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<strong>Ozean</strong> Journal of Applied Sciences 2(2), 2009Figure 2. RRT with Local Exchange Moves (RRTLEM)Figure 3. 1-0 Exchange Move with RRTFigure 4. 1-1 Exchange Move with RRTIn 1-0 Exchange move with RRT, 1-1 Exchange move with RRT and 2-Opt Exchange move with RRT asthe initial solution, we use the solution given Convex-Hull constructive heuristic and Or-Opt improvementheuristic (Or (1976), Stewart (1977)). During the search process, current solution (cs) is the route fromwhich new solutions (s’) are obtained and best solution (bs) is the route whose cost is the best among thesolutions created. Cost of solution s, f(s), denotes the total route cost using the sequence stored in s. When151
<strong>Ozean</strong> Journal of Applied Sciences 2(2), 2009uphill moves are allowed for a local search move, cs can be assigned a new solution whose cost is worsethan cost of cs but better than cost of bs plus dev. dev is a predefined percentage (rate) of the cost of bs, andwhenever a new bs is found, dev is also updated. Uphill moves create the opportunity for cs to escape fromtrapping local minima. After executing iterative statements, starting from the bs, we apply each local searchmove once more. The idea is inspired from the study (Li et.al., 2007), but important modifications are addedthat will improve the performance. Note that in our algorithm, there are two parameters that must be finetuned in order to obtain best performance. These are the number of iterations, noi, and percentage value,rate, that is used to calculate the deviation.Figure 5. 2-opt Move with RRTNeighbor list (NL) is an important topic that should be explained. During local searches, it is more rationalto try exchanges between nodes or edges that are away from each other at most a reasonable amount ofdistance. For example, for exchanging two nodes, it is not necessary to exchange the node at the most leftand the node at the most right. To avoid from these unprofitable moves, we build neighbor lists for eachnode.CASE STUDIESThis section explains the test problems. These problems are selected among literature studies. Thecomplexity of the problem is considered as a criterion in choosing problems. Each following case hasdifferent size in path length and number of nodes. Chosen problems are 10 bolt assembly problem, 14 holedrilling problem and 442 point PCB drilling problem.10 Bolt AssemblyThis problem is chosen as a benchmark problem because Huang et.al. (1997) have also solved this problemby using GA. In the case, a metal plate with have 10 bolts at locations shown in Figure 6 is considered.Bolts are to be inserted into the pre-drilled holes. The objective is to minimize the movement while passingover and inserting a bolt into each hole.152
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