Ali Eshragh

A hybrid simulation-optimization algorithm for the Hamiltonian cycle problem

In this paper, we propose a new hybrid algorithm for the Hamiltonian cycle problem by synthesizing the Cross Entropy method and Markov decision processes. In particular, this new algorithm assigns a random length to each arc and alters the Hamiltonian cycle problem to the travelling salesman problem. Thus, there is now a probability corresponding to each arc that denotes the probability of the event “this arc is located on the shortest tour.” Those probabilities are then updated as in cross entropy method and used to set a suitable linear programming model. If the solution of the latter yields any tour, the graph is Hamiltonian. Numerical results reveal that when the size of graph is small, say less than 50 nodes, there is a high chance the algorithm will be terminated in its cross entropy component by simply generating a Hamiltonian cycle, randomly. However, for larger graphs, in most of the tests the algorithm terminated in its optimization component (by solving the proposed linear program).

Planning of complex supply chains: A performance comparison of three meta-heuristic algorithms

Abstract Businesses have more complex supply chains than ever before. Many supply chain planning efforts result in sizable and often nonlinear optimization problems that are difficult to solve using standard solution methods. Meta-heuristic and heuristic solution methods have been developed and applied to tackle such modeling complexities. This paper aims to compare and analyze the performance of three meta-heuristic algorithms in solving a nonlinear green supply chain planning problem. A tactical planning model is presented that aims to balance the economic and emissions performance of the supply chain. Utilizing data from an Australian clothing manufacturer, three meta-heuristic algorithms including Genetic Algorithm, Simulated Annealing and Cross-Entropy are adopted to find solutions to this problem. Discussions on the key characteristics of these algorithms and comparative analysis of the numerical results provide some modeling insights and practical implications. In particular, we find that (1) a Cross-Entropy method outperforms the two popular meta-heuristic algorithms in both computation time and solution quality, and (2) Simulated Annealing may produce better results in a time-restricted comparison due to its rapid initial convergence speed.

On transition matrices of Markov chains corresponding to Hamiltonian cycles

In this paper, we present some algebraic properties of a particular class of probability transition matrices, namely, Hamiltonian transition matrices. Each matrix

Fisher Information for a partially observable simple birth process

P

Tactical supply chain planning under a carbon tax policy scheme: A case study

P in this class corresponds to a Hamiltonian cycle in a given graph

A NEW APPROACH TO DISTRIBUTION FITTING: DECISION ON BELIEFS

G