def obtain_wireless_signal_coverage(self):
"""
According to the position of mobile devices and edge sites, judge whether mobile devices are covered by edge
sites' wireless signal.
:return: lists stored indices of connectable edge sites, power gains, and mobile devices, respectively, and
distances from mobile devices to connectable edge sites
"""
connectable_servers, connectable_distances, connectable_gains = [], [], []
global_distances = [] # a 'N * M' matrix stored distances between each user and each edge site
for i in range(len(self.__user_info)):
tmp_s, tmp_d, tmp_g = [], [], []
tmp_gains = []
for j in range(len(self.__edge_info)):
distance = ToolFunction.obtain_geo_distance(self.__user_info[i], self.__edge_info[j])
if distance <= self.__edge_info[j][2]:
# under signal coverage
tmp_s.append(j)
tmp_d.append(distance)
tmp_gains.append(ToolFunction.obtain_channel_power_gain(self.__path_loss_const, distance))
tmp_g.append(distance)
connectable_servers.append(tmp_s)
connectable_distances.append(tmp_d)
connectable_gains.append(tmp_gains)
global_distances.append(tmp_g)
connectable_users = []
for j in range(len(self.__edge_info)):
tmp_u = []
for i in range(len(self.__user_info)):
if global_distances[i][j] <= self.__edge_info[j][2]:
tmp_u.append(i)
connectable_users.append(tmp_u)
return connectable_servers, connectable_users, connectable_distances, connectable_gains, global_distances
def obtain_overall_costs(self, edge_selections):
"""
Calculate the overall costs, which is the sum of cost of each mobile device.
:param edge_selections: the edge selection decisions for all mobile devices
:return: overall costs
"""
parameter = self.get_parameter()
overall_costs = 0
for i in range(parameter.get_user_num()):
if parameter.get_task_requests()[i] == 1:
division = int(sum(edge_selections[i]))
if division:
# cost = self.obtain_time_consumption(
# division, edge_selections[i], parameter.get_connectable_gains[i])
transmit_times = ToolFunction.obtain_transmit_times(division, edge_selections[i], parameter,
parameter.get_connectable_gains()[i])
edge_exe_times = ToolFunction.obtain_edge_exe_times(division, parameter)
edge_times = transmit_times + edge_exe_times
cost = max(edge_times) + parameter.get_local_exe_time() + parameter.get_coordinate_cost() * division
else:
cost = parameter.get_drop_penalty()
else:
cost = 0
overall_costs += cost
return overall_costs
def obtain_time_consumption(self, division, edge_selection, channel_power_gains):
"""
Calculate the time consumption on transmission and edge execution for one mobile device.
:param division: the number of chosen edge sites (not zero)
:param edge_selection: the edge selection decision of one mobile devices
:param channel_power_gains: the channel power gains of one mobile devices to every connectable servers
:return: the time consumption on transmission and edge execution
"""
parameter = self.get_parameter()
transmit_times = ToolFunction.obtain_transmit_times(division, edge_selection, parameter, channel_power_gains)
edge_exe_times = ToolFunction.obtain_edge_exe_times(division, parameter)
edge_times = transmit_times + edge_exe_times
time_consumption = max(edge_times) + parameter.get_local_exe_time() + parameter.get_coordinate_cost() * division
return time_consumption
def generate_random_ins(self):
"""
Generate random instance for those dimensions whose labels are True. In this version, we check whether the two
constraints can be satisfied. (Actually, we first generate random edge_selections, and then convert it to an
instance.)
:return: a feasible instance
"""
parameter = self.get_parameter()
assignable_nums = np.repeat(parameter.get_max_assign(), parameter.get_server_num())
edge_selections = self.greedy_sample(assignable_nums)
ins_features = []
for i in range(parameter.get_user_num()):
if parameter.get_task_requests()[i] == 1:
division = int(sum(edge_selections[i]))
if division:
times = self.obtain_time_consumption(division, edge_selections[i],
parameter.get_connectable_gains()[i])
energys = ToolFunction.obtain_transmit_energy(division, edge_selections[i], parameter,
parameter.get_connectable_gains()[i])
# satisfy the constraint
if times >= parameter.get_ddl() or energys > self.__battery_energy_levels[i]:
edge_selections[i] = np.zeros(len(edge_selections[i]))
else:
pass
for j in range(len(edge_selections[i])):
ins_features.append(edge_selections[i][j])
dimension = Dimension(parameter.get_dim_size())
instance = Instance(dimension)
instance.set_features(ins_features)
return instance
def generate_task_request(self):
"""
Generate task request from Bernoulli Distribution.
:return: a numpy array denoted task request, presented in [0, 1, ..., 1]
"""
return ToolFunction.sample_from_bernoulli(self.__user_num, self.__task_request_prob)
def racos(self, optimization_func):
"""
The optimization algorithm, RACOS.
:return: no return
"""
self.clear()
self.generate_solutions(optimization_func)
# if sequential is not used
if not self.__online:
# begin iteration
for it in range(self.__iterations_num):
print('RACOS iteration #', it)
self.__next_population = []
for i in range(self.__sample_size):
while True:
self.reset()
chosen_pos_idx = ToolFunction.sample_uniform_integer(
0, self.__pos_num - 1)
eps = ToolFunction.sample_uniform_double(0, 1)
if eps <= self.__rand_prob:
non_chosen_dim = self.shrink(
self.__pos_population[chosen_pos_idx])
for j in range(len(non_chosen_dim)):
self.__labels[non_chosen_dim[j]] = False
ins = self.generate_from_pos_ins(
self.__pos_population[chosen_pos_idx])
if (not Racos.is_ins_in_list(ins, self.__pos_population, self.__pos_num)) \
and (not Racos.is_ins_in_list(ins, self.__next_population, i)):
ins.set_fitness(optimization_func(ins))
break
self.__next_population.append(ins)
self.__population = []
for i in range(self.__sample_size):
self.__population.append(self.__next_population[i])
self.update_pos_population()
self.update_optimal()
# print the best-so-far fitness for test
print('Best-so-far fitness:',
self.get_optimal_solution().get_fitness())
else:
# sequential mode is not interested in this paper
pass
def obtain_edge_selections(self):
"""
Obtain the feasible solution with greedy policy on computation.
:return: edge_selections, every row denotes a mobile device who has task request
"""
parameter = self.get_parameter()
# first initialize with zero
edge_selections = []
for i in range(parameter.get_user_num()):
edge_selection = np.repeat(
0, len(parameter.get_connectable_servers()[i]))
edge_selections.append(edge_selection)
# for every edge site, generate a random integer with [0, max_assign], and distribute connections to
# connectable mobile devices
for j in range(parameter.get_server_num()):
assign_num = parameter.get_max_assign()
connectable_user_num = len(parameter.get_connectable_users()[j])
if assign_num >= connectable_user_num:
# every mobile device in it can be chosen
for i in range(connectable_user_num):
user_index = parameter.get_connectable_users()[j][i]
edge_index = list.index(
parameter.get_connectable_servers()[user_index], j)
edge_selections[user_index][edge_index] = 1
else:
# randomly choose assign_num users to distribute j's computation capacity
user_indices = random.sample(
parameter.get_connectable_users()[j], assign_num)
for i in range(len(user_indices)):
user_index = user_indices[i]
edge_index = list.index(
parameter.get_connectable_servers()[user_index], j)
edge_selections[user_index][edge_index] = 1
# set those mobile devices who do not have task request to [0, 0, ..., 0]
# we can not delete them from the list because every row is the index of the corresponding mobile device
for i in range(parameter.get_user_num()):
if parameter.get_task_requests()[i] == 0:
edge_selections[i] = np.zeros(len(edge_selections[i]))
else:
division = int(sum(edge_selections[i]))
if division:
times = self.obtain_time_consumption(
division, edge_selections[i],
parameter.get_connectable_gains()[i])
energys = ToolFunction.obtain_transmit_energy(
division, edge_selections[i], parameter,
parameter.get_connectable_gains()[i])
# satisfy the constraint
if times >= parameter.get_ddl(
) or energys > self.get_battery_energy_levels()[i]:
edge_selections[i] = np.zeros(len(edge_selections[i]))
return edge_selections
def generate_random_ins(self):
"""
Generate a random instance for those dimensions whose labels are True.
:return: the generated instance
"""
instance = Instance(self.__dimension)
for i in range(self.__dimension.get_dim_size()):
instance.set_feature(
i,
ToolFunction.sample_uniform_integer(self.__regions[i][0],
self.__regions[i][1]))
return instance
def update_labels(self):
"""
Update self.__labels according to the number of uncertain bits.
:return: no return
"""
dims = [n for n in range(self.__dimension.get_dim_size())]
for i in range(self.__uncertain_bits_num):
index = ToolFunction.sample_uniform_integer(
0,
self.__dimension.get_dim_size() - i - 1)
self.__labels[dims[index]] = False
dims.remove(dims[index])
def obtain_perturbation_para(self):
"""
Calculate the lower bound of perturbation parameter used in Lyapunov Optimization.
:return: the lower bound of perturbation parameter
"""
max_achievable_rate = ToolFunction.obtain_achieve_rate(self.__bandwidth, self.__max_channel_power_gain,
self.__transmit_power, self.__noise)
part1 = self.__v * max_achievable_rate / (self.__transmit_power * self.__edge_input_size)
part2 = self.__server_num * self.__drop_penalty - self.__edge_input_size / max_achievable_rate - \
self.__edge_input_size * self.__unit_cpu_num / self.__edge_cpu_freq
max_energy_all = self.__local_exe_energy + self.__server_num * \
self.__transmit_power * (self.__ddl - self.__local_exe_time)
return part1 * part2 + min(max_energy_all, self.__max_transient_discharge)
def shrink(self, instance):
"""
Shrink the dimensions.
:param instance: the chosen instance
:return: the shrunken dimensions with size only being self.__uncertain_bits_num
"""
non_chosen_dimension = [
n for n in range(self.__dimension.get_dim_size())
]
chosen_dimension = []
while not self.is_distinguish(instance, chosen_dimension):
tmp = non_chosen_dimension[ToolFunction.sample_uniform_integer(
0,
len(non_chosen_dimension) - 1)]
chosen_dimension.append(tmp)
non_chosen_dimension.remove(tmp)
while len(non_chosen_dimension) > self.__uncertain_bits_num:
tmp = non_chosen_dimension[ToolFunction.sample_uniform_integer(
0,
len(non_chosen_dimension) - 1)]
chosen_dimension.append(tmp)
non_chosen_dimension.remove(tmp)
return non_chosen_dimension
def generate_from_pos_ins(self, pos_instance):
"""
Generate an instance from an exist positive instance.
:param pos_instance: the exist positive instance
:return: the generated instance
"""
instance = Instance(self.__dimension)
for i in range(self.__dimension.get_dim_size()):
if not self.__labels[i]:
instance.set_feature(
i,
ToolFunction.sample_uniform_integer(
self.__regions[i][0], self.__regions[i][1]))
else:
instance.set_feature(i, pos_instance.get_feature(i))
return instance
def update_energy_levels(self):
"""
Update the cost & virtual energy levels according to the involution expression \eqref{10}.
:return: no return
"""
parameter = self.get_parameter()
for i in range(parameter.get_user_num()):
division = int(sum(self.__edge_selections[i]))
if division:
self.__battery_energy_levels[i] = self.__battery_energy_levels[i] + \
self.__harvested_energys[i] - ToolFunction.obtain_transmit_energy(
division, self.__edge_selections[i], parameter, parameter.get_connectable_gains()[i]) - \
parameter.get_local_exe_energy()
else:
# check whether need to minus local_exe_energys
# if self.__battery_energy_levels[i] < parameter.get_local_exe_energy():
# self.__battery_energy_levels[i] = self.__battery_energy_levels[i] + self.__harvested_energys[i]
# else:
# self.__battery_energy_levels[i] = self.__battery_energy_levels[i] + \
# self.__harvested_energys[i] - parameter.get_local_exe_energy()
self.__battery_energy_levels[i] = self.__battery_energy_levels[i] + self.__harvested_energys[i]
self.__virtual_energy_levels[i] = self.__battery_energy_levels[i] - parameter.get_perturbation_para()
def obtain_sub_problem_es(self, edge_selections):
"""
Calculate the optimization goal of sub-problem $\mathcal{P}_2^{es}$.
:param edge_selections: the edge selection decisions for all mobile devices
:return: the optimization goal of $\mathcal{P}_2^{es}$
"""
parameter = self.get_parameter()
optimization_func_value = 0
for i in range(parameter.get_user_num()):
division = int(sum(edge_selections[i]))
if division:
energy_consumes = parameter.get_local_exe_energy() + \
ToolFunction.obtain_transmit_energy(division, edge_selections[i], parameter,
parameter.get_connectable_gains()[i])
negative_part = self.__virtual_energy_levels[i] * energy_consumes
else:
if self.__battery_energy_levels[i] < parameter.get_local_exe_energy():
negative_part = 0
else:
negative_part = self.__virtual_energy_levels[i] * parameter.get_local_exe_energy()
optimization_func_value -= negative_part
optimization_func_value += parameter.get_v() * self.obtain_overall_costs(edge_selections)
return optimization_func_value
def obtain_edge_selections(self):
"""
Obtain the feasible solution with greedy policy on communication.
:return: edge_selections, every row denotes a mobile device who has task request
"""
parameter = self.get_parameter()
# deep copy the connectable servers and gains
shadow_servers, shadow_gains, edge_selections = [], [], []
for i in range(parameter.get_user_num()):
tmp_s, tmp_g = [], []
for j in range(len(parameter.get_connectable_servers()[i])):
tmp_s.append(parameter.get_connectable_servers()[i][j])
tmp_g.append(parameter.get_connectable_gains()[i][j])
shadow_servers.append(tmp_s)
shadow_gains.append(tmp_g)
edge_selections.append(
np.zeros(len(parameter.get_connectable_servers()[i])))
best_gains, best_servers = [], []
for i in range(parameter.get_user_num()):
best_gain = max(shadow_gains[i])
best_gains.append(best_gain)
best_server_idx = shadow_gains[i].index(best_gain)
best_servers.append(shadow_servers[i][best_server_idx])
checked = [False] * parameter.get_user_num()
while False in checked:
# satisfy the maximum assignment constraint
for j in range(parameter.get_server_num()):
connected_users = [
idx for idx, server in enumerate(best_servers)
if server == j
]
if len(connected_users):
# at least one mobile device choose this server
connected_gains = [best_gains[i] for i in connected_users]
# only the user with the best channel power gains can be chosen
lucky_user = connected_users[connected_gains.index(
max(connected_gains))]
checked[lucky_user] = True
# update best connectable information (remove j)
for i in range(parameter.get_user_num()):
if not checked[i]:
if shadow_servers[i].count(j) != 0:
server_idx = shadow_servers[i].index(j)
shadow_servers[i].pop(server_idx)
shadow_gains[i].pop(server_idx)
else:
# this server is not chosen by any mobile device
continue
# re-calculate the best server and gains for each mobile device
for i in range(parameter.get_user_num()):
if len(shadow_gains[i]) != 0:
best_gains[i] = max(shadow_gains[i])
best_server_index = shadow_gains[i].index(
best_gains[i])
best_servers[i] = shadow_servers[i][best_server_index]
else:
checked[i] = True
# obtain edge_selections from best_servers
for i in range(parameter.get_user_num()):
if parameter.get_task_requests()[i] == 1:
if best_servers[i]:
edge_idx = parameter.get_connectable_servers()[i].index(
best_servers[i])
edge_selections[i][edge_idx] = 1
# check whether the constraints can be satisfied
division = int(sum(edge_selections[i]))
if division:
times = self.obtain_time_consumption(
division, edge_selections[i],
parameter.get_connectable_gains()[i])
energys = ToolFunction.obtain_transmit_energy(
division, edge_selections[i], parameter,
parameter.get_connectable_gains()[i])
# satisfy the constraint
if times >= parameter.get_ddl(
) or energys > self.get_battery_energy_levels()[i]:
edge_selections[i] = np.zeros(len(edge_selections[i]))
return edge_selections
def generate_from_pos_ins(self, pos_instance):
"""
Generate an instance from an exist positive instance.
:param pos_instance: the exist positive instance
:return: a feasible instance
"""
parameter = self.get_parameter()
assignable_nums = np.repeat(parameter.get_max_assign(), parameter.get_server_num())
edge_selections = self.greedy_sample(assignable_nums)
ins_features = []
for i in range(parameter.get_user_num()):
if parameter.get_task_requests()[i] == 1:
division = int(sum(edge_selections[i]))
if division:
times = self.obtain_time_consumption(division, edge_selections[i],
parameter.get_connectable_gains()[i])
energys = ToolFunction.obtain_transmit_energy(division, edge_selections[i], parameter,
parameter.get_connectable_gains()[i])
# satisfy the constraint
if times >= parameter.get_ddl() or energys > self.__battery_energy_levels[i]:
edge_selections[i] = np.zeros(len(edge_selections[i]))
else:
pass
for j in range(len(edge_selections[i])):
ins_features.append(edge_selections[i][j])
dimension = Dimension(parameter.get_dim_size())
instance = Instance(dimension)
instance.set_features(ins_features)
# update from the chosen positive instance
for i in range(len(instance.get_features())):
if self.get_labels()[i]:
instance.set_feature(i, pos_instance.get_feature(i))
# re-check whether the maximum assignable nums is satisfied
edge_selections = self.instance_to_edge_selections(instance)
for j in range(parameter.get_server_num()):
if assignable_nums[j] >= len(parameter.get_connectable_users()[j]):
continue
connect_users = []
for i in range(len(parameter.get_connectable_users()[j])):
user_idx = parameter.get_connectable_users()[j][i]
edge_idx = list.index(parameter.get_connectable_servers()[user_idx], j)
if edge_selections[user_idx][edge_idx] == 1:
connect_users.append(user_idx)
if len(connect_users) <= assignable_nums[j]:
continue
permitted_connect_users = random.sample(connect_users, assignable_nums[j])
non_permitted = [u for u in connect_users if u not in permitted_connect_users]
for i in range(len(non_permitted)):
user_idx = non_permitted[i]
edge_idx = list.index(parameter.get_connectable_servers()[user_idx], j)
edge_selections[user_idx][edge_idx] = 0
# re-check whether the ddl and energy consumption are satisfied
for i in range(parameter.get_user_num()):
if parameter.get_task_requests()[i] == 1:
division = int(sum(edge_selections[i]))
if division:
# times = self.obtain_time_consumption(division, edge_selections[i],
# parameter.get_connectable_gains()[i])
transmit_times = ToolFunction.obtain_transmit_times(division, edge_selections[i], parameter,
parameter.get_connectable_gains()[i])
edge_exe_times = ToolFunction.obtain_edge_exe_times(division, parameter)
edge_times = transmit_times + edge_exe_times
times = max(edge_times) + parameter.get_local_exe_time() + \
parameter.get_coordinate_cost() * division
energys = ToolFunction.obtain_transmit_energy(division, edge_selections[i], parameter,
parameter.get_connectable_gains()[i])
# satisfy the constraint
if times >= parameter.get_ddl() or energys > self.__battery_energy_levels[i]:
edge_selections[i] = np.zeros(len(edge_selections[i]))
else:
pass
# get final instance from the new edge_selections
ins_features = []
for i in range(parameter.get_user_num()):
if parameter.get_task_requests()[i] == 1:
for j in range(len(edge_selections[i])):
ins_features.append(edge_selections[i][j])
instance.set_features(ins_features)
return instance
def __init__(self, time_slot_length=2e-3, time_horizon=50, ddl=2e-3, drop_penalty=2e-3, coordinate_cost=1e-6,
task_request_prob=0.6, unit_cpu_num=737.5, local_input_size=50, local_cpu_freq=1.5e9,
switched_cap=1e-28, max_transient_discharge=0.04, edge_input_size=2000, max_assign=8,
edge_cpu_freq=4.5e9, bandwidth=5e5, noise=1e-13, transmit_power=1, path_loss_const=1e-4,
min_distance=150, max_distance=600, max_channel_power_gain=1.02e-13, max_harvest_energy=4.8e-4,
v=5e-4):
"""
Initialization.
Without loss of generality, we set properties of every mobile device and every edge site the same, respectively.
:param time_slot_length: the length of time slot in second
:param time_horizon: the length of time horizon, i.e., the number of time slots
:param ddl: the deadline of computation task (unit: second)
:param drop_penalty: the penalty for dropping the computation task (unit: second)
:param coordinate_cost: the cost for coordination/collaboration of edge sites (unit: second) [--tunable--]
:param task_request_prob: the task request probability of all users under Bernoulli process
:param unit_cpu_num: number of CPU-cycles required to process one bit computation task (num/bit)
:param local_input_size: the input data size of the computation task for local execution (in bits)
:param local_cpu_freq: the CPU-cycle frequency of all mobile devices
:param switched_cap: the effective switched capacitance of all mobile devices
:param max_transient_discharge: the maximum allowable transient discharge of mobile devices [--danger--]
:param edge_input_size: the input data size of the computation task for edge/remote execution (in bits)
:param max_assign: maximum number of assignments (acceptable mobile devices) of all edge sites [--tunable--]
:param edge_cpu_freq: the CPU-cycle frequency of all edge servers
:param bandwidth: the bandwidth of allocated edge sites for mobile devices (static allocation) (unit: Hz)
:param noise: the background noise power of edge sites (unit: W)
:param transmit_power: the transmitting power of mobile devices (unit: W)
:param path_loss_const: the pass-loss constant for transmission
:param min_distance: the minimum distance from mobile device to edge site under wireless signal coverage
:param max_distance: the maximum distance from mobile device to edge site under wireless signal coverage
:param max_channel_power_gain: the 'empirical' maximum channel power gain under exponential distribution
with 4e8 trials
:param max_harvest_energy: the maximum harvestable energy at each time slot (unit: J)
:param v: the tuning parameter of Lyapunov Optimization (unit: J^2/sec) [--tunable--]
"""
# =============================== basic parameters ===============================
# parameters for scenario construction
self.__time_slot_length = time_slot_length
self.__time_horizon = time_horizon
self.__ddl = ddl
self.__drop_penalty = drop_penalty
self.__coordinate_cost = coordinate_cost
self.__task_request_prob = task_request_prob
self.__unit_cpu_num = unit_cpu_num
# parameters for local execution
self.__local_input_size = local_input_size
self.__local_cpu_freq = local_cpu_freq
self.__switched_cap = switched_cap
self.__max_transient_discharge = max_transient_discharge
# parameter for edge execution
self.__edge_input_size = edge_input_size
self.__max_assign = max_assign
self.__edge_cpu_freq = edge_cpu_freq
# parameter for communication, energy harvesting and V
self.__bandwidth = bandwidth
self.__noise = noise
self.__transmit_power = transmit_power
self.__path_loss_const = path_loss_const
self.__min_distance = min_distance
self.__max_distance = max_distance
self.__max_channel_power_gain = max_channel_power_gain
self.__max_harvest_energy = max_harvest_energy
self.__v = v
# =============================== position information ===============================
# read scenario data from dataset: initial users and servers' position
self.__user_info, self.__edge_info = self.import_scenario()
# get number of edge servers and users
self.__user_num = len(self.__user_info)
self.__server_num = len(self.__edge_info)
# user position information
self.__connectable_servers, self.__connectable_users, self.__connectable_distances, self.__connectable_gains, \
self.__global_distances = self.obtain_wireless_signal_coverage()
# mobility management
self.__latitude_drv, self.__longitude_drv = self.obtain_derivation()
# =============================== random events ===============================
self.__harvestable_energys = ToolFunction.generate_harvestable_energys(self.__max_harvest_energy,
self.__user_num)
self.__task_requests = self.generate_task_request()
# =============================== execution & cost information ===============================
# calculate local execution time
self.__local_exe_time = self.__local_input_size * self.__unit_cpu_num / self.__local_cpu_freq
# calculate local execution energy consumption
self.__local_exe_energy = self.__switched_cap * self.__local_input_size * self.__unit_cpu_num * \
(self.__local_cpu_freq ** 2)
# calculate the lower bound of perturbation parameter
self.__perturbation_para = self.obtain_perturbation_para()
# calculate the dimension size
self.__dim_size = self.calculate_dim_size()