Cost analysis

Flop Count

Objective Functions

• Sum = dim * 1
• Sum of Squares = dim * 2
• Sphere = dim * 2
• Griewank = dim * 6
• Rastigrin = dim * 7
• Rosenbrock = (dim-1) * 8

GWO

Total Flops = 4n + population_size * objective_func_flopCount + max_iter(31n + population_size*objective_func_flopCount)

Pengu

Squirrel

Total Flops =

PSO

• n = population_size*dim

Flop count for each function

• pso_rand_init = 5n
• pso_eval_fitness = population_size*objective_func_flopCount
• pso_gen_init_velocity = 5 + 2n
• pso_generate_vel_limit = 2 flops
• pso_update_velocity = 11n flops
• pso_update_position = n flops

Flop Count in Initialization

• 7 + 7n + population_size*objective_func_flopCount flops

Flop Count Iteration

• max_iter*(12n + swarm_size*obj_func_flops) flops

Total Flop Count

• 7 + 7n + swarm_size*obj_func_flops + max_iter*(12n + swarm_size*obj_func_flops) flops

Memory Usage

PSO

Initialisation

All in number of floats:

• min_vel = 1
• max_vel = 1
• current_positions = dim * swarm size
• local_best_position = dim * swarm size
• current_fitness = swarm size
• local_best_fitness = swarm size
• p_velocity = dim * swarm size
• global_best_fitness = 1 (copy)
• pso_best_fitness() uses 1 temporary float
• pso_gen_init_velocity() temporarily assigns swarm size * dim array

Iteration

For every iteration:

• pso_best_fitness() uses 1 temporary float, called once per iteration

Teardown

Solution memory allocation:

• best_solution = dim

Total Memory Usage

This does not count the temporary allocation in the initialization of pso_gen_init_velocity().

In floats:

4 + 3(dim * swarm) + (2 * swarm) + iter + dim

In bytes:

16 + 12(dim * swarm) + (8 * swarm) + [4 * (iter + dim)]

Example

For dimension size 100, swarm size 10^6, iteration count 1000:

16 + 12*10^8 + 8*10^6 + 4*1100 = 1,208,004,416 = 2^(30.17)

This is slightly more than 1GB of memory (2^(30) bytes). Note that memory consumption is mostly determined by the 12(dim * swarm) term.