a multi-objective bisexual reproduction genetic algorithm for ...

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remembers the N recent moves. Any new move that is already in the tabu list is
avoided, that is, a tabu. This approach prevents the recently tried movements and
prevents the search from cycling round the local optimal area thus driving the search
towards a different direction in the search space, resulting in better opportunity
towards global optimal.
The decision to move to a transformed solution state is usually based on the
steepest descent or mildest ascent in the objective function value. With this strategy, a
heuristic accepts a marginal and temporary deterioration in its objective function
value in exchange for opportunities to escape from a local optimal and move towards
the global optimal, as illustrated in Figure 2-3. Figure 2-5 presents the tabu search
algorithm.
1. Generate an initially random but feasible solution s.
2. Repeat:
i. Attempt to find an improved feasible solution s' with the objective function
value z(s'), avoid using moves already stored in the tabu list.
ii. Compute the moves from s to s’.
iii. Update tabu list by adding the latest move so that it is set as a tabu for some subsequent
moves.
iv. If z(s') < z(s) + (mildest ascent tolerance) then
perform exchanges: s := s', z(s) := z(s')
End if
Until (no improved solution is found) or (stopping criteria is met)
FIGURE 2-5 Tabu search algorithm
Result z(s') is the best estimated minimum, it does not guarantee to find the
global minimum but stands a better chance as compared to gradient descent approach.
2.2.4.3 Genetic Algorithms
The idea of genetic algorithms is based on the evolutionary principle developed
by Darwin [6]. A “population” of feasible timetables is maintained. The “fittest”
timetables are selected to form the basis of the next iteration, or “generation”, thus
improving the overall fitness whilst maintaining diversity.