A new hybrid method for solving nonlinear fractional differential equations

In this paper, numerical solution of initial and boundary value problems for nonlinear fractional differential equations is considered by pseudospectral method. In order to avoid solving systems of nonlinear equations resulting from the method, the residual function of the problem is constructed, as well as a suggested unconstrained optimization model solved by PSOGSA algorithm. Furthermore, the research inspects and discusses the spectral accuracy of Chebyshev polynomials in the approximation theory. The following scheme is tested for a number of prominent examples, and the obtained results demonstrate the accuracy and efficiency of the proposed method

Chaos embedded opposition based learning for gravitational search algorithm

Due to its robust search mechanism, Gravitational search algorithm (GSA) has achieved lots of popularity from different research communities. However, stagnation reduces its searchability towards global optima for rigid and complex multi-modal problems. This paper proposes a GSA variant that incorporates chaos-embedded opposition-based learning into the basic GSA for the stagnation-free search. Additionally, a sine-cosine based chaotic gravitational constant is introduced to balance the trade-off between exploration and exploitation capabilities more effectively. The proposed variant is tested over 23 classical benchmark problems, 15 test problems of CEC 2015 test suite, and 15 test problems of CEC 2014 test suite. Different graphical, as well as empirical analyses, reveal the superiority of the proposed algorithm over conventional meta-heuristics and most recent GSA variants.Comment: 33 pages, 5 Figure

進化的及び樹状突起のメカニズムを考慮したソフトコンピューティング技術の提案

富山大学・富理工博甲第117号・宋振宇・2017/03/23富山大学201

樹状突起ニューロン計算および差分進化アルゴリズムに関する研究

富山大学・富理工博甲第118号・陳瑋・2017/03/23富山大学201

Generalized Schwarzschild's method

We describe a new finite element method (FEM) to construct continuous equilibrium distribution functions of stellar systems. The method is a generalization of Schwarzschild's orbit superposition method from the space of discrete functions to continuous ones. In contrast to Schwarzschild's method, FEM produces a continuous distribution function (DF) and satisfies the intra element continuity and Jeans equations. The method employs two finite-element meshes, one in configuration space and one in action space. The DF is represented by its values at the nodes of the action-space mesh and by interpolating functions inside the elements. The Galerkin projection of all equations that involve the DF leads to a linear system of equations, which can be solved for the nodal values of the DF using linear or quadratic programming, or other optimization methods. We illustrate the superior performance of FEM by constructing ergodic and anisotropic equilibrium DFs for spherical stellar systems (Hernquist models). We also show that explicitly constraining the DF by the Jeans equations leads to smoother and/or more accurate solutions with both Schwarzschild's method and FEM.Comment: 14 pages, 7 Figures, Submitted to MNRA

Symbiotic Organisms Search Algorithm: theory, recent advances and applications

The symbiotic organisms search algorithm is a very promising recent metaheuristic algorithm. It has received a plethora of attention from all areas of numerical optimization research, as well as engineering design practices. it has since undergone several modifications, either in the form of hybridization or as some other improved variants of the original algorithm. However, despite all the remarkable achievements and rapidly expanding body of literature regarding the symbiotic organisms search algorithm within its short appearance in the field of swarm intelligence optimization techniques, there has been no collective and comprehensive study on the success of the various implementations of this algorithm. As a way forward, this paper provides an overview of the research conducted on symbiotic organisms search algorithms from inception to the time of writing, in the form of details of various application scenarios with variants and hybrid implementations, and suggestions for future research directions

Enhancement of bees algorithm for global optimisation

This research focuses on the improvement of the Bees Algorithm, a swarm-based nature-inspired optimisation algorithm that mimics the foraging behaviour of honeybees. The algorithm consists of exploitation and exploration, the two key elements of optimisation techniques that help to find the global optimum in optimisation problems. This thesis presents three new approaches to the Bees Algorithm in a pursuit to improve its convergence speed and accuracy. The first proposed algorithm focuses on intensifying the local search area by incorporating Hooke and Jeeves’ method in its exploitation mechanism. This direct search method contains a pattern move that works well in the new variant named “Bees Algorithm with Hooke and Jeeves” (BA-HJ). The second proposed algorithm replaces the randomly generated recruited bees deployment method with chaotic sequences using a well-known logistic map. This new variant called “Bees Algorithm with Chaos” (ChaosBA) was intended to use the characteristic of chaotic sequences to escape from local optima and at the same time maintain the diversity of the population. The third improvement uses the information of the current best solutions to create new candidate solutions probabilistically using the Estimation Distribution Algorithm (EDA) approach. This new version is called Bees Algorithm with Estimation Distribution (BAED). Simulation results show that these proposed algorithms perform better than the standard BA, SPSO2011 and qABC in terms of convergence for the majority of the tested benchmark functions. The BA-HJ outperformed the standard BA in thirteen out of fifteen benchmark functions and is more effective in eleven out of fifteen benchmark functions when compared to SPSO2011 and qABC. In the case of the ChaosBA, the algorithm outperformed the standard BA in twelve out of fifteen benchmark functions and significantly better in eleven out of fifteen test functions compared to qABC and SPSO2011. BAED discovered the optimal solution with the least number of evaluations in fourteen out of fifteen cases compared to the standard BA, and eleven out of fifteen functions compared to SPSO2011 and qABC. Furthermore, the results on a set of constrained mechanical design problems also show that the performance of the proposed algorithms is comparable to those of the standard BA and other swarm-based algorithms from the literature

A Novel Algorithm for Solving Structural Optimization Problems

In the past few decades, metaheuristic optimization methods have emerged as an effective approach for addressing structural design problems. Structural optimization methods are based on mathematical algorithms that are population-based techniques. Optimization methods use technology development to employ algorithms to search through complex solution space to find the minimum. In this paper, a simple algorithm inspired by hurricane chaos is proposed for solving structural optimization problems. In general, optimization algorithms use equations that employ the global best solution that might cause the algorithm to get trapped in a local minimum. Hence, this methodology is avoided in this work. The algorithm was tested on several common truss examples from the literature and proved efficient in finding lower weights for the test problems

Minimum-Fuel Trajectory Design in Multiple Dynamical Environments Utilizing Direct Transcription Methods and Particle Swarm Optimization

Particle swarm optimization is used to generate an initial guess for designing fuel-optimal trajectories in multiple dynamical environments. Trajectories designed in the vicinity of Earth use continuous or finite low-thrust burning and transfer from an inclined or equatorial circular low-Earth-orbit to a geostationary orbit. In addition, a trajectory from near-Earth to a periodic orbit about the cislunar Lagrange point with minimized impulsive burn costs is designed within a multi-body dynamical environment. Direct transcription is used in conjunction with a nonlinear optimizer to find locally-optimal trajectories given the initial guess. The near-Earth transfers are propagated at low-level thrust where neither the very-low-thrust spiral solution nor the impulsive transfer is an acceptable starting point. The very-high-altitude transfer is designed in a multi-body dynamical environment lacking a closed-form analytical solution. Swarming algorithms excel given a small number of design parameters.When continuous control time histories are needed, employing a polynomial parameterization facilitates the generation of feasible solutions. For design in a circular restricted three-body system, particle swarm optimization gains utility due to a more global search for the solution, but may be more sensitive to boundary constraints. Computation time and constraint weighting are areas where a swarming algorithm is weaker than other approaches