On initial populations of a genetic algorithm for continuous optimization problems

Genetic algorithms are commonly used metaheuristics for global optimization, but there has been very little research done on the generation of their initial population. In this paper, we look for an answer to the question whether the initial population plays a role in the performance of genetic algorithms and if so, how it should be generated. We show with a simple example that initial populations may have an effect on the best objective function value found for several generations. Traditionally, initial populations are generated using pseudo random numbers, but there are many alternative ways. We study the properties of different point generators using four main criteria: the uniform coverage and the genetic diversity of the points as well as the speed and the usability of the generator. We use the point generators to generate initial populations for a genetic algorithm and study what effects the uniform coverage and the genetic diversity have on the convergence and on the final objective function values. For our tests, we have selected one pseudo and one quasi random sequence generator and two spatial point processes: simple sequential inhibition process and nonaligned systematic sampling. In numerical experiments, we solve a set of 52 continuous test functions from 16 different function families, and analyze and discuss the results.     

Heuristic for a new multiobjective scheduling problem

We consider a telecommunication problem in which the objective is to schedule data transmission to be as fast and as cheap as possible. The main characteristic and restriction in solving this multiobjective optimization problem is the very limited computational capacity available. We describe a simple but efficient local search heuristic to solve this problem and provide some encouraging numerical test results. They demonstrate that we can develop a computationally inexpensive heuristic without sacrificing too much in the solution quality.     

On generalized trade-off directions in nonconvex multiobjective optimization

Trade-off information related to Pareto optimal solutions is important in multiobjective optimization problems with conflicting objectives. Recently, the concept of trade-off directions has been introduced for convex problems. These trade-offs are characterized with the help of tangent cones. Generalized trade-off directions for nonconvex problems can be defined by replacing convex tangent cones with nonconvex contingent cones. Here we study how the convex concepts and results can be generalized into a nonconvex case. Giving up convexity naturally means that we need local instead of global analysis. Received: December 2000 / Accepted: October 2001?Published online February 14, 2002     

Constructing a Pareto front approximation for decision making

An approach to constructing a Pareto front approximation to computationally expensive multiobjective optimization problems is developed. The approximation is constructed as a sub-complex of a Delaunay triangulation of a finite set of Pareto optimal outcomes to the problem. The approach is based on the concept of inherent nondominance. Rules for checking the inherent nondominance of complexes are developed and applying the rules is demonstrated with examples. The quality of the approximation is quantified with error estimates. Due to its properties, the Pareto front approximation works as a surrogate to the original problem for decision making with interactive methods.     

On constrained hemivariational inequalities and their approximation

We prove the existence of a solution of a constrained hemivariational inequality, and, develop a fully discrete approximation of it. The relation between the constrained hemivariational inequality and a problem of finding substationary points of the corresponding potential function is also studied.     

Atmospheric pressure chemical vapour synthesis of silicon–carbon nanoceramics from hexamethyldisilane in high temperature aerosol reactor

Silicon–carbon nanoceramics have been synthesised from hexamethyldisilane (HMDS) by the atmospheric pressure chemical vapour synthesis (APCVS). Direct aerosol phase synthesis enables continuous production of high purity materials in one-stage process. The particle formation is based on the decomposition of the precursor in a high temperature reactor. Reaction of the gas phase species leads to homogeneous nucleation and formation of the nanoparticles with a narrow size distribution (geometric mean diameter range of particle number size distribution 160–200 nm with 1.5–1.6 geometric standard deviation at reaction temperatures 800–1200 °C). A systematic investigation of the influence of the process temperature on the powder characteristics, including the particle size, crystallinity, chemical structure, surface and bulk composition and surface morphology, was carried out. At the reactor temperature of 800 °C, the synthesised nanoparticles were amorphous preceramics containing mostly SiC₄, Si–CH₂–Si and Si–H units. The composition of the powder turned towards nanocrystalline 3C–SiC (crystal size under 2 nm) when the reaction temperature was increased to 1200 °C. The reaction temperature appeared to be a key parameter controlling the structure and properties of the synthesised powders.     

Aerosol characterization and lung deposition of synthesized TiO2 nanoparticles for murine inhalation studies

This study presents a novel exposure protocol for synthesized nanoparticles (NPs). NPs were synthesized in gas phase by thermal decomposition of metal alkoxide vapors in a laminar flow reactor. The exposure protocol was used to estimate the deposition fraction of titanium dioxide (TiO₂) NPs to mice lung. The experiments were conducted at aerosol mass concentrations of 0.8, 7.2, 10.0, and 28.5 mg m^?3. The means of aerosol geometric mobility diameter and aerodynamic diameter were 80 and 124 nm, and the geometric standard deviations were 1.8 and 1.7, respectively. The effective density of the particles was approximately from 1.5 to 1.7 g cm^?3. Particle concentration varied from 4 × 10⁵ cm^?3 at mass concentrations of 0.8 mg m^?3 to 12 × 10⁶ cm^?3 at 28.5 mg m^?3. Particle phase structures were 74% of anatase and 26% of brookite with respective crystallite sized of 41 and 6 nm. The brookite crystallites were approximately 100 times the size of the anatase crystallites. The TiO₂ particles were porous and highly agglomerated, with a mean primary particle size of 21 nm. The specific surface area of TiO₂ powder was 61 m² g^?1. We defined mice respiratory minute volume (RMV) value during exposure to TiO₂ aerosol. Both TiO₂ particulate matter and gaseous by-products affected respiratory parameters. The RMV values were used to quantify the deposition fraction of TiO₂ matter by using two different methods. According to individual samples, the deposition fraction was 8% on an average, and when defined from aerosol mass concentration series, it was 7%. These results show that the exposure protocol can be used to study toxicological effects of synthesized NPs.     

Using box indices in supporting comparison in multiobjective optimization

Because of the conflicting nature of criteria or objectives, solving a multiobjective optimization problem typically requires interaction with a decision maker who can specify preference information related to the objectives in the problem in question. Due to the difficulties of dealing with multiple objectives, the way information is presented plays a very important role. Questions posed to the decision maker must be simple enough and information shown must be easy to understand. For this purpose, visualization and graphical representations can be useful and constitute one of the main tools used in the literature. In this paper, we propose to use box indices to represent information related to different solution alternatives of multiobjective optimization problems involving at least three objectives. Box indices are an intelligible and easy to handle way to represent data. They are based on evaluating the solutions in a natural and rough enough scale in order to let the decision maker easily recognize the main characteristics of a solution at a glance and to facilitate comparison of two or more solutions in an easily understandable way.     

A comment on the early onset of semi-inclusive scaling in proton-proton collisions

The present experimental evidence for the scaling of multiplicity distributions predicted by Koba, Nielsen and Olesen is examined critically. Our results indicate that the approximate scaling observed experimentally is not necessarily connected with an “early” approach to the asymptotic limit. Some simple models are shown to predict an extremely slow approach to scaling. The possibility of distinguishing between “early” scaling ang the “quasi-scaling” exhibited by these models with experiments at ISR is discussed.