# Performance of Multi-chaotic PSO on a shifted benchmark functions set

## Summary (1 min read)

### INTRODUCTION

- In recent years there has been a significant development in the area of evolutionary computational techniques (ECTs) such as the PSO algorithm [1] [2] [3] [4] .
- In this research the performance of PSO algorithm with multi-chaotic PRNG [9] is investigated on two shifted benchmark functions.
- The shifted benchmark functions are designed in order to better simulate the time-variant real-world problems.

### PARTICLE SWARM OPTIMIZATION ALGORITHM

- The PSO algorithm is inspired in the natural swarm behavior of birds and fish.
- Each particle in the population represents a candidate solution for the optimization problem that is defined by the cost function (CF).
- The maximum velocity was limited to 0.2 times the range as it is usual.
- Finally the linear decreasing inertia weight [3, 4] is used in the typically referred GPSO design that was used in this study.
- A new w for each iteration is given by (3), where t stands for current iteration number and n stands for the total number of iterations.

### TEST FUNCTIONS

- In order to investigate on the performance of multi-chaotic PSO algorithm on functions closer to real problem than static test function, two shifted function were chosen.
- Shifted function global optimum moves with each start of the algorithm but keeps their basic characteristic thus simulates the time-variant real problems.
- Following shifted test functions were used in this study.

### EXPERIMENT

- Two different instances of multi-chaotic PSO [9] are investigated here.
- In the multi-chaotic approach two different CPRNGs are switched when the algorithm seems to stagnate (for details see [9] ).
- In the first design in this study the optimization starts with Lozi map based CPRNG and it is switched to CPRNG based on Arnold´s Cat map.
- In the second design the CPRNGs are used in opposite order.

### CONCLUSION

- In this study the performance of multi-chaotic PSO was investigated on two different shifted benchmark functions.
- The aim was to investigate the performance of this design on closer to real-world problems.
- Results presented in this work support claim that using two different CPRNGs within one run of the algorithm may improve the performance of PSO algorithm on various optimization tasks.
- The second designed combination of Arnold´s Cat map based CPRNG and Lozi map based CPRNG outperformed the canonical version in both cases.

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##### References

35,104 citations

### "Performance of Multi-chaotic PSO on..." refers background in this paper

...INTRODUCTION In recent years there has been a significant development in the area of evolutionary computational techniques (ECTs) such as the PSO algorithm [1-4]....

[...]

...It was introduced by Eberhart and Kennedy in 1995 [1]....

[...]

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### "Performance of Multi-chaotic PSO on..." refers background or methods in this paper

...The new position of each particle is then given by (2), where xi is the new particle position: 1 1 t i t i t i v x x (2) Finally the linear decreasing inertia weight [3, 4] is used in the typically referred GPSO design that was used in this study....

[...]

...INTRODUCTION In recent years there has been a significant development in the area of evolutionary computational techniques (ECTs) such as the PSO algorithm [1-4]....

[...]

1,687 citations

689 citations

### "Performance of Multi-chaotic PSO on..." refers background or methods in this paper

...The new position of each particle is then given by (2), where xi is the new particle position: 1 1 t i t i t i v x x (2) Finally the linear decreasing inertia weight [3, 4] is used in the typically referred GPSO design that was used in this study....

[...]

...INTRODUCTION In recent years there has been a significant development in the area of evolutionary computational techniques (ECTs) such as the PSO algorithm [1-4]....

[...]