method of practicably optimal point. The optimization results reveal that the proposed algorithm has strong convergence and stability, and appears to be an efficient alternative for obtaining the practicably optimal points.(5) For the purpose of avoiding the disadvantages of the harmony search algorithm, a learned harmony search (LHS) algorithm is proposed. The adaptive parameter harmony memory consideration rate (HMCR) is designed based on the change of objective function value and a learning strategy is used to accelerate the search speed. Then the pitch adjustment rate (PAR) is adjusted dynamically to enhance the global search. The 16 classic test functions are tested, and the results show that LHS algorithm outperforms the other four harmony search algorithms. Finally, LHS algorithm is applied to 100-1 knapsack problems and a classic knapsack example, and the result shows that the LHS algorithm is better than others.(6) For the flexible job shop scheduling problems with many objectives, a new continuous solution method is proposed in this paper. Based on the priority levels of the starting time corresponding to each operation and the processing flow chart, novel encoding methods are raised to alleviate the difficulty in the settlement of multi-objective flexible job shop scheduling problems in continuous space. New neighborhood structures are established to improve the solution quality and search efficiency according to the empirical knowledge and heuristic rules. Moreover, effective local search schemes are carried out on the machine selection component and operation scheduling component Experiments on five practical instances from literatures are conducted and the comparison result verifies the effectiveness of the proposed algorithm.