Firefly Algorithm for Cardinality Constrained Mean-Variance Portfolio Optimization Problem with Entropy Diversity Constraint

Table 5

Experimental results for five metaheuristics.

Index	𝑁	Performance indicators	GA	TS	SA	PSO	mFA
Hang Seng	31	Mean Euclidean distance	0.0040	0.0040	0.0040	0.0049	0.0003
		Variance of return error (%)	1.6441	1.6578	1.6628	2.2421	1.2387
		Mean return error (%)	0.6072	0.6107	0.6238	0.7427	0.4715
		Execution time	18	9	10	34	20
DAX 100	85	Mean Euclidean distance	0.0076	0.0082	0.0078	0.0090	0.0009
		Variance of return error (%)	7.2180	9.0309	8.5485	6.8588	7.2569
		Mean return error (%)	1.2791	1.9078	1.2817	1.5885	1.3786
		Execution time	99	42	52	179	71
FTSE 100	89	Mean Euclidean distance	0.0020	0.0021	0.0021	0.0022	0.0004
		Variance of return error (%)	2.8660	4.0123	3.8205	3.0596	2.7085
		Mean return error (%)	0.3277	0.3298	0.3304	0.3640	0.3121
		Execution time	106	42	55	190	94
S&P 100	98	Mean Euclidean distance	0.0041	0.0041	0.0041	0.0052	0.0003
		Variance of return error (%)	3.4802	5.7139	5.4247	3.9136	3.6026
		Mean return error (%)	1.2258	0.7125	0.8416	1.4040	0.8993
		Execution time	126	51	66	214	148
Nikkei	225	Mean Euclidean distance	0.0093	0.0010	0.0010	0.0019	0.0000
		Variance of return error (%)	1.2056	1.2431	1.2017	2.4274	1.2015
		Mean return error (%)	5.3266	0.4207	0.4126	0.7997	0.4892
		Execution time	742	234	286	919	367