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Tong Sheung Yuen
Since we are in the process of updating the Lighter𠏋 addresses and choosing reunion site, I thought it might be interesting to find out where all the Lighters are and at the same time pick out a reunion site assuming the only issue is the aggregate travel distance. To do this, I take the address list given to us by CC Luk at the Vancouver Reunion and count the number of members in each of the major geographical locations. For convenience, I divide our world into eight centers, Hong Kong , Sidney, Tokyo, Chicago, San Francisco, Vancouver, Toronto and London. Every Lighter is assigned to one of the centers nearest to where he/she lives. Every one in the States east of the Rockies is assigned to Chicago and every one in Canada east of the Canadian Rockies is assigned to Toranto. Every one in Europe is assigned to London. The result is shown in Table 1.
Table 1 Lighter Distribution
| Center | Number of Lighters |
| Hong Kong | 81 |
| Sidney | 6 |
| Japan | 3 |
| Chicago | 42 |
| San Francisco | 32 |
| Vancouver | 5 |
| Toronto | 17 |
| London | 2 |
| Total: | 188 |
These numbers are not precise since many of us had moved since 1994. Some of us might have moved more than once. Nevertheless, for our purpose, this should be adequate. Interestingly, if we sum the Lighters in the top three and the bottom five regions together, we have 90 members in the East and 98 members in the West. Almost right down the middle.
It appears then the centroid of the Lighters is somewhere in the middle of the Pacific ocean. Being an engineer, I want to determine this location more precisely. Perhaps, there is an island in the middle of the ocean suitable as a permanent reunion site for us. What do I mean by "centroid" In this discussion, it is the location where the average distance between this point and all the Lighters is less than any other location on this earth.
Now, in all likelihood, there is no airline going to this location and there may be no facility in this location for our Reunion. This is just an academic exercise. But, I am curious. If you are a teacher or college professor, this may be an interesting exercise for your students.
Table 2 Latitude and Longitude of Lighter Centers
| Center | Latitude | Longitude |
| Hong Kong | 22.2 N | 114.2 E |
| Sidney | 33.87 S | 151.2 E |
| Japan | 35.75 N | 139.75 E |
| Chicago | 41.87 N | 87.64 W |
| San Francisco | 37.78 N | 122.41 W |
| Vancouver | 49.32 N | 123.08 E |
| Toronto | 43.65 N | 79.38 W |
| London | 51.5 N | 0 |
To carry out this optimization, the latitude and longitude of the eight centers will be needed. They are given in Table 2. Connie, my wife, always said that my books, which take up more shelve space than her clothing, are useless. She is only 99% right. These latitudes and longitudes come from a 1986 ALMANAC on one of the shelves.
The actual minization process is a bit tedious because the distance between two points on a sphere is a great circle and not a straight line and there are a multitude of local optimum. I shall not bore you with the details except to say that a genetic algorithm (GA) on my PC is used to do the optimization. GA seems to be a powerful technique. I am a novice at this but I am surprise at what it can do and how simple it appears to be. If anyone of you is working in this area and care to share your knowledge, I am listening.
The result is a little surprising. The centroid is actually very near Vancouver at 49 N and 126.22 W. It is only 123 miles west of Vancouver. The average distance travel for each of us is around 3333 nautical miles. (A mile is 1760 yards and a nautical mile is 2000 yards.) As we all know, Vancouver, BC was our 35th reunion site. Gina had picked the optimum site for our class reunion. The actual distance travelled by our classmates to this site is shown in Table 3.
Table 3 Distance to the Centroid
| Center | Distance, nm |
| Hong Kong | 5439 |
| Sidney | 6639 |
| Japan | 3963 |
| Chicago | 1661 |
| San Francisco | 712 |
| Vancouver | 123 |
| Toronto | 1933 |
| London | 4157 |
I would be remissed if I do not tell you the average travel distance involved had Hong Kong or San Franciso been the chosen site of our reunion. Turns out the difference from the optimum is quite small for either site. For Hong Kong, the average distance is 3500 nautical miles and for San Franciscon the distance is 3464 nautical miles.
Cheers. See you in Toronto.
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