Page 38 - Fister jr., Iztok, and Andrej Brodnik (eds.). StuCoSReC. Proceedings of the 2017 4th Student Computer Science Research Conference. Koper: University of Primorska Press, 2017
P. 38
sharing information between agents is described in three • the number of agents was set to values N ∈ {1, 5, 8, 10,
steps, as follows: 16, 20, 25}, from which only the feasible (Table 1) were
considered,
1. step: The best vectors from all agents are found.
• the scale size was initially drawn randomly from uni-
2. step: From these vectors, find the one that is the most form distribution in interval Fi(0) ∈ [0, 1],
diverse from the best vector in current agent based on
Euclidian distance (Eq. (11)). • the crossover probability was initially drawn randomly
from uniform distribution in interval CRi(0) ∈ [0, 1],
3. step: Using Euclidian distance (Eq. (11)), find two
vectors that are closest to each other in the current • the diversity threshold in Algorithm 2 was set to
agent (Algorithm 3) and replace the worse based on threshold = 1.
fitness function result, with the vector found is step 2.
4.1 Dynamic optimization benchmark
Distance between vectors is calculated as Euclidean distance:
Algorithms in the study were tested on benchmark test suite
d(p, q) = D (11) provided by CEC’09 organizers for Competition on Dynamic
Optimization [7], which uses the generalized dynamic bench-
(pj − qj )2, mark generator. Benchmark defines seven change types:
small-step change (T1), large-step change (T2), random
j=1 change (T3), chaotic change (T4), recurrent change (T5), re-
current change with noise (T6), and random change with
where p and q represent D dimensional vector. changed dimension (T7).
There are six test functions defined in the real-space:
Algorithm 2 Calculate diversity and exchange vectors • F1: Rotation peak function (with 10 and 50 peaks)
• F2: Composition of Sphere’s function
1: for each agent a do • F3: Composition of Rastrigin’s function
2: Calculate population diversity for a (Eq. (9, 10)) • F4: Composition of Griewank’s function
3: if a.diversity < threshold then • F5: Composition of Ackley’s function
4: bestVectors[] =BestVectorForEachAgent() • F6: Hybrid Composition function
5: Find the most diverse vector from the best vector
in a
6: r = IndexOfMostSimillar (a)
7: Replace vector on index r with the most remote
vector
Algorithm 3 Algorithm that finds vector to replace In summary, there are 49 specific test cases and each test
case contains 60 changes. Test cases run independently 20
NP: size of agent’s population times to obtain the mark on specific case. Overall perfor-
Agent’s population is ordered by fitness value mance perf is the sum of the performance measures obtained
for each function and each change type as follows:
1: function IndexOfMostSimillar(a)
2: for i = 0 to (NP - 2) do 49 (12)
3: for j = i + 1 to (NP - 1) do
4: distance = EuclidianDistance(a[i], a[j]) perf = mark i · 100,
5: if distance < smallestDistance then
6: smallestDistance = distance i=1
7: ind = j
where the performance measure mark i is defined as follows:
8: return a[ind ]
wi R C
R·C
4. EXPERIMENT AND RESULTS marki = rlj , (13)
The goal of our experimental work was twofold. Firstly to l=1 j=1
test the MAS-jDE with different parameters settings, and
thus find the best settings for parameters: the population where wi denotes weight of the problem i (see [7] for more de-
size NP and the number of agents N . Secondly to compare tails), R the number of runs and C is the number of changes
the results obtained by the MAS-jDE with the results of (in our case R = 20 and C = 60). The variable rlj is ex-
the other state-of-the-art algorithms. In both experiments, pressed as:
all algorithms solved CEC’09 benchmark test functions for
DOP. S (14)
The algorithm MAS-jDE used the following parameters dur- rlj = rlljast/(1 + (1 − rlsj )/S),
ing experiments:
s=1
• the total population size was varied as NP MAS ∈ {50,
100, 200, 400}, where rlljast denotes the relative ratio between fitness value of
best individual and global optimum of the j-th environment,
rlsj the relative ratio between fitness value of best individual
and global optimum at the s-th sampling during one change,
and S is total number of samples for each environment.
StuCoSReC Proceedings of the 2017 4th Student Computer Science Research Conference 38
Ljubljana, Slovenia, 11 October
steps, as follows: 16, 20, 25}, from which only the feasible (Table 1) were
considered,
1. step: The best vectors from all agents are found.
• the scale size was initially drawn randomly from uni-
2. step: From these vectors, find the one that is the most form distribution in interval Fi(0) ∈ [0, 1],
diverse from the best vector in current agent based on
Euclidian distance (Eq. (11)). • the crossover probability was initially drawn randomly
from uniform distribution in interval CRi(0) ∈ [0, 1],
3. step: Using Euclidian distance (Eq. (11)), find two
vectors that are closest to each other in the current • the diversity threshold in Algorithm 2 was set to
agent (Algorithm 3) and replace the worse based on threshold = 1.
fitness function result, with the vector found is step 2.
4.1 Dynamic optimization benchmark
Distance between vectors is calculated as Euclidean distance:
Algorithms in the study were tested on benchmark test suite
d(p, q) = D (11) provided by CEC’09 organizers for Competition on Dynamic
Optimization [7], which uses the generalized dynamic bench-
(pj − qj )2, mark generator. Benchmark defines seven change types:
small-step change (T1), large-step change (T2), random
j=1 change (T3), chaotic change (T4), recurrent change (T5), re-
current change with noise (T6), and random change with
where p and q represent D dimensional vector. changed dimension (T7).
There are six test functions defined in the real-space:
Algorithm 2 Calculate diversity and exchange vectors • F1: Rotation peak function (with 10 and 50 peaks)
• F2: Composition of Sphere’s function
1: for each agent a do • F3: Composition of Rastrigin’s function
2: Calculate population diversity for a (Eq. (9, 10)) • F4: Composition of Griewank’s function
3: if a.diversity < threshold then • F5: Composition of Ackley’s function
4: bestVectors[] =BestVectorForEachAgent() • F6: Hybrid Composition function
5: Find the most diverse vector from the best vector
in a
6: r = IndexOfMostSimillar (a)
7: Replace vector on index r with the most remote
vector
Algorithm 3 Algorithm that finds vector to replace In summary, there are 49 specific test cases and each test
case contains 60 changes. Test cases run independently 20
NP: size of agent’s population times to obtain the mark on specific case. Overall perfor-
Agent’s population is ordered by fitness value mance perf is the sum of the performance measures obtained
for each function and each change type as follows:
1: function IndexOfMostSimillar(a)
2: for i = 0 to (NP - 2) do 49 (12)
3: for j = i + 1 to (NP - 1) do
4: distance = EuclidianDistance(a[i], a[j]) perf = mark i · 100,
5: if distance < smallestDistance then
6: smallestDistance = distance i=1
7: ind = j
where the performance measure mark i is defined as follows:
8: return a[ind ]
wi R C
R·C
4. EXPERIMENT AND RESULTS marki = rlj , (13)
The goal of our experimental work was twofold. Firstly to l=1 j=1
test the MAS-jDE with different parameters settings, and
thus find the best settings for parameters: the population where wi denotes weight of the problem i (see [7] for more de-
size NP and the number of agents N . Secondly to compare tails), R the number of runs and C is the number of changes
the results obtained by the MAS-jDE with the results of (in our case R = 20 and C = 60). The variable rlj is ex-
the other state-of-the-art algorithms. In both experiments, pressed as:
all algorithms solved CEC’09 benchmark test functions for
DOP. S (14)
The algorithm MAS-jDE used the following parameters dur- rlj = rlljast/(1 + (1 − rlsj )/S),
ing experiments:
s=1
• the total population size was varied as NP MAS ∈ {50,
100, 200, 400}, where rlljast denotes the relative ratio between fitness value of
best individual and global optimum of the j-th environment,
rlsj the relative ratio between fitness value of best individual
and global optimum at the s-th sampling during one change,
and S is total number of samples for each environment.
StuCoSReC Proceedings of the 2017 4th Student Computer Science Research Conference 38
Ljubljana, Slovenia, 11 October
