Rajesh Matai

Traveling Salesman Problem: an Overview of Applications, Formulations, and Solution Approaches

1.1 Origin The traveling salesman problem (TSP) were studied in the 18th century by a mathematician from Ireland named Sir William Rowam Hamilton and by the British mathematician named Thomas Penyngton Kirkman. Detailed discussion about the work of Hamilton & Kirkman can be seen from the book titled Graph Theory (Biggs et al. 1976). It is believed that the general form of the TSP have been first studied by Kalr Menger in Vienna and Harvard. The problem was later promoted by Hassler, Whitney & Merrill at Princeton. A detailed dscription about the connection between Menger & Whitney, and the development of the TSP can be found in (Schrijver, 1960).

Solving multi objective facility layout problem by modified simulated annealing

Modified simulated annealing has been applied for solving multi objective facility layout problem (MOFLP).Proposed approach in paper makes the multi objective layout design process independent of decision maker.Proposed modified simulated annealing is efficient and effective in solving large sized MOFLP. This paper proposes a modified simulated annealing approach for solving multi objective facility layout problem. Multi objective facility layout problem is solved by using different objective weights which are generated by decision maker. Thus layout design process is decision maker dependent. However proposed approach in this paper makes layout design process independent of decision maker. Proposed approach can also incorporate any number of objectives that may be qualitative or quantitative in nature. Computational results show superiority of proposed heuristic approach than other approaches available in literature. Finally, comparison was also made with best solution qualities for the 15 single objective test problems of Nugxx series taken from QAPLIB. Comparisons were made in terms of the quality of the solutions obtained and the computational time required and this comparison shows efficiency and effectiveness of proposed modified simulated annealing algorithm.

Modified simulated annealing based approach for multi objective facility layout problem

In this paper a modified simulated annealing (SA) based approach is presented for solving multi objective facility layout problem (MOFLP). It can incorporate more than two objectives that may be qualitative or quantitative in nature. Computational results show superiority of the proposed modified SA based approach for MOFLP over past approaches available in literature. To validate the proposed SA based approach, it is tested on instances taken from the literature which shows that the proposed approach provides promising results.

A new heuristic approach for solving facility layout problem

This paper proposes a new heuristic approach for solving facility layout problem (FLP) which is traditionally formulated as quadratic assignment problem (QAP). In this paper, FLP is formulated as linear assignment problem (LAP) consisting of facility pair and location pair. Being linear in nature LAP can be solved efficiently. Solution of LAP provides lower bound on corresponding QAP formulation of FLP. Heuristic procedure is applied to solve FLP from sets of LAP solution. Proposed heuristic is tested on benchmark instances taken from literature and compared with other heuristics available in literature. Computational results show that proposed heuristic provides a good quality approximate solution. This solution can be taken as initial solution for any improvement heuristic to get optimal/near optimal solution for FLP.

Non-greedy systematic neighbourhood search heuristic for multi-objective facility layout problem

In this paper a non-greedy systematic neighbourhood search heuristic is presented for solving multi-objective facility layout problem. It can incorporate more than two objectives that may be qualitative or quantitative in nature. Computational results show superiority of our proposed heuristic algorithm than other algorithms available in literature. Finally, comparison was also made with best solution qualities for the 15 single objective test problems of Nugxx series taken from QAPLIB and this comparison also shows efficiency and effectiveness of proposed heuristic algorithm.

A Non-greedy Local Search Heuristic for Facility Layout Problem

This paper proposes a non-greedy local search heuristic for solving facility layout problem. The proposed heuristic works on non-greedy systematic pair wise exchange of two facilities, that is 2-exchange local search based on non-greedy strategy. Pair wise exchanges are accepted if the objective function value after the exchange is lowered or smaller than the average objective function increment divided by an intensity factor. Proposed heuristic is tested on commonly used Nugxx series problems and computational results show efficiency and effectiveness of proposed heuristic.