The Application of Fuzzification for Solving Quadratic Functions

This paper describes an approximation algorithm for solving standard quadratic optimization problems(StQPs) over the standard simplex by using fuzzification technique. We show that the approximate solution of the algorithm is an epsilon -critical point and satisfies epsilon-delta condition. The algorithm is compared with IBM ILOG CPLEX (short for CPLEX). The computational results indicate that the new algorithm is faster than CPLEX. Especially for infeasible problems. Furthermore, we calculate 100 instances for different size StQP problems. The numerical experiments show that the average computational time of the new algorithm for calculating the first local minimizer is in BigO(n) when the size of the problems is less or equal to 450.

Variance Bounding of Delayed-Acceptance Kernels

A delayed-acceptance version of a Metropolis–Hastings algorithm can be useful for Bayesian inference when it is computationally expensive to calculate the true posterior, but a computationally cheap approximation is available; the delayed-acceptance kernel targets the same posterior as its associated “parent” Metropolis-Hastings kernel. Although the asymptotic variance of the ergodic average of any functional of the delayed-acceptance chain cannot be less than that obtained using its parent, the average computational time per iteration can be much smaller and so for a given computational budget the delayed-acceptance kernel can be more efficient. When the asymptotic variance of the ergodic averages of all $$L^2$$ L 2 functionals of the chain are finite, the kernel is said to be variance bounding. It has recently been noted that a delayed-acceptance kernel need not be variance bounding even when its parent is. We provide sufficient conditions for inheritance: for non-local algorithms, such as the independence sampler, the discrepancy between the log density of the approximation and that of the truth should be bounded; for local algorithms, two alternative sets of conditions are provided. As a by-product of our initial, general result we also supply sufficient conditions on any pair of proposals such that, for any shared target distribution, if a Metropolis-Hastings kernel using one of the proposals is variance bounding then so is the Metropolis-Hastings kernel using the other proposal.

Comparison of Genetic Algorithm and Harmony Search Method for 2D Geometry Optimization.

There are many applications of Genetic Algorithm (GA) and Harmony Search (HS) Method for solving problems in civil engineering design. The question is, still, which method is better for geometry optimization of a steel structure. The purpose of this paper is to compare GA and HS performance for geometric optimization of a steel structure. This problem is solved by optimizing a steel structure using GA and HS and then comparing the structure’s weight as well as the time required for the calculation. In this study, GA produced a structural weight of 2308.00 kg to 2387.00 kg and HS scored 2193.12 kg to 2239.48 kg. The average computational time required by GA is 607 seconds and HS needed 278 seconds. It concludes that HS is faster and better than GA for geometry optimization of a steel structure.

Numerical Study on the Quasi-Dimensional Model of Diesel Engine for Performance Optimization

In this paper, a phase-divided spray mixing model is proposed and the quasi-dimensional model of diesel engine working process is developed. The software MATLAB/Simulink is utilized to build the quasi-dimensional model of diesel engine working process, and the performance for diesel engine is simulated. The simulation results agree with experimental data quite well which indicates that the simplified quasi-dimensional model has high precision for predicting diesel engine performance. By utilization of this simulation model, the average computational time for one diesel engine working process is 36 s, which presents good real time operating performance of the model. On the basis of the principle of orthogonal test design, the performance of diesel engine was optimized by use of the quasi-dimensional model.