A binary particle swarm optimization based on the surrogate information with proportional acceleration coefficients for the 0-1 multidimensional knapsack problem

The 0-1 multidimensional knapsack problem (MKP) has been proven it belongs to difficult NP-hard combinatorial optimization problems. There are various search algorithms based on population concept to solve these problems. The particle swarm optimization (PSO) technique is adapted in our study, which proposes a novel PSO algorithm, namely, the binary PSO based on surrogate information with proportional acceleration coefficients (BPSOSIPAC). The proposed algorithm was tested on 135 benchmark problems from the OR-Library to validate and demonstrate the efficiency in solving multidimensional knapsack problems. The results were then compared with those in the other nine existing PSO algorithms. The simulation and evaluation results showed that the proposed algorithm, BPSOSIPAC, is superior to the other methods according to success rate, average number of function evaluations, average number of function evaluations of successful runs, average error (AE), mean absolute deviation, mean absolute percentage error, least error, standard deviation, best profit, mean profit, worst profit, AE of best profit (%), and AE of mean profit deviation (%).

[1]  S. Senju,et al.  An Approach to Linear Programming with 0--1 Variables , 1968 .

[2]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

[3]  Seth D. Guikema,et al.  Enhanced speciation in particle swarm optimization for multi-modal problems , 2011, Eur. J. Oper. Res..

[4]  Saman K. Halgamuge,et al.  Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients , 2004, IEEE Transactions on Evolutionary Computation.

[5]  Jing J. Liang,et al.  Comprehensive learning particle swarm optimizer for global optimization of multimodal functions , 2006, IEEE Transactions on Evolutionary Computation.

[6]  Hasan Pirkul,et al.  A heuristic solution procedure for the multiconstraint zero‐one knapsack problem , 1987 .

[7]  Russell C. Eberhart,et al.  A discrete binary version of the particle swarm algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[8]  J. Kennedy,et al.  Population structure and particle swarm performance , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[9]  Russell C. Eberhart,et al.  chapter seven – The Particle Swarm , 2001 .

[10]  Y. Toyoda.  A Simplified Algorithm for Obtaining Approximate Solutions to Zero-One Programming Problems , 1975 .

[11]  Maw-Sheng Chern,et al.  Particle swarm optimization with time-varying acceleration coefficients for the multidimensional knapsack problem , 2014 .

[12]  Yupu Yang,et al.  Particle swarm with equilibrium strategy of selection for multi-objective optimization , 2010, Eur. J. Oper. Res..

[13]  Magdalene Marinaki,et al.  A Hybrid Multi-Swarm Particle Swarm Optimization algorithm for the Probabilistic Traveling Salesman Problem , 2010, Comput. Oper. Res..

[14]  Gary G. Yen,et al.  Immune-inspired evolutionary algorithm for constrained optimization , 2012, 2012 IEEE Congress on Evolutionary Computation.

[15]  Ramiro Villeda Rodriguez,et al.  ORLIB, an operations research library , 1981 .

[16]  R. J. Kuo,et al.  Integration of particle swarm optimization-based fuzzy neural network and artificial neural network for supplier selection , 2010 .

[17]  G. Raidl,et al.  An improved genetic algorithm for the multiconstrained 0-1 knapsack problem , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[18]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[19]  Min Kong,et al.  A new ant colony optimization algorithm for the multidimensional Knapsack problem , 2008, Comput. Oper. Res..

[20]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[21]  Siti Mariyam Hj. Shamsuddin,et al.  Binary Accelerated Particle Swarm Algorithm (BAPSA) for discrete optimization problems , 2012, Journal of Global Optimization.

[22]  John E. Beasley,et al.  A Genetic Algorithm for the Multidimensional Knapsack Problem , 1998, J. Heuristics.

[23]  Alper Ekrem Murat,et al.  A discrete particle swarm optimization method for feature selection in binary classification problems , 2010, Eur. J. Oper. Res..

[24]  LiFeng-Chia,et al.  Particle swarm optimization for the economic and economic statistical designs of the control chart , 2011 .

[25]  R. Eberhart,et al.  Empirical study of particle swarm optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[26]  Kusum Deep,et al.  A Modified Binary Particle Swarm Optimization for Knapsack Problems , 2012, Appl. Math. Comput..

[27]  Li-Yeh Chuang,et al.  Chaotic maps based on binary particle swarm optimization for feature selection , 2011, Appl. Soft Comput..

[28]  Mauro Birattari,et al.  Swarm Intelligence , 2012, Lecture Notes in Computer Science.

[29]  Arnaud Fréville,et al.  The multidimensional 0-1 knapsack problem: An overview , 2004, Eur. J. Oper. Res..

[30]  Samuel P. Marin,et al.  Balancing and optimizing a portfolio of R&D projects , 2001 .

[31]  Aijia Ouyang,et al.  A hybrid immune PSO for constrained optimization problems , 2010, 2010 IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA).

[32]  G. Raidl.  Weight-codings in a genetic algorithm for the multi-constraint knapsack problem , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[33]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[34]  Labed Said,et al.  A Modified Hybrid Particle Swarm Optimization Algorithm for Multidimensional Knapsack Problem , 2011 .

[35]  Nicos Christofides,et al.  Capital Budgeting Under Uncertainty - An Integrated Approach Using Contingent Claims Analysis and Integer Programming , 2001, Oper. Res..

[36]  Abdollah Homaifar,et al.  Constrained Optimization Via Genetic Algorithms , 1994, Simul..

[37]  Ali Azadeh,et al.  A particle swarm algorithm for inspection optimization in serial multi-stage processes , 2012 .

[38]  Min Kong,et al.  Apply the Particle Swarm Optimization to the Multidimensional Knapsack Problem , 2006, ICAISC.

[39]  Kusum Deep,et al.  A Socio-Cognitive Particle Swarm Optimization for Multi-Dimensional Knapsack Problem , 2008, 2008 First International Conference on Emerging Trends in Engineering and Technology.

[40]  Jun Zhang,et al.  A Novel Set-Based Particle Swarm Optimization Method for Discrete Optimization Problems , 2010, IEEE Transactions on Evolutionary Computation.