The tabu search manager determines the search path for the ATS process. The strategy reviews the current parameters and determines the phase and search context for the next iteration. The manager controls movement between the request assignment (partitioning) group and the route improvement (ordering) group based on the number of iterations since the last iteration resulting in the best solution found to that point in the
search. The search context is based on the current status of tracking parameters and transitions between super-diversify, diversify, and intensify. Intensification searches are focused within conjugacy classes that contain good solutions. Diversification occurs when the current search path fails to find good solutions or the process has detected an attractor basin. Phase I ends by establishing the current solution as the new incumbent solution.
The tabu search strategy manager determines the appropriate phase search context and move neighborhood to apply to the incumbent solution. These decisions are based on collected search data, objective function values and pre-defined search parameters. Two move manager schemes are used. Both search manager schemes are examined in Chapter VI. The first search scheme does not utilize elite lists during the second phase or intensification portion of the search process. The second search scheme maintains two elite lists to store solution data for both the best feasible and near feasible solutions found during the search process. The elite list size is a user pre-defined parameter and has a default size of five for this dissertation. Each elite list is sequenced in descending order based on solution objective function values. ATS utilizes the elite list as a restart mechanism during the second phase of the search process. The search manager monitors the iteration since last good solution (ISGS) parameter that maintains the number of iterations since the search process last found a new best (feasible or near feasible) solution. The consecutive infeasible iterations (CI) parameter tracks the consecutive number of iterations resulting in infeasible solutions and is used by the search manager to diversify. The choose first improving move (CFIM) is a boolean parameter that controls
the move manager’s selection process. The move manager selects the first improving move from the move neighborhood scheme when the CFIM parameter is true. This serves as a diversification scheme allowing visits to areas of the solution space the ATS process might not normally visit. When the CFIM parameter is set to false, the move manager examines all moves in the neighborhood scheme before selecting the best move. Figure 5-9 illustrates the move manager process for establishing the search phase and search context where ATS is utilizing elite lists. The search process contains two main phases consisting of an exploration and intensification phase. Once the move manager selects the appropriate search phase, it determines the search context (intensify, diversify, or super-diversify) based on solution characteristics.
The ATS search process begins in an exploration phase and the CFIM parameter is set to true. This allows the search process to traverse a greater number of regions in the solution space. The search manager tracks both the best feasible and best near feasible solutions discovered during the search process. Each iteration, if the solution is a new best solution (feasible or near feasible), the manager updates the appropriate elite list and resets the ISGS and CI counters. The discovery of a new best solution might be an indication of a promising region so the search process enters a mini-intensification search phase to explore the local area. If the incumbent solution is not a new best solution, the search manager increments the ISGS counter and checks to see if the solution is infeasible. The move manager increments the CI parameter for an infeasible incumbent solution and resets the CI parameter if the solution is feasible or near feasible. The
search manager next determines if the ISGS counter has surpassed a pre-defined tolerance or number of poor solutions.
Figure 5-9 ATS Strategy Move Manager
Current Solution
New Best Feasible Solution?
New Best Near Feasible Solution?
Is Solution Infeasible? Update Feasible Elite List Update Near Feasible Elite List Is ISGS ≥ tolerance? Is CI ≥ tolerance? Diversify Intensify SolutionRepair ISGS = 0 CI = 0 eliteCounter = 0 solutionRepair = TRUE ISGS = 0 CI = 0 CFIM = FALSE eliteCounter++ Select Move Evaluate NBH Perform Move Terminate Is eliteCounter ≥ eliteSize? Select Next Elite Solution Yes Yes No No No Yes No Yes No Yes ISGS++ CI = 0 CI++ Yes No Phase II Elite List Implementation
The search manager checks the CI tolerance level if the ISGS counter has not surpassed its tolerance. Surpassing the CI tolerance indicates that the search process is exploring an undesirable region of the solution space. This triggers a solution repair phase that targets infeasibility. Once the ISGS parameter surpasses this tolerance, the search process enters a more focused search phase. The CFIM parameter is set to false allowing the move manager to examine all moves and the elite list solutions are activated. The ATS process selects the first solution in the elite list as the new incumbent solution and repeats the phase one search process until the ISGS parameter surpasses the pre- defined tolerance. At this point, the next solution is selected from the elite list and the cycle begins again until exhausting all elite list solutions.
5.8 Summary
This chapter described the algorithm for the ATS process. The ATS consists of two main phases: the preprocessing phase and the ATS search phase. The preprocessing phase initializes the ATS and provides the initial solution to the ATS phase. The ATS search phase is comprised of five components. The five components are the neighborhood move generator, solution evaluator, tabu structure manager, perform move operator and search manager. The neighborhood move generator generates one of several available move neighborhoods based on guidance from the search manager. The search manager is the heart of the process and controls the search process through a cycle of the first four components. The search manager monitors a set of counters and parameters to dynamically select the appropriate search phase and search context for each iteration.
The next chapter describes the design of experiment conducted in this research to determine the main characteristics that impact the ATS process.
VI Analysis of the ATS and Experimental Results
Researchers often conduct experiments to examine how their particular heuristic performs compared to other heuristics for a certain problem class and how well it solves a set of problem instances for the problem class. Myers and Montgomery (1995) and many others have traditionally proposed a factorial design process for this type of experimentation. This research utilizes a process outlined by Combs and Moore (2004) based on an empirical science approach proposed by Hooker (1994, 1995).
This empirical science approach evaluates the heuristic’s performance based on the characteristics of the problem instead of testing its ability to solve a set of benchmark problems. Hooker’s (1995) approach suggests running a controlled experiment over a variety of parameter settings to evaluate the heuristic’s performance. This research utilizes a fractional factorial experiment to determine how the characteristics of adaptive tabu search affect problem performance measures such as the number of depots, the number of supply points and the number of vehicles or collectively the distribution network’s logistics footprint and how LPDPTW problem changes affect tabu search performance. The set of benchmark problems in this research serve as a common platform to evaluate how changes to the above ATS characteristics affect solution performance.