Aerospace and Electronic Systems Magazine September 2016 - 51

Fu, Zhang, and Yu
position where UAV starts running collision avoidance function, supposing (0, 0) is located in the bottom left corner of
the grid array. The grid is then numbered in a positive direction on the x-axis (horizontally to the right) and in a positive
direction on the z-axis (vertically going up).
C

Step 2: Initialize BBO parameters, covering the total habitat size n, maximum generation count Tmax, number of species in each habitat k, maximum mutation probability mmax,
maximum immigration rate I, maximum emigration rate E,
elitism number of best habitats to keep from one generation
to the next D. Randomly initialize a habitat of k waypoints
G = [G1, G2, ..., Gk] in the longitudinal plane under the flight
range. G1 and Gk represent the pre-defined start point and
goal point, respectively. A set G can produce a candidate trajectory. Initialize a set of habitat S = [S1, S2, ..., Sn], and each
individual corresponds to a potential trajectory that connects
the start to the goal one.
Step 3: Calculate the cost of each candidate trajectory with
respect to (11), (12), and (13). Sort the habitats from the best
performance to the worst one. Select the first D number of
solution as elite habitats.
Step 4: Compute the immigration rate lk and emigration rate
mk for each path according to (15) and (16). Initialize the
solution probability Pi. Modify the non-elite solution probabilistically with the hybrid immigration and emigration as
shown in Figure 17. Re-map the fitness to the series of habitats. Compute the new probabilities for each solution.
Step 5: Calculate the mutation rate mi for each trajectory.
Sort the solution following the probability Pi. Mutate only
the worst half of the solution as described in Figure 18. Recalculate the cost of path.
Step 6: Replace the habitats with their new versions. Ensure each individual is legal with respect to the constraints as
mentioned in the section "Problem Formulation". Calculate
the cost of each habitats and order from the best to the worst.
Replace the worst solution with the previous generation's
elite.

given by Mr. Phil Cole and Mr. Puthy Soupin at Marinvent Inc.
during the NSERC project period. The authors would also like
to express their sincere gratitude to the Associate Editor and the
anonymous reviewers for their insightful comments and suggestions which helped significantly to improve the quality of the article in both technical and presentation aspects. Furthermore, the
authors would like to thank Mr. Sean Zhang for the proofreading
and comments that helped to improve the manuscripts presentation significantly.

REFERENCES
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Step 7: End the generation when Tmax is reached. Output the
optimal solution with cost value.
Step 8: Characterize the optimal solution by the UAV constraints following the concept of differential flatness and calculate the feasible trajectory.

[10]

[11]

ACKNOWLEDGMENTS
The authors would like to acknowledge the financial support from
the Natural Sciences and Engineering Research Council of Canada (NSERC) through an Engage Project Grant with industrial supporting partner of Marinvent Inc. for initializing this research, as
well as NSFC through #61573282, SPNSF through #2015JZ020,
and the Fundamental Research Funds for the Central Universities through #531107040965 for the work reported in this article. The authors would like to thank the strong support and help
SEPTEMBER 2016

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IEEE A&E SYSTEMS MAGAZINE

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