faty
Get Complete Project Material File(s) Now! »
The basic algorithm
The PSO algorithm represents each candidate solution by the position of a particle in multi-dimensional hyperspace. Throughout the optimization process velocity and displacement updates are applied to each particle to move it to a di↵erent position and thus a di↵erent solution in the search space. The velocity update is often thought to be the most critical component of the PSO algorithm since it incorporates the concepts of emergence and social intelligence. Figure 2.4 illustrates that the magnitude and direction of a particle’s velocity at time t is considered to be the result of three vectors: the particle velocity vector at time t1, the pbest position, which is a vector representation of the best solution found to date by the specific particle, and the gbest position, which is a vector representation of the best solution found to date by all the particles in the swarm. The gbest PSO [82] calculates the velocity of particle i in dimension j at time t + 1 using vij(t + 1) =wvij(t)+c1r1j(t)[ˆ xij(t)xij(t)] + c2r2j(t)[x⇤ j(t)xij(t)] (2.14)
where vij(t) represents the velocity of particlei in dimension j at time t, c1 and c2 are the cognitive and social acceleration constants, ˆ xij(t) andxij(t) respectively denotes the personal best (pbest) position and the position of particlei in dimension j at time t. x⇤ j(t) denotes the global best (gbest) position in dimensionj, w refers to the inertia weight, and r1j(t) andr2j(t) are sampled from a uniform random distribution,U(0,1).
Dfferential evolution
Originally developed from work done on Chebyshev’s polynomial fitting problems, differential evolution (DE) found its roots in the genetic annealing algorithm of Storn and Price [153]. Classified as a parallel direct search method [152], DE achieved third place on benchmark problems at the first international contest on evolutionary optimization in 1996. Since then, the number of DE research papers has increased significantly every year and DE is now well-known in the evolutionary computation community as an alternative to traditional EAs. The algorithm is considered to be easy to understand, simple to implement, reliable, and fast [123]. Application areas are just as diverse, as is the case for the PSO algorithm, and range from function optimization [153] to the determination of earthquake hypocenters [136].
1 Introduction
1.1 Objectives
1.2 Contributions
1.3 Thesis Outline
2 Single-method and Multi-method Literature
2.1 An overview of single-method optimization algorithms
2.2 An overview of multi-method optimization algorithms
2.3 Chapter summary
3 The Heterogeneous Meta-hyper-heuristic
3.1 Algorithm description
3.2 Summary
4 Initial Analysis of the Meta-hyper-heuristic Framework
4.1 Entity-to-algorithm selection strategies
4.2 Investigating the selection of low level meta-heuristics in the meta-hyper-heuristic framework
4.3 Investigating the use of local search in the meta-hyper-heuristic framework
4.4 Summary
5 Diversity Management in the Meta-hyper-heuristic Framework
5.1 An overview of existing diversity management strategies
5.2 Investigating alternative solution space diversity management strategies
5.3 Heuristic space diversity defined
5.4 Investigating alternative heuristic space diversity management strategies
5.5 Summary
6 Benchmarking the Heterogeneous Meta-hyper-heuristic
6.1 Investigating meta-hyper-heuristic performance versus other popular multimethod algorithms 6.2 Comparative analysis of selected multi-method algorithms
6.3 Summary
7 Conclusion
7.1 Summary
7.2 Future research opportunities
