SCIENCE CHINA Information Sciences, Volume 60, Issue 11: 112202(2017) https://doi.org/10.1007/s11432-016-9024-y

## A large-scale multi-objective flights conflict avoidance approach supporting 4D trajectory operation

• AcceptedJan 20, 2017
• PublishedSep 1, 2017
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### Abstract

Recently, the long-term conflict avoidance approaches based on large-scale flights scheduling have attracted much attention due to their ability to provide solutions from a global point of view. However, current approaches which focus only on a single objective with the aim of minimizing the total delay and the number of conflicts, cannot provide controllers with variety of optional solutions, representing different tradeoffs. Furthermore, the flight track error is often overlooked in the current research. Therefore, in order to make the model more realistic, in this paper, we formulate the long-term conflict avoidance problem as a multi-objective optimization problem, which minimizes the total delay and reduces the number of conflicts simultaneously. As a complex air route network needs to accommodate thousands of flights, the problem is a large-scale combinatorial optimization problem with tightly coupled variables, which make the problem difficult to deal with. Hence, in order to further improve the search capability of the solution algorithm, a cooperative co-evolution (CC) algorithm is also introduced to divide the complex problem into several low dimensional sub-problems which are easier to solve. Moreover, a dynamic grouping strategy based on the conflict detection is proposed to improve the optimization efficiency and to avoid premature convergence. The well-known multi-objective evolutionary algorithm based on decomposition (MOEA/D) is then employed to tackle each sub-problem. Computational results using real traffic data from the Chinese air route network demonstrate that the proposed approach obtained better non-dominated solutions in a more effective manner than the existing approaches, including the multi-objective genetic algorithm (MOGA), NSGAII, and MOEA/D. The results also show that our approach provided satisfactory solutions for controllers from a practical point of view.

### References

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• Figure 1

• Figure 2

• Figure 3

(Color online) (a) The relationship between the number of flights and the conflict situation in every two hours; (b) the relationship between the number of flights and the conflict situation as the considered time accumulates.

• Figure 4

•

Algorithm 1 The framework of the proposed method

Initialize the population $g=0$.

//Main loop:

while $g$ ( < ) maxgen do

Evaluate all individuals in the population.

Compute the non-dominated solutions.

//cooperative co-evolution.

Divide the decision variables into groups based on the dynamic grouping strategy.

Decision variables in each group generate its subpopulation.

for each subpopulation

Use the MOEA/D framework with a genetic algorithm.

Evaluate all individuals in the subpopulation, and compute the non-dominated solutions.

end for

Obtain the non-dominated solutions.

(g = g + 1.)

end while

•

Algorithm 2 Algorithmic flow of MOEA/D with GA

Require:

(1) A stopping criterion;

(2) $np$: the number of the sub-problems;

(3) An uniform spread of n weight vectors: ${\lambda~^1},~\ldots,~{\lambda~^{np}}$;

(4) $T$: the number of the weight vectors in the neighborhood of each weight vector;

Output:Approximation to the PF and PS.

Procedure:

Step 1 Initialization:

Step 1.1 Compute the Euclidean distances between the weight vectors and work out the $T$ closest weight vectors to each weight vector. For each (i = 1, …, np), set (B(i) = i_1 …, i_T ), where (λ ^i_1 …, λ ^i_T) are the $T$ closest weight vectors to (λ ^i).

Step 1.2 Generate an initial population (x¹ …, x^np). Calculate the fitness values of the population.

Step 1.3 Initialize (z = (z_1 …, z_m), where (z_j =

min _1 łe i łe nf_jx^i).

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