A new metaheuristic for optimization: Optics inspired optimization (OIO)

Due to the law of reflection, a concave reflecting surface/mirror causes the incident light rays to converge and a convex surface/mirror causes the light rays to reflect away so that they all appear to be diverging. These converging and diverging behaviors cause that the curved mirrors show different image types depending on the distance between the object and the mirror. We model such optical phenomena metaphorically into the searching process of numerical optimization by a new algorithm called optics inspired optimization (OIO). OIO treats the surface of the numerical function to be optimized as a reflecting surface in which each peak is assumed to reflect as a convex mirror and each valley to reflect as a concave one. Each individual is assumed to be an artificial object (or light point) that its artificially glittered ray is reflected back by the function surface, given that the surface is convex or concave, and the artificial image is formed (a candidate solution is generated within the search domain) based on the mirror equations adopted from physics of optics. Besides OIO, we introduce different variants of it, called ROIO (Rotation based OIO), and COIO (Convex combination based OIO) algorithms and conduct an extensive computational effort to find out the merit of the new algorithms. Our comparisons on benchmark test functions and a real world engineering design application (i.e., optimization of a centrifuge pump) demonstrate that the new algorithms are efficient and compete better than or similar to most of state of the art optimization algorithms with the advantage of accepting few input parameters.     

Optimal resilient power grid operation during the course of a progressing wildfire

We study a two-stage stochastic and nonlinear optimization model for operating a power grid exposed to a natural disaster. Although this approach can be generalized to any natural hazard of continuous (and not instantaneous) nature, our focus is on wildfires. We assume that an approaching wildfire impacts the power grid by reducing the transmission capacity of its overhead lines. At the time when proactive decisions have to be taken, the severity of the wildfire is not known. This introduces uncertainty. In this paper, we extend previous work by more realistically capturing this uncertainty and by strengthening the mathematical programming formulation through standard reformulation techniques. With these reformulation techniques, the resulting two-stage, convex mixed-integer quadratically constrained programming formulation can be efficiently solved using commercial quadratic programming solvers as demonstrated on a case study on a modified version of the IEEE 123-bus test system with 100 scenarios. We also quantify the uncertainties through a second case study using the following three standard metrics of two-stage stochastic optimization: the expected value of perfect information, the expected result of using the expected value solution and the value of the stochastic solution.     

Regulator problem for uncertain linear discrete-time systems with constrained control

A necessary and sufficient condition to test the robustness of a regulator of uncertain linear systems with constrained control is given. The candidate regulator for this test is that stabilizing nominal systems. An illustrative example is also given.     

Fuzzy Weirstrass theorem and convex fuzzy mappings

The convexity and continuity of fuzzy mappings are defined through a linear ordering and a metric on the set of fuzzy numbers. The local-global minimum property of real-valued convex functions is extended to convex fuzzy mappings. It is proved that a strict local minimizer of a quasiconvex fuzzy mapping is also a strict global minimizer. Characterizations for convex fuzzy mappings and quasiconvex fuzzy mappings are given. In addition, the Weirstrass theorem is extended from real-valued functions to fuzzy mappings.     

A new stereological principle for test lines in three-dimensional space

A new principle is presented to generate isotropic uniform random (IUR) test lines hitting a geometric structure in three-dimensional space (3D). The principle therefore concerns the estimation of surface area, volume, membrane thickness, etc., of arbitrary structures with piecewise smooth boundary. The principle states that a point-sampled test line on an isotropic plane through a fixed point in 3D is effectively an invariant test line in 3D. Particular attention is devoted to the stereology of particles, where an alternative to the surfactor method is obtained to estimate surface area. An interesting case arises when the particle is convex. The methods are illustrated with synthetic examples.     

A stochastic maximum principle for systems with jumps, with applications to finance

We consider a stochastic control problem with linear dynamics with jumps, convex cost criterion, and convex state constraint, in which the control enters the drift, the diffusion, and the jump coefficients. We allow these coefficients to be random, and do not impose any L^p-bounds on the control.

We obtain a stochastic maximum principle for this model that provides both necessary and sufficient conditions of optimality. This is the first version of the stochastic maximum principle that covers the consumption–investment problem in which there are jumps in the price system.     

Robust control of polytopic systems by convex optimization

Robust control synthesis of linear time-invariant SISO polytopic systems is investigated using the polynomial approach. A convex set of all stabilizing controllers for a polytopic system is given over an infinite-dimensional space. A finite-dimensional approximation of this set is obtained using the orthonormal basis functions and represented by a set of LMIs thanks to the KYP lemma. Then, an LMI based convex optimization problem for robust pole placement with sensitivity function shaping in two- and infinity-norm is proposed. The simulation results show the effectiveness of the proposed method.     

EFFECTIVE PARALLELIZATION TECHNIQUES FOR LOOP NESTS WITH NON-UNIFORM DEPENDENCES

The parallelism of loop nests with non-uniform dependences is difficult to extract and ineffectively explored by the existing parallelization schemes. In this paper, we propose new efficient techniques in extracting parallelism of loop nests with non-uniform dependences using their irregularity. By this way, current highly parallel multiprocessor systems such as multithreaded and clustering multiprocessor systems can be fully utilized. These four mechanisms are (a) parallelization part splitting, (b) partial parallelization decomposition, (c) irregular loop interchange and (d) growing pattern detection. They explore parallelisms of special parallel patterns for nested loops with non-uniform dependences. The loop transformations used in uniform loops are also applied in non-uniform dependence loops after legality tests. We apply the results of classical convex theory and detect special parallel patterns of dependence vectors. We also proposed an algorithm that combines above mechanisms to enhance parallelism. We demonstrate that our technique gives much better speedup and extracts more parallelism than the existing techniques. Thus, we are encouraged by these apparent enhancements to pursue further development.     

325MW空冷汽轮机低压缸末级动叶片Z型拉筋凸台及拉筋孔的加工

论述了 3 2 5MW空冷汽轮机低压缸第 6级 (末级 )动叶片上结构新颖、型面构成复杂的Z型拉筋凸台及凸台拉筋孔的加工工艺 ,并结合工厂的实际情况 ,分别对叶片内、背弧拉筋凸台的型线、凸台端面以及拉筋孔的加工进行了详细的分析研究 ,提出了切实可行的加工工艺方案。