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Assessing the performance of bio-inspired heuristics for single row layout problems

Assessing the performance of bio-inspired heuristics for single row layout problems. Berna ULUTAŞ B.Burak ULUTA Ş Eskisehir Osmangazi University Department of Industrial Engineering. 30 June-2 July 2010 Oprerations Research and Industrial Engineering Conference

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Assessing the performance of bio-inspired heuristics for single row layout problems

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  1. Assessing the performance of bio-inspired heuristics for single row layout problems Berna ULUTAŞ B.Burak ULUTAŞ Eskisehir Osmangazi University Department of Industrial Engineering 30 June-2 July 2010 Oprerations Research and Industrial Engineering Conference Sabanci University , Istanbul Turkey

  2. Outline • Single row facility layout problem (SRFLP) • Literature review • The algorithms to solve SRFLP • Experiments for the test problems • Results and discussion

  3. The Single Row Facility Layout Problem • Arrangement of n machines/departments on a straight line in a given direction • Named as • One dimensional layout • Linear Ordering Problem (LOP) where all machines have unit length

  4. Objective is to minimize the total material handling costs and to find the optimum layout for machines in one dimension

  5. SRLP examples

  6. SRLP examples (cont’)

  7. Literature review for SRFLP • Karp and Held (1967) Dynamic programming • Simmons (1969, 1971) Branch and bound algorithm • Love and Wong (1976) Linear mixed integer program • Picard and Queyranne (1981) Dynamic programming • Heragu and Kusiak (1988)Two heuristic constructive algorithms • Heragu and Kusiak (1991) Nonlinear model • Braglia (1997) Heuristics derived from scheduling problem • Djellab and Gourgand (2001) An iterative construction procedure • Ponnambalam and Ramkumar (2001), Chen et al. (2001), Ficko et al. (2004)GA

  8. Literature review for SRFLP (cont’) • Ponnambalam and Ramkumar (2001) GA+SA • Ponnambalam et al. (2005) Hybrid search heuristics (Flow Line Analysis (FLA)+SA, FLA +GA, FLA+GA+SA) • Anjos et al. (2005) Semidefinite programming relaxation • Solimanpur et al. (2005)ACO • Amaral et al. (2005)SA • Amaral (2006) Linear mixed integer program • Teo and Ponnambalam (2008) ACO+PSO • Amaral (2009) Linear programming • Samarghandi and Eshghi (2010) TS • Samarghandi et al. (2010) PSO

  9. The dimensions of the machines either are not considered or are assumed to be equal (Braglia, 1996) • The locations of facilities are predetermined (Kumar et al., 1995; Braglia, 1996) • The size of the machines is only considered in the physical layout of the machines (Heragu and Kusiak, 1988) • The method requires too much time to construct a layout, especially when applied to large instances of the SRFLP (Anjos et al., 2005).

  10. The problem in concern • Large size departments • Unequal dimensions (length) • No clearence • No backtracking

  11. Biologically inspired computing • genetic algorithms ↔ evolution • neural networks ↔ the brain • artificial immune systems ↔ immune system • emergent systems ↔ ants, bees • rendering (computer graphics) ↔ patterning and rendering of animal skins, bird feathers, mollusk shells and bacterial colonies • cellular automata ↔ life

  12. Clonal selection • Bacterial foraging

  13. CLONAL SELECTION ALGORITHM

  14. AIS algorithms Population based Network based Clonal selection Continuousmodels Bone marrow Discrete models Negative selection

  15. m5 m2 m1 m6 m4 m3 Encoding [m5 m2 m1 m6 m4 m3] = [5 2 1 6 4 3] Representation

  16. Step 1: Initialization • The antibodies are randomly generated based on the predetermined population size

  17. Step 2: Evaluation • For each antibody in the population, the objective function value is calculated

  18. Selection of antibodies are made based on their objective valuesFor example, layouts that have lower cost values have the largest share on the wheel Step 3: Selection and cloning

  19. Step 4: Hypermutation • For each antibody in the population, hypermutationoperator is applied • Then, objective value of the mutated antibody is calculated • If there is an improvement, the existing antibody is replaced with the mutated one

  20. Step 5: Receptor editing operator • A percentage of the antibodies (worst R% of the whole population) in the antibody population are eliminated and randomly created antibodies are replaced with them. • This procedure enables the algorithm to search new regions in the solution space.

  21. Step 6: Repeat Steps 2-5 until termination criterion is met • The algorithm is terminated if the best feasible solution has not improved after a predetermined number of iterations (i.e., 250).

  22. BACTERIA FORAGING ALGORITHM

  23. BFA • is based on the foraging (i.e., searching food) strategy of Escherichia coli bacteria

  24. Step 1.Initialization • The bacteria are randomly generated based on the predetermined population size

  25. Step 2. Chemotaxis • is a foraging strategy that implements a type of local optimization • the bacteria try to climb up the nutrient concentration, avoid noxious substances • search for ways out of neutral media • is similar with biased random walk model

  26. Step 3. Swarming • the bacteria move out from their respective places in ring of cells by moving up to the minimal value • bacteria usually tumble, followed by another tumble or tumble followed by run or swim • if the cost at present is better than the cost at the previous time or duration then the bacteria takes one more step in that direction

  27. Nclones copies of the solution are generated so that there are (Nclones+1) identical solutions • Inverse mutation is applied to each of the Nclones copies • The solution surviving the mutation is the non-dominated solution among the mutated solutions • All other solutions are discarded • Repeat the procedure for all the solutions in the population Tavakkoli-Moghaddam et al. (2007) A hybrid multi objective immune algorithm for a flow shop scheduling problem with bi-objectives: Weighted mean completion time and weighted mean tardiness

  28. Step 4. Reproduction • the bacteria are stored in ascending order based on their fitness • percent of the least healthy bacteria dies and others split into two which are placed in the same location • the population of bacteria remains constant

  29. Step 5. Repeat Steps 2-4 until termination criterion is met • The algorithm steps are repeated until the termination criterion is succeeded

  30. Algorithm parameters • Population size : 10 • Receptor editing / Reproduction rate : 10%

  31. Problem set 1Problems with optimum solutions

  32. Problem set 2Larger size test problem results for CSA

  33. Problem set 2Larger size test problem results for BFA

  34. Problem set 3Larger size test problem results for CSA

  35. Problem set 3Larger size test problem results for BFA

  36. Conclusions and Results • The performance metrics: • solution quality • speed of convergence • frequency of hitting the optimum • CSA and BFA outperformed best known results available in the literature • CSA obtained better results than BFA

  37. Further studies • Design of experiments to determine the optimum parameters • Experiments with different termination criteria and larger population size • New strategies to improve BFA search capabilities • Considering the elimination and dispersal events that are based on population level long-distance mobile behavior • Real life application of SRLP

  38. THANKS

  39. QUESTIONS?

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