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A Novel Musical Chairs Optimization Algorithm

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Abstract

A novel optimization algorithm called musical chairs algorithm (MCA) is introduced in this paper for a shorter convergence time and lower failure rate compared to other optimization algorithms. This idea is implemented by using several search agents at the beginning of optimization steps and reduces this number gradually by removing the worst solutions. This idea is inspired by the musical chairs game in which the players and chairs are reduced by one in each round of the game. The proposed methodology has been compared with 10 other optimization algorithms for 10 benchmark functions. The results obtained from this comparison study showed superior performance of the MCA compared to the other optimization algorithms for all benchmark functions and different numbers of search agents. The convergence time varied between 3.8% and 18.2% compared to the average convergence time for all optimization algorithms applied with all benchmark functions. At the same time, the failure rate of the MCA is 0% for all the benchmark functions, but other optimization algorithms give a percentage of the failure rate. Moreover, the MCA is applied to feature selection of load forecasting as a real-world application which is vital for smart grid applications. The MCA is modified from continuous to binary MCA (BMCA). The BMCA is compared to several optimization algorithms, where it outperforms other optimization algorithms to select the best set of features to quickly and correctly learn the forecasting model. The accuracy of the obtained results from BMCA is increased to 96.7% compared to 70% of other algorithms, and the convergence time is reduced to 0.096 s compared to 18 s for other optimization algorithms. The outstanding results of MCA compared to the other optimization algorithms prove its superiority for all types of applications even with very complex benchmark functions.

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Abbreviations

MCA:

Musical chairs algorithm

BMCA:

Binary musical chairs algorithm

SO:

Snake optimizer

FLA:

Fick's law algorithm

NFL:

No free lunch

PSO:

Particle swarm optimization

BA:

Bat algorithm

NESTPSO:

Nested particle swarm optimization

BA-BA:

Bat algorithm-bat algorithm or nested bat algorithm

MPPT:

Maximum power point tracker

PV:

Photovoltaic

LSA:

Lightning search algorithm

ALO:

Ant lion optimizer

MFO:

Moth-flame optimization

CSA:

Crow search algorithm

HHO:

Harris hawk optimizer

NB:

Naïve Bayes

IPSO:

Improved particle swarm optimization

GWO:

Gray wolf optimization

IGWO:

Improved gray wolf optimization

WOA:

Whale optimization algorithm

FA:

Firefly algorithm

Chimp:

Chimpanzee algorithm

SCA:

Sine cosine algorithm

F1, F2,…., F10:

Labels of the 10 benchmark functions, which are; De Jong’s sphere, Schwefel’s problems 2.22, Schwefel’s problem 1.2, Schwefel’s problem 2.21, Ackley, Rastrigin, Brown, Powell Sum, Griewank, and Salomon

V i(t + 1):

The speed of ith particle at the next iteration

V i(t):

The speed of ith particle at the current iteration

t :

An index of the current iteration

P p i(t):

The best position of ith particle (the personal best position) at the current iteration

P i(t):

The current position of ith particle at the current iteration

P G(t):

The best position in the swarm (the global best position) at the current iteration

P i(t + 1):

The update position of ith particle at the next iteration

ω :

The inertia weight

c 1 and c 2 :

The cognitive constant and the social acceleration constant, respectively

r 1 and r 2 :

Two random numbers which are independently generated

Y :

The constriction factor used to represent the relation between the control parameters of the PSO

bVc :

The best fitness value of chairs

bPc :

The best position of chairs

\(\vec{V}_{{\text{c}}}\) :

A vector representing the fitness values of chairs

\(P_{p,{k}}^{g}\) :

The position of player k at the iteration g

K :

The order of each player, K = K0, K0 −1,…..2

K 0 :

The starting number of search agents (swarm size)

g :

The generation (iteration) number, g = 1,2,…..,G,…., G0

G :

The total number of iterations when the stopping strategy is validated

G 0 :

The maximum number of iterations

M :

The increment or step size of the MCA

\(u\) and v :

Two matrices with a uniform distribution

σ u and σ v :

The variances of u and v, respectively

β :

L’evy flights that provide a random walk for players

R :

A random variable (\(R \in [ - 1,\;1]\))

P pk :

Initial positions of K0 players; Ppk (k = 1,2,….., K0)

V p(P p):

The objective function for all players; Pp = (Pp1, Pp2,…..,Pp,K+1)T

\(\vec{V}_{p}^{g}\) :

The vector representing the values of search agents (players) during the iteration g

\(\varepsilon_{1}\) :

A predefined tolerance value (\(\varepsilon_{1}\) is selected to be 10–5 in this study)

std:

The standard deviation

NSS:

The number of calling the objective function (convergence time)

N T :

The whole number of occurrences

FR:

Failure Rate

N F :

The whole number of failure occurrences

\({\text{bV}}_{c}^{G}\) :

The best fitness value obtained from each simulation in every single run

\(V_{{{\text{opt}}}}\) :

The known optimum fitness value

\(\varepsilon_{2}\) :

Predefined tolerance to represent the maximum allowable difference between the best fitness and the theoretical best fitness of each benchmark function under study

fet:

The total number of electrical features

v Pk :

The fitness value of the kth player

A(P k):

The accuracy of the NB method based on the chosen features in the kth player

P f bin_k(iteration + 1):

The binary value of kth player at fth binary bit in the next iteration iteration + 1

r(0,1):

A random value between [0, 1]

s(Pf k):

The sigmoid function which represents the probability of fth binary bit where it takes 0 or 1 value

e :

The base of the natural logarithm

D :

The variable that refers to the order of objective function (Dimensionality)

f min :

The global minima that represent the minimum fitness value

u b and l b :

The upper bound and lower bound respectively

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Acknowledgements

This work was supported by the King Saud University, Saudi Arabia, Deanship of Scientific research, Research Chair Saudi Electricity Company Chair in Power System Reliability and Security.

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Authors and Affiliations

  1. Sustainable Energy Technologies Center, King Saud University, Riyadh, 11421, Saudi Arabia

    Ali M. Eltamaly

  2. Electrical Engineering Department, Mansoura University, Mansoura, Egypt

    Ali M. Eltamaly

  3. K.A.CARE Energy Research and Innovation Center at Riyadh, Riyadh, 11451, Saudi Arabia

    Ali M. Eltamaly

  4. Saudi Electricity Company Chair in Power System Reliability and Security, King Saud University, Riyadh, 11421, Saudi Arabia

    Ali M. Eltamaly

  5. Computers and Control Department, Faculty of Engineering Mansoura University, Mansoura, Egypt

    Asmaa H. Rabie

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  1. Ali M. Eltamaly
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Correspondence to Ali M. Eltamaly.

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Eltamaly, A.M., Rabie, A.H. A Novel Musical Chairs Optimization Algorithm. Arab J Sci Eng 48, 10371–10403 (2023). https://doi.org/10.1007/s13369-023-07610-5

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