Simulated annealing, an analogy between statistical mechanics and combinatorial optimization, has attracted considerable attention due to its potential in dealing with certain traditional optimization problems. However, it has been shown to be parameter sensitive and require more computational effort to produce high quality solutions than traditional heuristics. The present paper reports on a new approach to applying this method to a class of quadratic assignment problems, i.e., the facility layout problem. This approach combines the simulated annealing methodology with a specific layout design rule, which in the case of this study is a "Move Desirability Table" . Two annealing methods are proposed based on this approach which differ only in cooling schedule. The first method produces high quality solutions, while the second method is faster with a slight degradation in the quality of solutions and therefore suitable for larger problems. Performance of the two methods was numerically tested on standard problems as well as two larger problems (n = 50 and n = 100; n is the number of facilities) and was compared to that of Wilhelm & Ward, Connolly and other heuristics, e.g., QAPH4, CRAFT, biased sampling and the revised Hillier procedure. As the experimental results, it was found that except, in the case of n = 50, 100, the proposed methods are computationally faster than Wilhelm & Ward and that the solution qualities of t,he proposed methods in all the cases are superior to those of Wilhelm & Ward, Connolly and other heuristic procedures.

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In this paper, a consistency improving of the comparison matrix in binary AHP (Analytic Hierarchy Process) is studied. As its byproducts, we propose a method to count the cycles of length 3 and to find the locations of the cycles in a complete directed graph. We apply our proposed consistency improving method to various examples including three actual sports games. Comparing our method with ordinary improving method, we can show the usefulness of our method.

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This article presents analytical and numerical approaches for statistically testing parameter estimates of a regression hyperplane, using Empirical Regression Quantile (ERQ) technique. The analytical approach uses its asymptotic property of ERQ to determine the standard error of parameter estimates. The asymptotical results are replaced and compared with a computer intensive technique referred to as "a bootstrap method." Furthermore, Leverage Treatment, Method (LTM) is proposed for dealing with a leverage point problem that may seriously affect ERQ results. It is not trivial to detect the leverage point in a multivariate date set. An important feature of the LTM is that, it fully utilizes dual variables derived from ERQ for identifying the leverage point. The proposed ERQ/LTM is applied to two illustrative examples in which the technique is compared with other conventional methods.

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This paper presents a new method with trust region technique for solving the nonlinear least squares problem with linear inequality constraints. The method proposed in this paper stems from the one presented in a recent paper by the authors. The method successively constructs trust region constraints, which are ellipsoids centered at the iterative points, in such a way that they lie in the relative interior of the feasible region. Thus the method belongs to the class of interior point, methods, and hence we may expect that the generated sequence approaches a solution smoothly without the combinatorial complications inherent to traditional active set methods. We establish a convergence theorem for the proposed method and show its practical efficiency by numerical experiments.

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There is a rooted tree. A person selects a vertex except the root, hides in it and stays there. The searcher is at the root and then examines each vertex until he finds the hider, traveling along edges of the tree. Associated with the examination are a traveling cost dependent on the distance from the last vertex examined and a fixed examination cost. The searcher wishes to minimize the expected cost of finding the hider, whereas the hider wishes to maximize it. The problem is formulated as a two-person zero-sum game and it is solved.

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The present paper deals with an optimal stopping problem with several possible search areas in which travel costs are assumed among the areas. In terms of the future availability of an offer once obtained and passed up, the following two cases are considered: (1) it becomes instantly and forever unavailable and (2) it remains forever available, called a no recall model and a recall model, respectively. The main results obtained here are as follows: 1 . Both models have a reservation value property, and the reservation values are nondecreasing in the number of periods, t, remaining up to deadline and converge as t → ∞; 2. Their limits in both models do not always become the same, which coincide in conventional optimal stopping problems; 3. In the recall model, there may exist double critical points w_* and w*(w_* < w*) in terms of the present offer w in the sense that, if w < w_*, then the optimal next search area. is i, if w_* < w < w*, then j ≠ i, and if w* < w, then again i; and 4. Suppose the travel cost is independent, of the starting search area. Then, in the recall model, the reservation value is independent, of both the remaining periods and the current search area. Furthermore, in this case, the reservation values in both models converge to the same value as t → ∞.

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This paper deals with a vehicle routing problem of finding the minimum number of capacitated vehicles(AGVs) used for delivery from a central depot, to demand points while meeting the delivery times requirements. Recently, with a ongoing progress in CIM, a product,ion system which can efficiently control and utilize automated facilities is strongly required. As part of this system, AGV scheduling that can timely supplies these automated facilities with parts, tools, and other things have become more and more important. In order to meet the demands with only a few available AGVs efficiently, a method to clarify of the minimum number of AGVS required for a given production planning is useful(to check the feasibility of the production planning) . First, we formulate our vehicle routing problem with time constraints. After that, we introduce a heuristic algorithm for this problem. The heuristic algorithm first, transforms the problem to the one with no capacity constraints. By the out-of-kilter method, t,he relaxed problem is solved. Using the resulting "optimum" but infeasible set of tours, the algorithm then cuts off each of tours which exceed capacity constraints into smaller segments in such a manner that the segmented tours satisfy the constraints. Given a set of tours satisfying the capacity constraints, the problem which assigns those tours to AGVs is also solved by the out-of-kilter method. The results of an evaluation of this method indicate that, the proposed heuristic is useful and promising. It is also shown that the size of vehicle capacity and/or the location of depot have significant effects on the result obtained through this heuristic process. The larger the capacity becomes, the smaller the influence of relaxing capacity constraints becomes and the more useful this heuristic becomes. When the depot is not centrally located, the larger the distances from demand points to the depot become, the less useful the heuristic becomes.

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An efficient cost scaling algorithm is presented for the independent assignment problem of Iri and Tomizawa, which is equivalent to the weighted matroid intersection problem of Edmonds. Our algorithm in general can be viewed as a generalization of Orlin and Ahuja's scaling algorithm for the ordinary assignment problem. On a bipartite graph with n vertices and integer arc costs bounded by C, an optimal r-independent assignment can be found in O(√<rgt:n^2 log(rC)) time by our algorithm under an independence oracle for matorids.

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