Abstract. Instances of constraint satisfaction problems can be solved efficiently if they are representable as a tree decomposition of small width. Unfortunately, the task of finding a decomposition of minimum width is NP-complete itself. Therefore, several heuristic and metaheuristic methods have been developed for this problem. In this paper we investigate the application of different variants of Ant Colony Optimization algorithms for the generation of tree decompositions. Furthermore, we extend these implementations with two local search methods and we compare two heuristics that guide the ACO algorithms. Our computational results for selected instances of the DIMACS graph coloring library show that the ACO metaheuristic gives results comparable to those of other decomposition methods such as branch and bound and tabu search for many problem instances. One of the proposed algorithms was even able to improve the best known upper bound for one problem instance. Nonetheless, for some larger problems the best existing methods outperform our algorithms.
Background Various methods of intrapartum analgesia are available these days. Pethidine, meptazinol and epidural analgesia are among the most commonly used techniques. A relatively new one is patient-controlled intravenous analgesia with remifentanil, although the experiences published so far in Germany are limited. Our goal was to study the influence of these analgesic techniques (opioids vs. patient-controlled intravenous analgesia with remifentanil vs. epidural analgesia) on the second stage of labour and on perinatal outcome. Material and Methods We conducted a retrospective study with 254 parturients. The women were divided into 4 groups based on the analgesic technique and matched for parity, maternal age and gestational age (opioids n = 64, patient-controlled intravenous analgesia with remifentanil n = 60, epidural analgesia n = 64, controls without the medicinal products mentioned n = 66). Maternal, fetal and neonatal data were analysed. Results The expulsive stage was prolonged among both primiparas and multiparas with patient-controlled intravenous analgesia with remifentanil (79 [74] vs. 44 [55] min, p = 0.016, and 28 [68] vs. 10 [11] min, p < 0.001, respectively) and epidural analgesia (90 [92] vs. 44 [55] min, p = 0.004, and 22.5 [73] vs. 10 [11] min, p = 0.003, respectively) compared with the controls. The length of the pushing stage was similar among primiparas in all groups but prolonged compared with the controls in multiparas with patient-controlled intravenous analgesia with remifentanil (15 [17] vs. 5 [7] min, p = 0.001) and epidural analgesia (10 [15] vs. 5 [7] min, p = 0.006). The Apgar, umbilical arterial pH and base excess values were similar between the groups, as were the rates of acidosis and neonatal intensive care unit admission. Conclusion Parturients with patient-controlled intravenous analgesia with remifentanil and epidural analgesia showed a prolonged expulsive stage compared with the opioid group and controls. The short-term neonatal outcome was not influenced by the three methods examined.
This chapter deals with the application of evolutionary approaches and other metaheuristic techniques for generating tree decompositions. Tree decomposition is a concept introduced by Robertson and Seymour [34] and it is used to characterize the difficulty of constraint satisfaction and NP-hard problems that can be represented as a graph. Although in general no polynomial algorithms have been found for such problems, particular instances can be solved in polynomial time if the treewidth of their corresponding graph is bounded by a constant. The process of solving problems based on tree decomposition comprises two phases. First, a decomposition with small width is generated. Basically in this phase the problem is divided into several sub-problems, each included in one of the nodes of the tree decomposition. The second phase includes solving a problem (based on the generated tree decomposition) with a particular algorithm such as dynamic programming. The main idea is that by decomposing a problem into sub-problems of limited size, the whole problem can be solved more efficiently. The time for solving the problem based on its tree decomposition usually depends on the width of the tree decomposition. Thus it is of high interest to generate tree decompositions having small widths.Finding the treewidth of a graph is an NP-hard problem [2]. In order to solve this problem different algorithms have been proposed in the literature. Exact methods such as branch and bound techniques can be used only for small graphs. Therefore, metaheuristic algorithms based on genetic algorithms [18] , simulated annealing [22], tabu search [14], iterated local search [29] , and antcolony optimization ([7], [9]) have been proposed in the literature to generate good upper bounds for larger graphs. Such techniques have been applied very successfully and they are able to find the best existing upper bounds for many benchmark problems in the literature.In this chapter we will first introduce the concept of tree decomposition, and then give a survey on metaheuristic techniques used to generate tree decompositions. Three approaches based on genetic algorithms, iterated local search and ant-colony optimization that were proposed in the literature will be described in detail. Finally, we will also mention briefly two recent approaches that exploit tree decompositions within metaheuristic search.
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