A New Reactive Algorithm For Gate Assignment Problem In Airport Ground Operations Management M.M. Yenisey, T. Özcan (Istanbul Üniv.) B. Yağmahan (Uludağ Üniv.) A. Aktel (Turkish Inst. Of Man. Sci.)

Gate Assignment Problem is an important research area in airport management. Why?

The most common modelling approach is 0-1 Integer Linear Programming. We can see graph theory approaches as well. i.e. Flow network, clique partitioning And stochastic features are embedded into models in some studies.

The model can be formulated single or multi objective form The model can be formulated single or multi objective form. Generally, passenger walking distance/time, luggage/cargo load/unload time, no of assigned/unassigned gates, deviation from planned scedule are defined as objectives.

Solution approaches are B&B, Dynamic Programming, simplex method, Lagrangian relaxation The problem becomes NP-hard rapidly as the size increases. Hence, exact solution approaches can be unsufficient.

Heuristic and metaheuristic approaches are used Heuristic and metaheuristic approaches are used. Tabu search, greedy algorithm, GA, SA, Bee Colony Optimization, and/or hybrid approaches made of different heuristics or metaheuristics

What we did. We developed a reactive algorithm based on GA What we did? We developed a reactive algorithm based on GA. This algorithm is originally developed for the hybrid flowshop scheduling problem. We basically used the study of Ding et al (2005).

Min 𝑖=1 𝑛 𝑦 i,m+1 (1) Min 𝑖=1 𝑛 𝑗=1 𝑛 𝑘=1 𝑚+1 𝑙=1 𝑚+1 𝑓 i,j wk,l yi,k yj,l + 𝑖=1 𝑛 𝑓 0,i w0,i + 𝑖=1 𝑛 𝑓 i,0 wi,o (2) s.t. 𝑘=1 𝑚+1 𝑦 i,k = 1 (1≤i≤n) (3) yi,k yj,k ( dj-ai)( di-aj) ≤ 0 (1≤i, j≤n, k≠m+1) (4) yi,k ∈ {1,0} (1 ≤ i ≤ n, 1 ≤ k ≤ m+1) (5)

Proposed Genetic Algorithm 1. Generate the initial population ; 2. Evaluate the fitness values of the individuals in the population; 3. If the last flight is assigned, STOP; 4. While a new fligth come to the airport; 4.1. Select two mates from the population 4.2. Apply crossover on two mates to form two children 4.3. Apply mutation on each child 4.4. Determine the next generation 5. Go to Step 2;

Genetic Algorithm: Chromosome Structure A chromosome is composed of permutation of flights and permutation of gates. F5 F2 F1 F3 F4 G4 G3 G1 G2 G10 Random numbers between 0 and 1 is used to form a chromosome 0,35 0,63 0,18 0,42 0,83 0,76 0,39 0,51 0,36 A permutation is determined by sorting the double numbers in ascending 2 7 1 5 9 8 4 6 3

Genetik Algorithm: Solution Candidate A solution candidate is determined by assigning the flights to the gates G2 F2,F5,F4,F3,F1 G3 G1 A greedy method is used to assign the fligths to the gates

Genetic Algorithm: Solution Candidate Fligths are assigned to the gates according to the permutation order of flights and gates to minimize the difference of flight arrival time and the available time of a gate. Any fligth is assigned to an available gate with latest available time of the gates. If no gates available, the fligth is assignd to the apron. The basic steps are: 1- Sort flights according to the chormosome permutation and sort gates according to the chromosome ermutation. Let ai arrival time of flight i and gk represents available time of gate k. 2- For each flight i, find gate k such that gk < ai and ai - gk is minimized if such k exists, assign flight i to gate k, if k does not exist, assign flight i to the apron.

GA: Fitness Function Fitness = Transfer Passengers Total Walking Distance+ Embarking Passengers Total Walking Distance+ Disembarking Passengers Total Walking Distance

Parent Selection: Tournament Selection Selected solutions are compared according to the fitness values.

GA: Crossover and Mutation Crossover: A child genes are formed by taking the averages of parents’ genes. Mother Father Child Mutation: A random value (pm , mutation probability) is added to the child genes.

GA: Determining Next Generation Next generation is formed according to the fitness values of the parent and child solutions. Initial Pop Parents Par1 Par2 Selection Fitness based replacement Pool Childs

For the first problem, our algorithm finds the optimum For the first problem, our algorithm finds the optimum. But the first problem is a small-sized one.

Our algorithm works well for the second problem and finds the optimum.

And finally, the third problem; our algorithm produces a good solution in reasonable time.

Is our algorithm good enough Is our algorithm good enough? We compared against the Greedy Heuristic of Ding et al (2005).

Yes, our algorithm obtains better solutions Yes, our algorithm obtains better solutions. However, we should proceed and check against well-known solution approaches.

Thank you for your attention. Questions ???