This paper investigates the effect of adding three extensions to Central Force Optimization when it is used as the Global Search and Optimization method for the design and optimization of 6-elementYagi-Uda arrays. Tho...This paper investigates the effect of adding three extensions to Central Force Optimization when it is used as the Global Search and Optimization method for the design and optimization of 6-elementYagi-Uda arrays. Those exten</span><span><span style="font-family:Verdana;">sions are </span><i><span style="font-family:Verdana;">Negative</span></i> <i><span style="font-family:Verdana;">Gravity</span></i><span style="font-family:Verdana;">, </span><i><span style="font-family:Verdana;">Elitism</span></i><span style="font-family:Verdana;">, and </span><i><span style="font-family:Verdana;">Dynamic</span></i> <i><span style="font-family:Verdana;">Threshold</span></i> <i><span style="font-family:Verdana;">Optimization</span></i><span style="font-family:Verdana;">. T</span></span><span style="font-family:Verdana;">he basic CFO heuristic does not include any of these, but adding them substan</span><span style="font-family:Verdana;">tially improves the algorithm’s performance. This paper extends the work r</span><span style="font-family:Verdana;">eported in a previous paper that considered only negative gravity and which </span><span style="font-family:Verdana;">showed a significant performance improvement over a range of optimized a</span><span style="font-family:Verdana;">rrays. Still better results are obtained by adding to the mix </span><i><span style="font-family:Verdana;">Elitism</span></i><span style="font-family:Verdana;"> and </span><i><span style="font-family:Verdana;">DTO</span></i><span style="font-family:Verdana;">. An overall improvement in best fitness of 19.16% is achieved by doing so. While the work reported here was limited to the design/optimization of 6-</span></span></span><span><span><span style="font-family:""> </span></span></span><span><span><span style="font-family:""><span style="font-family:Verdana;">element Yagis, the reasonable inference based on these data is that any antenna design/optimization problem, indeed any Global Search and Optimiza</span><span style="font-family:Verdana;">tion problem, antenna or not, utilizing Central Force Optimization as the Gl</span><span style="font-family:Verdana;">obal Search and Optimization engine will benefit by including all three extensions, probably substantially.展开更多
A six-element Yagi-Uda array is optimally designed using Central Force Optimization (CFO) with a small amount of pseudo randomly injected negative gravity. CFO is a simple, deterministic metaheuristic analogizing grav...A six-element Yagi-Uda array is optimally designed using Central Force Optimization (CFO) with a small amount of pseudo randomly injected negative gravity. CFO is a simple, deterministic metaheuristic analogizing gravitational kinematics (motion of masses under the influence of gravity). It has been very effective in addressing a wide range of antenna and other problems and normally employs only positive gravity. With positive gravity the six element CFO-designed Yagi array described here exhibits excellent performance with respect to the objectives of impedance bandwidth and forward gain. This paper addresses the question of what happens when a small amount of negative gravity is injected into the CFO algorithm. Does doing so have any effect, beneficial, negative or neutral? In this particular case negative gravity improves CFO’s exploration and creates a region of optimality containing many designs that perform about as well as or better than the array discovered with only positive gravity. Without some negative gravity these array configurations are overlooked. This Yagi-Uda array design example suggests that antennas optimized or designed using deterministic CFO may well benefit by including a small amount of negative gravity, and that the negative gravity approach merits further study.展开更多
Exact solution of the nonlinear boundary value problem for the basic equation and boundary condition of circular membrane under central force was obtained by using new simple methods. The existence and uniqueness of t...Exact solution of the nonlinear boundary value problem for the basic equation and boundary condition of circular membrane under central force was obtained by using new simple methods. The existence and uniqueness of the solution were discussed by using of modern immovable point theorems. Although specific problem is treated, the basic principles of the methods can be applied to a considerable variety of nonlinear problems.展开更多
This note describes optimally matching the seminal Fano Load using Central Force Optimization with Negative Gravity.This approach improves the best fitness by more than eighteen percent and suggests that some measure ...This note describes optimally matching the seminal Fano Load using Central Force Optimization with Negative Gravity.This approach improves the best fitness by more than eighteen percent and suggests that some measure of Negative Gravity should be used in all CFO runs.CFO is a deterministic Global Search and Optimization metaheuristic based on an analogy to gravitational kinematics,the motion of bodies moving under the influence of gravity.Positive gravity causes objects to move towards each other,whereas negative gravity causes them to fly apart.A small amount of negative gravity in CFO improves the algorithm’s exploration of the decision space by sampling regions that have been under-sampled or perhaps not sampled at all.The Fano Load problem illustrates this effect.While the possibility of Negative Gravity was mentioned in the original CFO paper,it was not used until recently when it was injected into optimization runs for Yagi-Uda antenna arrays.The results were compelling and led to the Fano Load problem being revisited.展开更多
The central government's regulations on the sale and purchase of horses in the Land within the Passes(Guanzhong關中)and their entry and exit from the Pass in the“Ordinances on Fords and Passes”(Jinguan ling津關...The central government's regulations on the sale and purchase of horses in the Land within the Passes(Guanzhong關中)and their entry and exit from the Pass in the“Ordinances on Fords and Passes”(Jinguan ling津關令)are important sources for understanding the horse policy of the early Western Han Dynasty and recognizing the relationship between the dynasty and the counties and vassal states outside the Pass.By examining the ordinances on the purchase and sale of horses,it is clear that the Han state strictly controlled horses,restricted private ownership of horses,and prohibited horses from exiting the Pass.However,some"privileged classes"still had the right to purchase horses from the Han government and take them out of the Pass after following some legal procedures,but this privilege was entirely dependent on the imperial power.Behind these regulations,it reflects the legislative thought of the supremacy of imperial power,"power over law"(“權大于法”),and the fundamental purpose of consolidating centralized power,weakening the strength of vassal states,and"strengthening the central forces while weakening the local ones"(“强幹弱枝”).展开更多
文摘This paper investigates the effect of adding three extensions to Central Force Optimization when it is used as the Global Search and Optimization method for the design and optimization of 6-elementYagi-Uda arrays. Those exten</span><span><span style="font-family:Verdana;">sions are </span><i><span style="font-family:Verdana;">Negative</span></i> <i><span style="font-family:Verdana;">Gravity</span></i><span style="font-family:Verdana;">, </span><i><span style="font-family:Verdana;">Elitism</span></i><span style="font-family:Verdana;">, and </span><i><span style="font-family:Verdana;">Dynamic</span></i> <i><span style="font-family:Verdana;">Threshold</span></i> <i><span style="font-family:Verdana;">Optimization</span></i><span style="font-family:Verdana;">. T</span></span><span style="font-family:Verdana;">he basic CFO heuristic does not include any of these, but adding them substan</span><span style="font-family:Verdana;">tially improves the algorithm’s performance. This paper extends the work r</span><span style="font-family:Verdana;">eported in a previous paper that considered only negative gravity and which </span><span style="font-family:Verdana;">showed a significant performance improvement over a range of optimized a</span><span style="font-family:Verdana;">rrays. Still better results are obtained by adding to the mix </span><i><span style="font-family:Verdana;">Elitism</span></i><span style="font-family:Verdana;"> and </span><i><span style="font-family:Verdana;">DTO</span></i><span style="font-family:Verdana;">. An overall improvement in best fitness of 19.16% is achieved by doing so. While the work reported here was limited to the design/optimization of 6-</span></span></span><span><span><span style="font-family:""> </span></span></span><span><span><span style="font-family:""><span style="font-family:Verdana;">element Yagis, the reasonable inference based on these data is that any antenna design/optimization problem, indeed any Global Search and Optimiza</span><span style="font-family:Verdana;">tion problem, antenna or not, utilizing Central Force Optimization as the Gl</span><span style="font-family:Verdana;">obal Search and Optimization engine will benefit by including all three extensions, probably substantially.
文摘A six-element Yagi-Uda array is optimally designed using Central Force Optimization (CFO) with a small amount of pseudo randomly injected negative gravity. CFO is a simple, deterministic metaheuristic analogizing gravitational kinematics (motion of masses under the influence of gravity). It has been very effective in addressing a wide range of antenna and other problems and normally employs only positive gravity. With positive gravity the six element CFO-designed Yagi array described here exhibits excellent performance with respect to the objectives of impedance bandwidth and forward gain. This paper addresses the question of what happens when a small amount of negative gravity is injected into the CFO algorithm. Does doing so have any effect, beneficial, negative or neutral? In this particular case negative gravity improves CFO’s exploration and creates a region of optimality containing many designs that perform about as well as or better than the array discovered with only positive gravity. Without some negative gravity these array configurations are overlooked. This Yagi-Uda array design example suggests that antennas optimized or designed using deterministic CFO may well benefit by including a small amount of negative gravity, and that the negative gravity approach merits further study.
文摘Exact solution of the nonlinear boundary value problem for the basic equation and boundary condition of circular membrane under central force was obtained by using new simple methods. The existence and uniqueness of the solution were discussed by using of modern immovable point theorems. Although specific problem is treated, the basic principles of the methods can be applied to a considerable variety of nonlinear problems.
文摘This note describes optimally matching the seminal Fano Load using Central Force Optimization with Negative Gravity.This approach improves the best fitness by more than eighteen percent and suggests that some measure of Negative Gravity should be used in all CFO runs.CFO is a deterministic Global Search and Optimization metaheuristic based on an analogy to gravitational kinematics,the motion of bodies moving under the influence of gravity.Positive gravity causes objects to move towards each other,whereas negative gravity causes them to fly apart.A small amount of negative gravity in CFO improves the algorithm’s exploration of the decision space by sampling regions that have been under-sampled or perhaps not sampled at all.The Fano Load problem illustrates this effect.While the possibility of Negative Gravity was mentioned in the original CFO paper,it was not used until recently when it was injected into optimization runs for Yagi-Uda antenna arrays.The results were compelling and led to the Fano Load problem being revisited.
文摘The central government's regulations on the sale and purchase of horses in the Land within the Passes(Guanzhong關中)and their entry and exit from the Pass in the“Ordinances on Fords and Passes”(Jinguan ling津關令)are important sources for understanding the horse policy of the early Western Han Dynasty and recognizing the relationship between the dynasty and the counties and vassal states outside the Pass.By examining the ordinances on the purchase and sale of horses,it is clear that the Han state strictly controlled horses,restricted private ownership of horses,and prohibited horses from exiting the Pass.However,some"privileged classes"still had the right to purchase horses from the Han government and take them out of the Pass after following some legal procedures,but this privilege was entirely dependent on the imperial power.Behind these regulations,it reflects the legislative thought of the supremacy of imperial power,"power over law"(“權大于法”),and the fundamental purpose of consolidating centralized power,weakening the strength of vassal states,and"strengthening the central forces while weakening the local ones"(“强幹弱枝”).
