Variable Number Of Dimensions Research Articles

Multi-Objective PSO with Variable Number of Dimensions for Space Robot Path Optimization

This paper aims to solve the space robot pathfinding problem, formulated as a multi-objective (MO) optimization problem with a variable number of dimensions (VND). This formulation enables the search and comparison of potential solutions with different model complexities within a single optimization run. A novel VND MO algorithm based on the well-known particle swarm optimization (PSO) algorithm is introduced and thoroughly described in this paper. The novel VNDMOPSO algorithm is validated on a set of 21 benchmark problems with different dimensionality settings and compared with two other state-of-the-art VND MO algorithms. Then, it is applied to solve five different instances of the space robot pathfinding problem formulated as a VND MO problem where two objectives are considered: (1) the minimal distance of the selected path, and (2) the minimal energy cost (expressed as the number of turning points). VNDMOPSO shows at least comparable or better convergence on the benchmark problems and significantly better convergence properties on the VND pathfinding problems compared with other VND MO algorithms.

Another evolution of generalized differential evolution: variable number of dimensions

The article proposes a multi-objective optimization method called Generalized Differential Evolution (GDE3) for a Variable Number of Dimensions (VND). The well-known generalized differential evolution is adapted to handle problems where the number of decision space variables is not a priori known. The performance of the method is assessed on a set of benchmark problems based on standard multi-objective test cases modified to depend on the number of decision space variables. Experimental results include a study of the setting of controlling parameters and a comparison with the state-of-the-art Variable-Length GDE3 (VLGDE3) algorithm. Finally, the novel approach is compared to the standard approach in a linear antenna array design problem.

Microwave Imaging Using Optimization With Variable Number of Dimensions

The solution to the microwave imaging problem is often provided by systems that employ global optimization methods that search for material properties of the selected investigation domain. A novel method for the solution of the microwave imaging problem based on the optimization with a variable number of dimensions is introduced in this article. Shapes of scatterers with an arbitrary complexity can be coded in the form of decision space vectors with varying sizes. The variable number of dimensions formulation of the problem is compared to a conventional approach that uses a regular grid of sub-domains and the optimization algorithm then searches for material properties of individual sub-regions. The influence of the investigation domain parameters like the signal to noise ratio of the measured field, or scatterer's material properties on the stability of the method is discussed in the paper.

PCB Decoupling Optimization With Variable Number of Capacitors

The decoupling of modern printed circuit boards introduces a very complex task. Powerful stochastic optimizers are usually used to determine values and positions of decoupling capacitors on the board. The number of capacitors used has to be determined a priori by the user which brings problems with convergence of the optimization process or can lead to a waste of resources when the noises are to be attenuated to a certain level. In this paper, an approach based on the combination of time-domain contour integral method and optimization with variable number of dimensions is introduced. The optimizer works with models having variable dimensions and searches for the optimal one. The approach is tested on two example power circuit boards with various noise attenuation limits and constraints on capacitor positions and values.

Particle swarm optimization for problems with variable number of dimensions

ABSTRACTSome real-life optimization problems, apart from dependence on the combination of state variables, also show dependence on the complexity of the model describing the problem. Changing model complexity implies changing the number of decision space dimensions.A new method called Particle Swarm Optimization for Variable Number of Dimensions is developed here. The well-known particle swarm optimization procedure is modified to handle spaces with a variable number of dimensions within a single run. Some well-known benchmark problems are modified to depend on the number of dimensions. Novel performance metrics are defined in the article to evaluate convergence properties of the method. Some recommendations for setting the optimization are made according to results of the method on the proposed benchmark test suite. The method is compared with conventional swarm strategies able to solve problems with variable number of dimensions.

Dynamics of Adaptation and Evolutionary Branching

We present a formal framework for modeling evolutionary dynamics with special emphasis on the generation of diversity through branching of the evolutionary tree. Fitness is defined as the long term growth rate which is influenced by the biotic environment leading to an ever-changing adaptive landscape. Evolution can be described as a dynamics in a space with variable number of dimensions corresponding to the number of different types present. The dynamics within a subspace is governed by the local fitness gradient. Entering a higher dimensional subspace is possible only at a particular type of attractors where the population undergoes evolutionary branching.

Algorithm AS 39: Arrays with a Variable Number of Dimensions

Algorithm AS 39: Arrays with a Variable Number of Dimensions

Effect of number of variable dimensions on reversal and nonreversal shifts.

Effect of number of variable dimensions on reversal and nonreversal shifts.

Produktiviteitsverhoging op grote schaal: Maatnormalisatie van kleding

SummaryThe article contains a short review of a campaign, undertaken in Holland during the last 12 years to arrive at standardized sizes for women's and men's clothing. The first campaign was undertaken by a department store, the second one by the clothing industry.The operational value of a sizing system depends on the value of three parameters which are not, of course, independent of each other: coverage of the system, number of sizes and average cost of alterations.The basis of the standardization is furnished by measuring a sample of the population of customers and by measuring the fitting‐tolerances of clothing.The proposed sizing systems are:a. Ladies' dresses — a two‐dimensional system based on waist girth and length of back, containing 14 sizes and giving a coverage of 90%.b. Men's suits — a system with a variable number of dimensions (2 to 4). The identification dimensions are waist girth, length of leg, hip girth and inclination of shoulder. The proposed system gives a coverage of 90% with 34 sizes. Both systems have been experimentally verified.Stress is laid on the necessity of an international sizing standardization.