Bio Inspired Computing Presentation

1. Ant Colony Optimization for
Simulated Dynamic Multi-Objective
Railway Junction Rescheduling
Md. Mamun Hasan
Course: CSE 6471
Roll No: 1907555

2. Introduction (Problem DM-RJRP)
• Efficient rescheduling of trains after a
perturbation
• The problem may be both dynamic and multi-
objective
• Dynamic because after a reschedule if another
perturbation occurs we have to reschedule it
again very quickly runtime.
• Multi-objective because we have multiple
objectives like both increase the energy
efficiency and decrease arrival time or delays

3. Introduction (Related Work)
• Rescheduling trains after a delay is a popular
research area.
• However the previous work in this field has
assumed that the problem is static.
• So far there has been little work in dynamic
rescheduling problems and even less in
dynamic multi-objective rescheduling
problems.

4. Introduction (Objective SDM-RJRP)
• Investigate the ant colony optimization
algorithms (They have investigated using
different modified versions of ACO) to solve a
simulated (Unfortunately, at the present time,
Network rail does not store the necessary data to
investigate such problems) dynamic multi-
objective railway rescheduling problem
• Identify the features of the algorithms that
enable them cope with a multi-objective problem
that is also dynamic.

5. Introduction (Why ACO)
• Effective in dynamic computational scheduling
problems
• Very suitable for adapting to multi-objective
problems by allowing some flexible
modifications

6. Problems and Algorithms
• DMOP: Dynamic multi-objective problem
• DM-RJRP: Dynamic multi-objective railway junction
rescheduling problem
• MOACO: Multi-objective ACO
• P-ACO: Population based ACO
• MMAS: MAX-MIN Ant system
• NSGA-2: a state of the art multi-objective algorithm
• FCFS: First Come First Served
• NSGA-2 with FCFS often used by railway dispatchers to
resolve perturbations
• We will modify two algorithms of MOACO are P-ACO and
MMAS to get the best algorithms for DM-RJRP

7. Related Work
• In a multi-objective problem with conflicting
objectives (like optimize both delay and energy cost)
there is no-single solution that is able to optimize all
the objectives simultaneously.
• Many researchers have tackled this problem by
combing the objectives into a single, often weighted,
objective.
• However its disadvantage is weights will have to
determined in advance using domain knowledge.
• In addition, this approach assumes that the relative
importance of each objective does not change over
time.

8. Pareto Optimal Set (POS)
• The previous single solution may not be always the
case.
• For example, in the early morning rush hour a train
dispatcher may wish to minimize overall delays where
as in the afternoon may wish to maintain connections
for long distance travelers.
• A more flexible approach is to produce a set of trade-
off solutions to provide the decision maker with a
choice of solutions.
• This will allow them as to make a decision as to which
solution best matches their requirements at a
particular moment in time.

9. Pareto Optimal Set (POS) Cont…
• In order to produce a set of trade-off
solutions, we need a means of comparing
solutions against each other.
• This is achieved using concept of dominance.
• A solution x1 is said to dominate a solution x2
(denoted as x1 < x2) if:
1. X1 is no worse than x2 in all objectives
2. X1 is better than x2 in at least in one objective

10. Pareto Optimal Set (POS) Cont…
• Each solution is compared with every other
solution.
• If a solution is not dominated by any other
solution, it is added to the non-dominated set of
solutions, also referred to as Pareto Optimal Set
(POS)
• The points that Pareto-optimal solutions maps to,
in the objective space, is known as Pareto-
optimal Front (POF)
• The POS is the set of trade-off solutions that
presented to the decision maker.

11. Multi-Objective Train Rescheduling
• So far there have been very little work that
produces a Pareto optimal trade-off solutions
for MO-RJRP.
• Previously a modified BB algorithm was tried
for a bi-objective MO-RJRP
• We have multiple objectives here
1. Reduce the delay
2. Reduce the energy consumption

12. Dynamic Train Rescheduling
• The dynamic nature of railway system is rarely considered
in train rescheduling research.
• But speed and location modifications may happen while
the algorithm is computing a solution.
• The BB algorithm used previously appears to have no
inbuilt mechanism to cope with dynamic change.
• Eaton and Yang found that a P-ACO algorithm
outperformed a FCFS heuristic when the changes were
frequent and of high magnitude.
• Further it was discovered that on the high frequency high
magnitude dynamic changes, ACO algorithms with
memory outperformed ACO algorithms that has no inbuilt
mechanism to cope with dynamic changes.

13. ACO for DMOP
• The modification of ACO algorithms for multi-
objective problems is a popular research area.
• Although ACO algorithms are originally
designed for single objective problem there
are several flexibility to modify design for
multi-objective problem like –
1. Allowing multiple colonies
2. Multiple pheromone matrices
3. Multiple heuristic matrices

14. ACO for DMOP (Inspiration)
• Population based nature means that multiple
trade-of solutions can be generated in one run
of the algorithm
• ACO has previously been applied to the
dynamic travelling salesman problem (DTSP)
with good results.
• The DTSP is a combinational problem similar
to DRJRP.

15. DM-RJRP (The problem objectives)
Objective 1 - Minimizing Timetable Deviation:
If ts is the scheduled arrival time and ta is the actual arrival time then
timetable deviation of train i is
The objective is to minimize the deviation, in minutes, for all trains at the
point of change c is
Where NT is the number of trains in the problem at change c

16. DM-RJRP (The problem objectives)
Objective 2 - Minimizing Additional Energy Expenditure:
Energy consumption equations by University of Birmingham
microscopic railway simulator, BRaVE
Fg is the calculated force required to overcome gravity, where wt is weight in
kilograms of the train, gt is gravity (a constant value of 9.806) and gd is
gradient (zero if track is level)
F is the force to move the train, where u, v are the speed in meters per second
E is the energy expended in joules, where d is the distance travelled in meters.
E is converted to kWh

17. DM-RJRP (The problem objectives)
Objective 2 - Minimizing Additional Energy Expenditure (Cont):
The objective is minimize the additional energy for all trains at
the point of change c
Where ExEi is the additional energy expended by train i, and
Es is the scheduled energy and Ea is the actual energy

18. DM-RJRP (The problem objectives)
• The relationship between energy usage and train
delay is complex
• The original assumption made was that a slightly
delayed train will use more additional energy
than a seriously delayed train
• But from equation a seriously delayed train often
found to use less energy
• A train that that spends a lot of time speeding up
and slowing down to avoid conflict with other
trains will expend more energy than a waiting
train

19. ACO for DM-RJRP
• The Basic ACO Algorithm
• An ant k, when at node i, chooses the next
node j in its neighborhood, probability is
• Unfortunately a computationally efficient and
effective problem specific heuristic is not
available.

20. MOACO for DM-RJRP
• There are many possible designs for MOACO as it
is a popular research area
• Much work has been carried out on modifying
ACO algorithms to make them suitable for multi-
objective problems
• Previous research assumes there is no single
effective way to introduce a multi-objective
aspect to an ACO algorithm
• In this work two multi-objective algorithms have
been chosen for investigation P-ACO and MMAS

21. Dynamic Multi-Objective P-ACO
• P-ACO is a population based ACO that has an
inbuilt memory P
• This memory allows solutions Q from before
the change to be carried over to the new
environment
• To make the P-ACO multi-objective, the single-
objective P-ACO is modified by adding a
pheromone and heuristic matrix for each
objective

22. Dynamic Multi-Objective MMAS
• MMAS was chosen because its base algorithm
was found to perform poorly on the DRJRP in
previous work
• Choosing an algorithm that performed poorly
allows us to investigate the modifications that are
necessary to improve its performance
• MMAS is based on m-ACO4(1,m) multi-objective
algorithm
• MMAS is similar to P-ACO in that it uses one ant
colony with multiple pheromone structures.

23. Dynamic Multi-Objective MMAS
• Ants make their decision as to which node to choose next by
randomly selecting one of the objective pheromone matrices to
using basic ACO equation
• At the end of an iteration, each pheromone matrix is updated
separately for each objective using the best iteration ant for that
objective. The update value for objective x is
• As in the base MMAS algorithm, pheromone values are initialized to
a maximum value. After each iteration all pheromone trails are
evaporated as following equation

24. Dynamic Multi-Objective MMAS
• MMAS has no inbuilt mechanism to cope with a dynamic
change apart from the evaporation of pheromone trails,
which can be slow.
• Poor performance on single objective DRJRP suggests that
applications need to be m-ACO4 to improve its
performance for multi-objective version of the DRJRP
• They have designed four versions of the MMAS algorithm
that either retain the pheromones or non-dominated after
a dynamic change or clear them.
1. DM-MMAS-SC
2. DM-MMAS- ST
3. DM-MMAS-NC
4. DM-MMAS-NT

25. DM-MMAS-SC
• Investigate the importance of retain the
pheromones after a dynamic change
• The pheromone matrix reinitialized to τmax to
remove all the old pheromone information
• The non-dominated archive is emptied of all
solutions

26. DM-MMAS- ST
• This version is closest to original behavior of
MMAS
• The pheromone values are retained and only
evaporation is used to remove old outdated
decisions
• As before non-dominated archive is emptied

27. DM-MMAS-NC
• Investigate the importance of retaining the
non-dominated archive between changes
• After a dynamic change non-dominated
archive of solutions is retained and repaired to
cope with new environment like DM-PACO
• For new trains pheromone values are
initialized to τmax
• The pheromone trails are cleared after each
change

28. DM-MMAS-NT
• Investigate both the importance of the
pheromone information and the non-
dominated archive after a dynamic change
• Therefore, both the non-dominated archive
and the pheromone information are retained

29. Experimental Study (DM-PACO Design)
• The best combination for DM-PACO was found
to be 12 ants with a memory of size 8
• For Both pheromone matrices τmax was set to
1 and the minimum pheromone value τinit was
set to 1/n, where n is the number of nodes.
• And pheromone update value (τmax - τinit)/k,
where k is the size of memory
• All pheromone levels are initialized to τinit

30. Experimental Study (MMAS Design)
• To make the DM-PACO and DM-MMAS more
comparable they make the same number of
ants for MMAS also
• The pheromone bounds for MMAS are given
by τmax=1/C and τmin= τmax/a, where C is the
fitness of the best ant and a is the constant
parameter of the algorithm
• For both pheromone matrices a was set to 25
and p to 0.5

31. Experimental Study
• Nine dynamic environments were investigated
• Involving all permutations of 3 different
magnitudes of change (2 trains, 5 trains, 8
trains)
• 3 different frequencies of changes (5 min, 10
mins, 15 mins)
• For all algorithms the POS at the time of
change was recorded

32. Experimental Study (Results)
• DM-MMAS-NT performs better than DM-MMAS-
ST for high magnitude, low to medium frequency
(m=8, f=5 to 10) and medium magnitude, high
frequency (m=5, f=10)
• DM-PACO-R performs better than DM-MMAS-NT
for high magnitude, medium magnitude (m=8,
f=10)

33. Conclusion
• It is apparent that all the ACO algorithms can find
a POS of solutions for the DM-RJRP
• However the algorithms based on P-ASO
performs better than the algorithms based on
MMAS
• The performance of MMAS can be improved by
retaining the non-dominated set of solutions
between changes
• The best performing algorithm DM-PACO-R also
outperformed NSGA-2 and FCFS

34. Thank You
References
• https://ieeexplore.ieee.org/document/78754
08/