Towards Constant Calculation in Disjunctive Inequalities Using Wound Treatment Optimization

When using the mixed-integer programming to model situations where the limit of the variables follows a box constraint, we find nonlinear problems. To solve this, linearization techniques of these disjunctive inequality constraints are typically used, including constants associated to the variable bounds called M-constants or big-M. Calculation of these constants is an open problem since their values affect the reliability of the optimal solution and convergence of the optimization algorithm. To solve this problem, this work proposes a new population-based metaheuristic optimization method, namely wound treatment optimization (WTO) for calculating the M-constant in a typical domain known as the fixed-charge transportation problem. WTO is inspired on the social wound treatment present in ants after raids. This method allows population diversity that allows to find near-optimal solutions. Experiments of the WTO method on the fixed-charge transportation problem validated its performance and efficiency to find tighten solutions of the M-constant that minimizes the objective function of the problem.

[1]  Mustafa Servet Kiran,et al.  Particle swarm optimization with a new update mechanism , 2017, Appl. Soft Comput..

[2]  Ignacio E. Grossmann,et al.  Improved Big-M reformulation for generalized disjunctive programs , 2015, Comput. Chem. Eng..

[3]  Jeffrey D. Camm,et al.  Cutting Big M Down to Size , 1990 .

[4]  Erik T Frank,et al.  Wound treatment and selective help in a termite-hunting ant , 2018, Proceedings of the Royal Society B: Biological Sciences.

[5]  John N. Hooker,et al.  Solving Fixed-Charge Network Flow Problems with a Hybrid Optimization and Constraint Programming Approach , 2002, Ann. Oper. Res..

[6]  Mohammad Shahidehpour,et al.  Optimal Traffic-Power Flow in Urban Electrified Transportation Networks , 2017, IEEE Transactions on Smart Grid.

[7]  Qi Zhang,et al.  Expanding scope and computational challenges in process scheduling , 2018, Comput. Chem. Eng..

[8]  Panos M. Pardalos,et al.  Minimum concave-cost network flow problems: Applications, complexity, and algorithms , 1991 .

[9]  Yudong Zhang,et al.  A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications , 2015 .

[10]  Paolo Toth,et al.  A matheuristic for the two-stage fixed-charge transportation problem , 2018, Comput. Oper. Res..

[11]  Farhad Ghassemi Tari,et al.  Prioritized K-mean clustering hybrid GA for discounted fixed charge transportation problems , 2018, Comput. Ind. Eng..

[12]  Hongbin Sun,et al.  Big-M Based MIQP Method for Economic Dispatch With Disjoint Prohibited Zones , 2014, IEEE Transactions on Power Systems.

[13]  W. M. Hirsch,et al.  The fixed charge problem , 1968 .

[14]  Mathieu Van Vyve,et al.  Fixed-charge transportation problems on trees , 2015, Oper. Res. Lett..

[15]  B. Walczak,et al.  Particle swarm optimization (PSO). A tutorial , 2015 .

[16]  Anthony Przybylski,et al.  Multi-objective branch and bound , 2017, Eur. J. Oper. Res..

[17]  R. A. Johnson,et al.  Predation by Megaponera foetens (Fabr.) (Hymenoptera: Formicidae) on termites in the Nigerian southern Guinea Savanna , 2004, Oecologia.

[18]  O. V. Gnana Swathika,et al.  Optimum coordination of overcurrent relays in distribution systems using big-m and revised simplex methods , 2017, 2017 International Conference on Computing Methodologies and Communication (ICCMC).

[19]  Ajith Abraham,et al.  Inertia Weight strategies in Particle Swarm Optimization , 2011, 2011 Third World Congress on Nature and Biologically Inspired Computing.

[20]  M. Balinski Fixed‐cost transportation problems , 1961 .

[21]  Yunfei Mu,et al.  Energy-Internet-oriented microgrid energy management system architecture and its application in China , 2018, Applied Energy.