Logic gate-based evolutionary algorithm for the multidimensional knapsack problem

Imperialist Competitive Algorithm with Independence and Constrained Assimilation

“…Next, large Glover and Kochenberger (GK) instances were solved and compared to eight heuristic algorithms from the literature in terms of average error percent (3) gap against best-known profit (BKS) from the literature. Compared algorithms include ACOwD, IWOA, Two-phase tabuevolutionary algorithm (TPTEA) [35], harmony search based algorithm NBHS2 proposed in [40], evolutionary algorithm with logic gates LGEA [36], shuffled complex evolution algorithm SCEcr [37], hyper-heuristic inspired CF-LAS [72] and BCSA -binary cuckoo search algorithm [41]. Table 3 is colour coded from red (worst average error %) to the best average error percent, in green, for each problem instance with dashes (-) representing scores that were not available.…”

“…ACOwD [31] NBHS2 [40] IWOA [42] LGEA [36] TPTEA [35] SCEcr [37] CF-LAS [72] BCSA [41] ICAwICA (this work)…”

“…It is worth noting that the average time to solution 𝑡 𝑎𝑣𝑔 (𝑠) almost doubles when solving instances with tightness Average error of mean profit on WEISH1-30 instances SACRO-BPPSO-TVAC [19] SACRO-CBPPSO-TVAC [19] QPSO* [18] TPTEA [15] SACRO-BPPSO-TVAC [19] SACRO-CBPPSO-TVAC [19] QPSO* [18] Avg Best 𝒕 𝒂𝒗𝒈 (𝒔) Finally, large Glover and Kochenberger (GK) instances were solved and compared to eight heuristic algorithms from the literature in terms of average error percent (2) gap against best known profit from the literature. Compared algorithms include ACOwD, IWOA, TPTEA, harmony search based algorithm NBHS2 proposed in [20], evolutionary algorithm with logic gates LGEA [16], shuffled complex evolution algorithm SCEcr [17], hyper-heuristic inspired CF-LAS [44] and BCSAbinary cuckoo search algorithm [21]. Table 4 is colour coded from red (worst average error %) to the best average error percent, in green, for each problem instance with dashes (-) representing scores that were not available.…”

“…Further investigation needs to be conducted to improve performance on the most complex benchmarks. LGEA [16] TPTEA [15] SCEcr [17] CF-LAS [44] BCSA [21] ICAwICA…”

“…Comprehensive literature review of solving MKPs was provided by [8] and a more recent MKP overview by [9] summarizes algorithms used for solving MKP. This paper focuses on the state-of-the-art population and metaheuristic algorithms used for solving MKP instances, such as ant colony optimization ( [10], [11]), various types of genetic algorithms ( [12], [13], [14]), evolutionary algorithms ( [15], [16], [17]), variations of particle swarm optimization algorithm ( [18], [19]), binary harmony search [20], binary cuckoo search algorithm [21], whale optimization algorithm [22] and etc. Most of the research in population-based algorithms focuses on small MKP instances with 𝑛 ≤ 100, while only few explore large instances with 𝑛 = 500 and above.…”