Executable specifications for hypothesis-based reasoning with Prolog and Constraint Handling Rules

Constraint Handling Rules (CHR) is an extension to Prolog which opens up a spectrum of hypothesis-based reasoning in logic programs without additional interpretation overhead. Abduction with integrity constraints is one example of hypothesis-based reasoning which can be implemented directly in Prolog and CHR with a straightforward use of available and efficiently implemented facilities.The present paper clarifies the semantic foundations for this way of doing abduction in CHR and Prolog as well as other examples of hypothesis-based reasoning that is possible, including assumptive logic programming, hypotheses with priority and scope, and nonmonotonic reasoning.Examples are presented as executable code so the paper may also serve the additional purpose of a practical guide for developing such programs, and it is demonstrated that the approach provides a seamless integration with existing constraint solvers.     

Using aspiration levels in an interior primal-dual multiobjective linear programming algorithm

We introduce in this paper a new multiple-objective linear programming (MOLP) algorithm. The algorithm is based on the single-objective path-following primal—dual linear programming algorithm and combines it with aspiration levels and the use of achievement scalarizing functions. The resulting algorithm falls in the class of interactive MOLP algorithms, as it requires interaction with the decision maker (DM) during the iterative process to obtain statements of aspirations for levels of objectives of the MOLP problem. The interior point algorithm is then used to trace a path of interates from a current (interior) solution and approach as closely as desired a non-dominated solution corresponding to the optimum of the achievement scalarizing function. The timing of the interaction with the DM is dependent on the progress of the interior algorithm. It can take place every few, pre-specified, iterations or after the duality gap achieved for the stated aspirations has fallen below a certain threshold. It is expected that an interior algorithm will speed up the overall process of searching and finding the most preferred MOLP solution—especially in large-scale problems—by avoiding the need for numerous pivot operations and their corresponding interactive sessions inherent in simplex-based algorithms.     

An Application of MCDM in Water Resources Problems

In this paper a practical application of MCDM in water resources problems is presented. Based on a real project for Qinhuangdao water resources management sponsored by Qinhuangdao Municipality, we construct a set of models for inflow forecast, reservoir operations, water supply and allocation, and flood routing for system optimal operation and flood management. A stochastic dynamic programming (DP) model with a fuzzy criterion is proposed for monthly reservoir operations. A series of goal programming (GP) models is built for water supply and allocation on different planning and operating levels. The DP–GP models fulfil the optimal operation tasks of a water resources management decision support system (WRMDSS) for Qinhuangdao water resources management.     

Indifference sets of reference points in multi‐objective integer linear programming

Reference point approaches for multi‐objective problems rely on the definition of an achievement scalarizing function that projects reference points onto the non‐dominated solution set. In this paper, we investigate the behaviour of reference points using a Tchebycheff metric‐based scalarizing function in multi‐objective pure integer linear programming (MOILP). Since the non‐dominated solutions are discrete in MOILP, there are multiple reference points that lead to the same solution, i.e. there are indifference sets on the reference point space. We investigate some properties of the reference points in MOILP and also the graphical representation of indifference sets for tri‐objective problems. We further investigate properties of the reference points when additional limitations on the objective function values are introduced. Copyright © 2001 John Wiley & Sons, Ltd.     

Material handling device selection in cellular manufacturing

This paper presents a new multi‐criteria decision model for the material handling device (MHD) selection problem in cellular manufacturing systems. Given a set of manufacturing cells based on several automatic work‐centres, the technique makes it possible to select a particular MHD for each cell in an integrated way, with different constraints being taken into consideration. The approach is based on two different multi‐attribute analyses executed with analytic hierarchy process (AHP) methodology, and a final integer linear programming including important limitations faced by the designer when making MHD investment decisions. An example using real data is provided to illustrate this methodology. Copyright © 2002 John Wiley & Sons, Ltd.     

The operation of Lake Kariba: A multiobjective decision analysis

The paper describes a successful application of Bayesian decision analysis to the operation of the Lake Kariba hydropower system. This management problem is complicated by the high uncertainty of the inflow process, multiple and conflicting objectives and the influence of time on some of the parameters in the management task. Inflows to the reservoir are forecast through dynamic linear models. Managerial preferences are modelled through a multiattribute utility function. Since the solution of the exact model is computationally too demanding, a heuristic method is applied to find a feasible control strategy. A comparison with results obtained by methods used previously demonstrates the superiority of the methodology presented here.     

Planning Beyond the Next Trial in Adaptive Experiments: A Dynamic Programming Approach

Experimentation is at the heart of scientific inquiry. In the behavioral and neural sciences, where only a limited number of observations can often be made, it is ideal to design an experiment that leads to the rapid accumulation of information about the phenomenon under study. Adaptive experimentation has the potential to accelerate scientific progress by maximizing inferential gain in such research settings. To date, most adaptive experiments have relied on myopic, one‐step‐ahead strategies in which the stimulus on each trial is selected to maximize inference on the next trial only. A lingering question in the field has been how much additional benefit would be gained by optimizing beyond the next trial. A range of technical challenges has prevented this important question from being addressed adequately. This study applies dynamic programming (DP), a technique applicable for such full‐horizon, “global” optimization, to model‐based perceptual threshold estimation, a domain that has been a major beneficiary of adaptive methods. The results provide insight into conditions that will benefit from optimizing beyond the next trial. Implications for the use of adaptive methods in cognitive science are discussed.     

Order-Constrained Solutions in <Emphasis Type="Italic">K</Emphasis>-Means Clustering: Even Better Than Being Globally Optimal

This paper proposes an order-constrained K-means cluster analysis strategy, and implements that strategy through an auxiliary quadratic assignment optimization heuristic that identifies an initial object order. A subsequent dynamic programming recursion is applied to optimally subdivide the object set subject to the order constraint. We show that although the usual K-means sum-of-squared-error criterion is not guaranteed to be minimal, a true underlying cluster structure may be more accurately recovered. Also, substantive interpretability seems generally improved when constrained solutions are considered. We illustrate the procedure with several data sets from the literature.     

Relating reference points and weights in MOLP

A frequent problem for decision makers (DMs) analysing decisions involving multiple objectives is the identification and selection of the most preferred option from the set of non‐dominated solutions. Two techniques, weighted sum optimization and reference point optimization, have been developed to address this problem for multiobjective linear programming problems (MOLP). In this paper, we examine the relationship between these two techniques. We demonstrate that the values of the dual variables associate with auxiliary constraints of the reference point technique are equal to the weight values used to compute the same non‐dominated solution via the weighted sum technique. This insight will enable the development of new interactive solution procedures for MOLPs which allow the DM to readily switch from one method to the other during the search for the most preferred non‐dominated solution. The advantages of the approach are discussed in the paper. Copyright © 1999 John Wiley & Sons, Ltd.     

A time–cost optimization of the national postal distribution network

The postal distribution network in the Czech Republic consists actually of 69 local transit centres (according to the administrative division of the Czech Republic). Each of them operates the post offices in the given region. Some of the important local transit centres can be selected as sorting centres—transhipment points for postal consignments. The aim of this paper is to present a bicriterial optimization model for the selection of the subset of transhipment points from the set of transit centres and choosing their appropriate equipment, such as sorting machines. Another important output of the model is the assignment of the transit centres to the sorting centres. There are two basic optimization criteria defined in this model: minimization of the sum of investment and operational costs connected with building and operating of the sorting centres and the maximization of the percentage of postal consignments delivered to the appropriate post office in the desired time (next day). The proposed model contains several thousands of zero‐one variables and constraints. The model has been verified, and the results accepted. Copyright © 1999 John Wiley & Sons, Ltd.