A self-adaptive multi-population based Jaya algorithm for engineering optimization
Introduction
Solving the complex optimization problems in the limited time is an indispensable issue in the field of engineering optimization. Due to the complexity of the problems the conventional methods become tedious and time consuming and these approaches do not guarantee the achievement of the optimal solution. Therefore, metaheuristic based computational methods are developed. These methods are capable of achieving the global or near global optimum solution with less information about the problems. Some of the well-known metaheuristic optimization algorithms are: genetic algorithm (GA) and its variants (real coded GA, parallel GA, hybrid interval GA, etc.), simulated annealing (SA) algorithm, tabu search (TS), ant colony optimization (ACO), particle swarm optimization (PSO) and its variants(e.g. niching PSO, culture-based PSO, aging theory inspired PSO, etc.), differential evolution (DE) and its variants (e.g. DE with multi-population ensemble, DE with self-adapting control parameter, DE with optimal external archive, etc.), harmony search algorithm (HS), non-dominated sorting genetic algorithm (NSGA-II), artificial bee colony (ABC) algorithm, imperialist competitive algorithm (ICA), biogeography based optimization (BBO), firefly algorithm (FFA), gravitational search algorithm (GSA), bat algorithm(BA), cuckoo search (CS) etc. Several metaheuristic algorithms are proposed in the last decade. Some prominent algorithms are: galaxy-based search algorithm, spiral optimization, teaching-learning-based optimization (TLBO), differential search algorithm, cuckoo search algorithm (CSA), colliding bodies optimization algorithm, centripetal accelerated particle swarm optimization algorithm, crisscross optimization algorithm, Lons motion algorithm, ant lion optimization, cat swarm optimization, etc. and hybrid algorithms [1], [2], [3], [4].
The advanced optimization algorithms have their own merits but they require tuning of their specific parameters. For example, SA algorithm needs initial annealing temperature and cooling schedule. GA needs proper setting of crossover probability, mutation probability, selection operator, etc.; NSGA-II needs crossover probability, mutation probability, SBX parameter, mutation parameter etc.; PSO needs inertia weight and social and cognitive parameters; HSA needs harmony memory consideration rate, number of improvisations, etc.; BBO algorithm requires immigration rate, emigration rate, etc. Similarly, ICA, DE and other algorithms (except TLBO algorithm) have respective specific parameters to be set for effective execution. These parameters are called algorithm-specific parameters and need to be controlled other than the common control parameters of number of iterations and population size. All population based algorithms need to tune the common control parameters but the algorithm-specific parameters are specific to the particular algorithm and these are also to be tuned as mentioned above.
The performance of the optimization algorithms is much affected by the algorithm-specific parameters. Increase in the computational cost or tending towards the local optimal solution is caused by the improper tuning of these parameters. Hence, to overcome the problem of tuning of algorithm-specific parameters, TLBO algorithm was proposed which is an algorithm-specific parameter less algorithm [2], [4]. Keeping in the view of the good performance of the TLBO algorithm, another algorithm-specific parameter less algorithm has been recently proposed and it is named as Jaya algorithm [5].
Multi-population based advanced optimization methods are used for improving the diversity of search by splitting the entire population into groups (sub-populations) and allocating these throughout the search space so that the problem changes can be detected effectively. This basic idea is used for keeping the diversity of the search process by allocating different sub-populations to different areas. Each population is subjected to either diversifying or intensifying the search processes of the algorithm [6], [7]. The interaction between the sub-populations takes place by means of a merge and divide process whenever there is a change in the solution is observed. The multi-population approaches are found effective while dealing with various problems and these have outperformed the existing fixed population size methods for different problems.
A self-organizing scout's multi-population evolutionary algorithm was proposed for the dynamic optimization problems [8]. A multi-swarm PSO algorithm was proposed by Li and Yang [9]. A clustering-based PSO was proposed by Yang and Li [10]. A multi-population HSA was proposed by Turky and Abdullah [11]. A multiple teacher based TLBO was proposed by Rao and Patel [12] for the optimization of heat exchanger. Nseef et al. [13] proposed a multi-population ABC algorithm for the optimization dynamic optimization problems [13].
The multi-population approaches are useful for maintaining the population diversity. The characteristics of the multi population optimization approaches are useful because [14]:
- a.
Overall diversity of the search process can be maintained by allocating the entire population into groups, because various sub-populations can be situated in different regions of the problem search space.
- b.
These are having the ability of search in various regions simultaneously.
- c.
Population based optimization methods can be easily integrated within this method.
The selection of number of sub-populations is a critical issue in algorithm's performance. It is related with the complexity of the problem. The size of sub-populations continuously changes during the search process. The solutions in the sub-populations may also not be enough for enough diversity. In order to address these issues, the present work proposes a self-adaptive multi-population (SAMP) Jaya algorithm for the engineering optimization problems. In order to effectively monitor the problem landscape changes, the SAMP-Jaya algorithm adaptively changes the number of sub-populations based on the change strength of the problem landscape.
The basic objectives of this study are:
- a.
To propose a SAMP-Jaya algorithm that adapts the number of sub-populations based on the change strength of the problem.
- b.
To investigate the performance of the proposed algorithm on standard benchmark problems.
- c.
To investigate the performance of the proposed algorithm for an engineering application of design of a plate-fin-heat exchanger (PFHE) for minimum entropy generation rate.
The optimization studies in the present work have shown that SAMP-Jaya algorithm is capable of producing highly competitive results in comparison to the latest optimization methods reported. The design of PFHE suggested by the present approach reduces the entropy generation rate in comparison to the other algorithms considered.
The next section describes the working of the proposed SAMP Jaya algorithm.
Section snippets
SAMP Jaya algorithm
The Jaya algorithm is based on the concept that the solution obtained for a given problem should move towards the best solution and avoid the worst solution. Let O(y) is an objective which is being optimized. Assume that at any iteration i, number of design variables is ‘d’ (i.e. q=1, 2… d) and population size ‘P’ (i.e. r =1, 2,…,P). If Yq,r,i is the value of the qth variable for the rth candidate during the ith iteration, then this value is modified as per the following Eq. (2.1).
Optimization results and discussion
The coding of the SAMP-Jaya algorithm is done in MATLAB R2009b and in a HP Pavilion g6 Notebook PC of 4 GB RAM memory, 1.9-GHz AMD A8 4500M APU CPU. Performance of the proposed algorithm is compared with different optimization algorithms: GA and its variants, PSO and its variants, DE and it variants, TLBO etc. For evaluating the performance of the proposed algorithm 30 unconstrained problems (Appendices A1 and A2) (including CEC 2015 functions), 6 constrained problems (Appendix B) and 4 well
Application of SAMP-Jaya algorithm for the case study of a PFHE design
This case study is considered from the literature [49]. The entropy generation minimization is considered as an objective function for a gas-to-air cross flow PFHE. The specific heat duty of the heat exchanger is 160 kW. The maximum dimension of the heat exchanger is 1×1 m2 and maximum number of hot layers is limited to 10. The specification and input data of the PFHE are shown in Table 24.
Various efforts are made by the researchers for developing optimal design of the heat exchanger considering
Conclusions
This study proposes a self-adaptive multi-population Jaya algorithm. The performance of the proposed approach is investigated on the unconstrained and constrained benchmark problems in addition to the computational expensive problems of the CEC 2015. The Friedman rank test is used to find the average rank of the algorithm and it is observed that the proposed algorithm is better than the other algorithms. Furthermore, the proposed method is used for the design optimization problem of a plate-fin
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