A physarum-inspired approach to supply chain network design

A supply chain is a system which moves products from a supplier to customers, which plays a very important role in all economic activities. This paper proposes a novel algorithm for a supply chain network design inspired by biological principles of nutrients’ distribution in protoplasmic networks of slime mould Physarum polycephalum. The algorithm handles supply networks where capacity investments and product flows are decision variables, and the networks are required to satisfy product demands. Two features of the slime mould are adopted in our algorithm. The first is the continuity of flux during the iterative process, which is used in real-time updating of the costs associated with the supply links. The second feature is adaptivity. The supply chain can converge to an equilibrium state when costs are changed. Numerical examples are provided to illustrate the practicality and flexibility of the proposed method algorithm

A physarum-inspired approach to supply chain network design

A supply chain is a system which moves products from a supplier to customers, which plays a very important role in all economic activities. This paper proposes a novel algorithm for a supply chain network design inspired by biological principles of nutrients’ distribution in protoplasmic networks of slime mould Physarum polycephalum. The algorithm handles supply networks where capacity investments and product flows are decision variables, and the networks are required to satisfy product demands. Two features of the slime mould are adopted in our algorithm. The first is the continuity of flux during the iterative process, which is used in real-time updating of the costs associated with the supply links. The second feature is adaptivity. The supply chain can converge to an equilibrium state when costs are changed. Numerical examples are provided to illustrate the practicality and flexibility of the proposed method algorithm

Fair Resource Allocation in Macroscopic Evacuation Planning Using Mathematical Programming: Modeling and Optimization

Evacuation is essential in the case of natural and manmade disasters such as hurricanes, nuclear disasters, fire accidents, and terrorism epidemics. Random evacuation plans can increase risks and incur more losses. Hence, numerous simulation and mathematical programming models have been developed over the past few decades to help transportation planners make decisions to reduce costs and protect lives. However, the dynamic transportation process is inherently complex. Thus, modeling this process can be challenging and computationally demanding. The objective of this dissertation is to build a balanced model that reflects the realism of the dynamic transportation process and still be computationally tractable to be implemented in reality by the decision-makers. On the other hand, the users of the transportation network require reasonable travel time within the network to reach their destinations. This dissertation introduces a novel framework in the fields of fairness in network optimization and evacuation to provide better insight into the evacuation process and assist with decision making. The user of the transportation network is a critical element in this research. Thus, fairness and efficiency are the two primary objectives addressed in the work by considering the limited capacity of roads of the transportation network. Specifically, an approximation approach to the max-min fairness (MMF) problem is presented that provides lower computational time and high-quality output compared to the original algorithm. In addition, a new algorithm is developed to find the MMF resource allocation output in nonconvex structure problems. MMF is the fairness policy used in this research since it considers fairness and efficiency and gives priority to fairness. In addition, a new dynamic evacuation modeling approach is introduced that is capable of reporting more information about the evacuees compared to the conventional evacuation models such as their travel time, evacuation time, and departure time. Thus, the contribution of this dissertation is in the two areas of fairness and evacuation. The first part of the contribution of this dissertation is in the field of fairness. The objective in MMF is to allocate resources fairly among multiple demands given limited resources while utilizing the resources for higher efficiency. Fairness and efficiency are contradicting objectives, so they are translated into a bi-objective mathematical programming model and solved using the ϵ-constraint method, introduced by Vira and Haimes (1983). Although the solution is an approximation to the MMF, the model produces quality solutions, when ϵ is properly selected, in less computational time compared to the progressive-filling algorithm (PFA). In addition, a new algorithm is developed in this research called the θ progressive-filling algorithm that finds the MMF in resource allocation for general problems and works on problems with the nonconvex structure problems. The second part of the contribution is in evacuation modeling. The common dynamic evacuation models lack a piece of essential information for achieving fairness, which is the time each evacuee or group of evacuees spend in the network. Most evacuation models compute the total time for all evacuees to move from the endangered zone to the safe destination. Lack of information about the users of the transportation network is the motivation to develop a new optimization model that reports more information about the users of the network. The model finds the travel time, evacuation time, departure time, and the route selected for each group of evacuees. Given that the travel time function is a non-linear convex function of the traffic volume, the function is linearized through a piecewise linear approximation. The developed model is a mixed-integer linear programming (MILP) model with high complexity. Hence, the model is not capable of solving large scale problems. The complexity of the model was reduced by introducing a linear programming (LP) version of the full model. The complexity is significantly reduced while maintaining the exact output. In addition, the new θ-progressive-filling algorithm was implemented on the evacuation model to find a fair and efficient evacuation plan. The algorithm is also used to identify the optimal routes in the transportation network. Moreover, the robustness of the evacuation model was tested against demand uncertainty to observe the model behavior when the demand is uncertain. Finally, the robustness of the model is tested when the traffic flow is uncontrolled. In this case, the model's only decision is to distribute the evacuees on routes and has no control over the departure time

A hybrid algorithm based on state-adaptive slime mold model and fractional-order ant system for the travelling salesman problem

open access articleThe ant colony optimization (ACO) is one efficient approach for solving the travelling salesman problem (TSP). Here, we propose a hybrid algorithm based on state-adaptive slime mold model and fractional-order ant system (SSMFAS) to address the TSP. The state-adaptive slime mold (SM) model with two targeted auxiliary strategies emphasizes some critical connections and balances the exploration and exploitation ability of SSMFAS. The consideration of fractional-order calculus in the ant system (AS) takes full advantage of the neighboring information. The pheromone update rule of AS is modified to dynamically integrate the flux information of SM. To understand the search behavior of the proposed algorithm, some mathematical proofs of convergence analysis are given. The experimental results validate the efficiency of the hybridization and demonstrate that the proposed algorithm has the competitive ability of finding the better solutions on TSP instances compared with some state-of-the-art algorithms