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The selection process is an important part of any optimization algorithm. Usually, an efficient selection process should balance between exploration of the search space and exploitation of the current knowledge about the best solutions. Cuckoo search (CS) is a simple yet powerful optimization algorithm inspired by the parasitic reproduction behavio...
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... n is the number of solutions. Table 1 shows an example of random selection scheme for 4 solutions ranked from best to worst. Each solution has an equal opportunity to be selected as a cuckoo that can be enhanced using Lévy flight (p i = 1/4 = 0.25). ...
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... all comparative tables, the best result for each benchmark function is highlighted with bold. Tables 8 to 11 (10D, 30D, 100D and 1000D, receptively) show the experimental results for each of the 20 benchmark functions described in Table 6. The results are in the format: average of best solutions over 100 independent runs (first row), standard deviation of the best (second row) and error function value EFV (third row) for the average of the best solutions. ...
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... EFV measures the distance from the global optimal solution to the average of the best solutions [32]. Table 7 shows a summary of Tables 8 to 11. The overall results suggest that all the proposed variations of the CS algorithm outperform the original CS algorithm (RCS variation). ...
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... in Tables 8 and 9, the obtained results in Table 10 (D=100 test functions) suggest that all the variations of CS perform better than RCS. Apparently, BCS achieves five best results for F2, F5,F10, F16 and F18 functions and EGCS achieves five best results for F4, F6, F7, F11 and F20 functions. ...
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... BCS achieves five best results for F2, F5,F10, F16 and F18 functions and EGCS achieves five best results for F4, F6, F7, F11 and F20 functions. No significant observation was noted when the dimensionality of the problems was increased to 1,000 as shown in Table 11. The only notable observation is that EGCS performs better than the other variations for six functions. ...
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... EGCS outperforms the other variations for complex test functions (selected functions from CEC 2005, F11-F20 in the current paper). Table 16 summarizes the experimental results of the variations of CS using the 20 test functions described in Table 6. The results are in the format: average number of iterations ±, standard deviation of iterations and the percentage of enhancement compared to RCS is given between two parentheses. ...
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... results are in the format: average number of iterations ±, standard deviation of iterations and the percentage of enhancement compared to RCS is given between two parentheses. In Table 16, the number of iterations for each algorithm was recorded when one of the following conditions is satisfied: ...
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... can be observed from Table 16 that the GCS and PCS variations converge faster to solutions for 5 test functions each (unimodal or basic multimodal functions). This may be because GCS follows a greedy approach that is suitable for reproducing solutions for simple functions. ...
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... µ 7 H 1 : at least one mean is different from the others. Tables 12 to 15 provide the ANOVA results for all the test functions with different dimensions (Table 12: D=10, Table 13: D=30, Table 14: D=100 and Table 15: D=1,000). As shown in the tables, the P -value for all the problems except for F3 (Step Function) is less than 5% and the value of F calculated (F -cal) is larger than the value of F critical (F -crit). ...
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... µ 7 H 1 : at least one mean is different from the others. Tables 12 to 15 provide the ANOVA results for all the test functions with different dimensions (Table 12: D=10, Table 13: D=30, Table 14: D=100 and Table 15: D=1,000). As shown in the tables, the P -value for all the problems except for F3 (Step Function) is less than 5% and the value of F calculated (F -cal) is larger than the value of F critical (F -crit). ...
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... 6.40E-05 5.37E-05 3.60E-05 Table 10: Experimental results of seven variations of cuckoo search for twenty benchmark functions, D=100, runs=100, iterations=10,000. RCS GCS PCS BCS ECS EGCS RLCS F1 1.79E-06 3.21E-07 4.49E-07 4.68E-07 2.84E-07 3.26E-07 2.25E-07 4.04E-06 4.27E-07 7.27E-07 8.56E-07 4.05E-07 7.14E-07 3.60E-07 1.79E-06 ...
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... 6.40E-05 5.37E-05 3.60E-05 Table 10: Experimental results of seven variations of cuckoo search for twenty benchmark functions, D=100, runs=100, iterations=10,000. RCS GCS PCS BCS ECS EGCS RLCS F1 1.79E-06 3.21E-07 4.49E-07 4.68E-07 2.84E-07 3.26E-07 2.25E-07 4.04E-06 4.27E-07 7.27E-07 8.56E-07 4.05E-07 7.14E-07 3.60E-07 1.79E-06 ...
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... Their selection is predicated on their consistent performance and resilience across diverse optimization challenges. Their legacy of success, coupled with their inherent capabilities of exploration and exploitation, underscores their suitability for our ambitious undertaking [11]. To elevate the potential of these bio-inspired solvers, we incorporate the ability of the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm, a wide-known clustering methodology by the scientific community [13,14]. ...
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... Big Sur. The algorithms were all programmed in Java . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 The size of population n and the fraction of abandon solutions p a in i CSPM and i CSPM2 were dynamically tuned over multiple simulations as recommended in [55]. The maximum number of iterations of each algorithm was limited to 10,000. ...
The Island Cuckoo Search ( i CSPM) algorithm is a new variation of Cuckoo Search (CS) that uses the island model and the Highly Disruptive Polynomial (HDP) mutation for solving a broad range of optimization problems. This article introduces an improved i CSPM algorithm called i CSPM with elite opposition-based learning and multiple mutation methods ( i CSPM2). i CSPM2 has three main characteristics. Firstly, it separates candidate solutions into a number of islands (sub-populations) and then divides the islands equally among four improved versions of CS: CS via Le'vy fights (CS1) [1], CS with HDPM mutation (CS10) [2], CS with Jaya mutation (CSJ) and CS with pitch adjustment mutation (CS11) [2]. Secondly, it uses Elite Opposition-based Learning (EOBL) to improve its convergence rate and exploration ability. Finally, it uses the Smallest Position Value (SPV) with scheduling problems to convert continuous candidate solutions into discrete ones. A set of 15 popular benchmark functions was used to compare the performance of iCSPM2 to the performance of the original i CSPM algorithm based on different experimental scenarios. Results indicate that i CSPM2 exhibits improved performance over i CSPM. However, the sensitivity analysis of i CSPM and i CSPM2 to their parameters indicates that their convergence behavior is sensitive to the island model parameters. Further, the single-objective IEEE CEC 2014 functions were used to evaluate and compare the performance of iCSPM2 to four well-known swarm optimization algorithms: DGWO [3], L-SHADE [4], MHDA [5] and FWA-DM [6]. The overall experimental and statistical results suggest that i CSPM2 has better performance than the four well-known swarm optimization algorithms. i CSPM2's performance was also compared to two powerful discrete optimization algorithms (GAIbH [7] and MASC [8]) using a set of Taillard's benchmark instances for the permutation flow shop scheduling problem. The results indicate that i CSPM2 performs better than GAIbH and MASC. The source code of i CSPM2 is publicly available at https://github.com/bilalh2021/iCSPM2
... The relevant efforts can be clustered into two main streams, namely the problem-independent and problem-dependent improvements. The former one enhances the performance by developing novel search operators such as selection scheme [22], migration strategy [23], and self-adapting control mechanism [24], which expands the application scope of the heuristic algorithms. The problem-dependent improvement incorporates the problem knowledge to construct the systematic rules so that the invalid search is reduced. ...
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