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Earlier we talked about objects that get passed by reference We said that when a message is called on a referenced object, the message is sent back to the server and is called against the original object This is fundamentally true What actually happens under the covers is that an ID for the referenced object, along with the message (say_hello), is sent back to the server The server then uses that ID to find the original object in the ObjectSpace and to call the message on it

(2.1.27) (2.1.28) (2.1.29) (2.1.30) (2.1.31)

\7 H=O \7. (Ep(r)E) = 0 = \7. [(E + (Er(r) - l)E) E]

](r) = -iWE(Er(r) - 1) E(r)

In this section, we use traditional one-point crossover method That is, we nd a certain point of the array and swap the part before and after the cross point to generate two new solutions However, because the number of nodes the route may pass through is not xed, it is dif cult to determine a xed crossover point In Papavassiliou et al [35] the crossover point is determined by (A + B)/4 , where A and B are the numbers of nodes that the two routes will pass through, respectively, and the operator is a rounding function, eg if it is before the crossover operation, there are two routes: [1 2 3 4 5 0 0 0 0 0] and [6 7 8 0 0 0 0 0 0 0].

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pj(r) =

~\7' ](r) =

-E\7 [(Er(r) - 1) E(r)]

(2.1.32)

We can make use of the scalar Green's function eiklr-r' I g(r, r') = 4 Jrr-r 1- -'I The solutions of scalar and vector potentials are

According to this procedure ( (A + B) /4 = 2), after the crossover we get: [1 2 8 0 0 0 0 0 0 0] and [6 7 3 4 5 0 0 0 0 0] Note that only part of the population will experience crossover operation; this rate is called the crossover rate The mutation operation randomly chooses a solution in the population and then slightly change it to generate a new solution In this way, there is a chance to nd better solution that cannot be found by only crossover operation In the algorithm, four mutation operators are used: (1) randomly delete a node from a route; (2) randomly add a node into a route; (3) randomly delete two nodes from a route; and (4) randomly add two nodes into a route Only part of population will experience the mutation operation (this is characterized by mutation rate).

(2.1.33)

The method of looking up an object in the ObjectSpace using the reference ID is called ID conversion DRb ships with three built-in ID converters: DRb::DRbIdConv, DRb::TimerIdConv, and DRb::GWIdConv It is also possible to build your own ID converter, as you will see a little later Depending on which ID converter you build, it can change how objects are looked up in the ObjectSpace, as well as how, and when, those objects get garbage-collected

A(r) =

if" ( - ) ' '

dr' g(r, r')fL](r')

(2.1.34) (2.1.35)

In order to enhance the local searching ability, those copies of the best solution of each generation are all treated by mutation operator In this way, the GA may nd a better solution that is close to the best solution of each generation In the repair operation, during crossover and mutation operation, illegal representation of route may be generated because duplicated elements (nodes) may appear in the same route In the algorithm, those duplicated nodes that would bring high cost to the route are deleted For example, there may be a route like [1 2 3 4 5 3 7 0 0 0], where node 3 is duplicated We can evaluate the cost of strings (2 3 4), (5 3 7) and the delay of strings (2 3 4), (5 3 7).

(- -')

Pi r,r -(r')

(- -')

(2.1.36)

E(r) = Enc(r)

If the weighted cost of string (2 3 4) is less than (5 3 7), node 3 in (5 3 7) will be discarded The computation ef ciency can be improved if after a minimum number of trails (MinTrails), when the algorithm has found a feasible solution and has made no more improvement for a speci c period of time, the computation process is stopped In the algorithm, the improvement is presented by the average cost change rate of the best solution.

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