Cognitive discrete gravitational search algorithm for solving 0-1 knapsack problem

Abstract

The Gravitational Search Algorithm (GSA) has been proposed for solving continues problems based on the law of gravity. In this paper, we propose a Cognitive Discrete GSA (called CDGSA) for solving 0-1 knapsack problem. The GSA has used a function of time to determine the number of the best particles for attracting others in each time, while our main idea is based on attracting each particle with two cognitive and social components. The cognitive component contains the best position of the particles up to now, while the social component contains the particle with the best position in the whole of the system at the current time and the particles with the best position in the neighborhood. In the other words, the cognitive component is such an appropriate actuator for embedding in the intelligent agents like robots. Such intelligent agent or robot is guided in the right direction with the help of its best previous position. Finally, by introducing discrete version of this idea, the efficiency of the proposed algorithm is measured for 0-1 knapsack problem. Experimental results on some benchmark and high dimensional problems illustrate that the proposed algorithm has gained the better accuracy in comparison of the other similar methods.

Fast Polynomial Time Approximate Solution for 0-1 Knapsack Problem

“…So the upper bound of KP is (8). e solution of L (19, λ 19 ) is u (19) � (u d 19i )as follows: 1,4,7,5,3,10,6,9,16,8,13,18,11,26,20,21,17,14,27,28,23,12,15,19,30,25,24,22,29).…”

“…While PTAS for KP typically require only O ( n ) storage, all FPTAS are based on dynamic programming and their memory requirement increases rapidly with the accuracy ɛ , which makes them impractical even for relatively big values of ɛ [ 3 ]. Heuristics rules are adopted to decrease the calculation in searching accurate approximation, such as harmony search algorithm [ 4 , 5 ], amoeboid organism algorithm [ 6 ], cuckoo search algorithm [ 5 , 7 ], binary monarch butterfly optimization [ 8 ], cognitive discrete gravitational search algorithm [ 9 ], bat algorithm [ 10 ], and wind driven optimization [ 11 ]. Nowadays, it is tend to combine different heuristics together in solving combinatorial optimization problem, such as mixed-variable differentiate evolution [ 12 ], self-adaptive differential evolution algorithm [ 13 ], two-stage cooperative evolutionary algorithm [ 14 ], cooperative water wave optimization algorithm with reinforcement learning [ 15 ], and cooperative multi-stage hyper-heuristic algorithm [ 16 ].…”

A Feature-Independent Hyper-Heuristic Approach for Solving the Knapsack Problem

“…Gómez et al proposed a Binary Particle Swarm strategy with a genetic operator, also for the multidimensional KP [36]. Another example of recent solving methods includes the one by Razavi and Sajedi, where the authors proposed using Gravitational Search (GSA) for solving the 0/1 KP [37]. Inspired by Quantum Computing, Patvardhan et al proposed a novel method to solve the KP by using a Quantum-Inspired Evolutionary Algorithm [38].…”

Binary social group optimization algorithm for solving 0-1 knapsack problem

“…Greedy strategy based self-adaption ant colony algorithm is introduced for the 0-1 knapsack problem (Du & Zu, 2015). In addition, many algorithms have been prospered for solving 0-1 KP such as Cognitive discrete gravitational search algorithm(CDGSA) (Razavi & Sajedi, 2015), wind driven Optimization(WDO) (Zhou et al, 2017), greedy degree and expectation efficiency (Lv et al, 2016), improved monkey algorithm (IMA) (Zhou et al, 2016a), monogamous pairs genetic algorithm (MPGA) (Lim et al, 2016), hybrid greedy and particle swarm (GPSO) (Nguyen, Wang & Truong, 2016), Quantum inspired social evolution (QSE) algorithm (Pavithr, 2016), binary particle swarm optimization based on the surrogate information with proportional acceleration coefficients (Lin et al, 2016), complex-valued encoding bat algorithm (Zhou et al, 2016b), cohort intelligence (CI) algorithm (Kulkarni et al, 2017), Migrating birds optimization (MBO) algorithm (Ulker & Tongur, 2017), binary flower pollination algorithm (BFPA) (Abdel-Basset et al, 2018a), binary bat algorithm (BBA) (Rizk-Allah et al, 2018), Social-Spider Optimization(SSO) Algorithm Nguyen et al, 2017), binary monarch butterfly optimization(BMBO) (Feng et al, 2016a), Binary Dragonfly Algorithm(BDA) (Abdel-Basset at al., 2017), Binary Fisherman Search (BFS) algorithm (Cobos et al, 2016),elite opposition-flower pollination algorithm (EOFPA) (Abdel-Basset et al, 2018b), Opposition-based learning monarch butterfly optimization with Gaussian perturbation(OLMBO) (Feng et al, 2017). In respect of the importance of knapsack problem in practical applications, developing new algorithms to solve large-scale types of knapsack problem applications undoubtedly becomes a true challenge.…”