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.     

Interactive Frameworks for Investigation of Goal Programming Models: Theory and Practice

This paper discusses means of introducing decision maker input into the goal programming model in order to produce more satisfactory solutions. Both formal interactive methods and informal trial-and-error approaches are discussed. The design criteria for the choice of the initial test solution and the stopping criteria for the final solution are detailed. The area of presentation of results to, and elicitation of preferences from, the decision maker is dealt with. Practical suggestions for means of parameter alteration to produce alternative solutions are given. Finally, the integration of the above issues into an integrated framework is discussed. © 1997 John Wiley & Sons, Ltd.     

Approximately Efficient Solutions in Vector Optimization

An approach to approximating solutions in vector optimization is developed for vector optimization problems with arbitrary ordering cones. This paper presents a study of approximately efficient points of a given set with respect to a convex cone in an ordered Banach space. Existence results for such approximately efficient points are obtained. A domination property related to these existence results is observed and then it is proved that each element of a given set is approximated by the sum of a point in a convex cone inducing the ordering and a point in a finite set consisting of such approximately efficient points of the set.     

Cleaning versus replacement in power plant air preheaters: a comparison between deterministic and stochastic goal programming models

Power plants lose efficiency when the air preheater elements are not replaced or cleaned as they deteriorate. Replacing is more expensive than cleaning but more secure to preserve power and lifetime. How many baskets should be then replaced and how many cleaned to achieve ‘satisficing’ goals of cost, power and lifetime? We design deterministic/stochastic goal programming approaches to this problem and develop a decision case for usual preheaters. Some discrepancies in results between both approaches appear, the deterministic model advising to replace less baskets than the stochastic, which is plausible due to the risk variable. Copyright © 2005 John Wiley & Sons, Ltd.     

Choice functions in multistage optimization

This paper is devoted to the multistage optimization problem with a vector-valued gain function. The notion of optimality is determined here by the choice function. The conditions for the choice function that guarantee the applicability and efficiency of dynamic programming are found.     

Generating consensus priority interval vectors for group decision‐making in the AHP

Many practical and important decision‐making problems are complicated by at least two factors: (1) the qualitative/subjective nature of some criteria often results in uncertainty in the individual ratings; and (2) group decision‐making is involved and some means of aggregating individual ratings is required. Traditionally, both individual and group priorities have been represented as point estimates, but this approach presents severe limitations for accommodating imprecision in the decision‐making process. This paper examines the group decision‐making problem in the context where priorities are represented as numeric intervals. A set of techniques that could be used at some of the phases of an analytic hierarchy process (AHP)‐based group decision‐making process, which has the objective of generating a ‘consensus’ priority that represents the group's opinion with regards to the relative importance of a set of N objects (e.g. criteria, alternatives), is presented. Copyright © 2000 John Wiley & Sons, Ltd.     

On portfolio management with value at risk and uncertain returns via an artificial neural network scheme

This paper focuses on the computation issue of portfolio optimization with scenario-based Value-at-Risk. The main idea is to replace the portfolio selection models with linear programming problems. According to the convex optimization theory and some concepts of ordinary differential equations, a neural network model for solving linear programming problems is presented. The equilibrium point of the proposed model is proved to be equivalent to the optimal solution of the original problem. It is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the portfolio selection problem with uncertain returns. Several illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper.     

Motor Programming When Sequencing Multiple Elements of the Same Duration

Motor programming at the self-select paradigm was adopted in 2 experiments to examine the processing demands of independent processes. One process (INT) is responsible for organizing the internal features of the individual elements in a movement (e.g., response duration). The 2nd process (SEQ) is responsible for placing the elements into the proper serial order before execution. Participants in Experiment 1 performed tasks involving 1 key press or sequences of 4 key presses of the same duration. Implementing INT and SEQ was more time consuming for key-pressing sequences than for single key-press tasks. Experiment 2 examined whether the INT costs resulting from the increase in sequence length observed in Experiment 1 resulted from independent planning of each sequence element or via a separate "multiplier" process that handled repetitions of elements of the same duration. Findings from Experiment 2, in which participants performed single key presses or double or triple key sequences of the same duration, suggested that INT is involved with the independent organization of each element contained in the sequence. Researchers offer an elaboration of the 2-process account of motor programming to incorporate the present findings and the findings from other recent sequence-learning research.     

Combined Effects of Movement Velocity and Duration on Programming Time: Spijkers (1989) Revisited

The goal of the present study was to determine the combined effects of movement velocity and duration on motor programming. Subjects were submitted to a two-choice reaction time task that could be completed by aiming movements differing in the mean velocity at which they were to be produced as well as by their movement time. The results of the present study indicate that, in each pair of responses used, the responses having the higher mean velocity were initiated faster than those having the lower mean velocity. Contrary to Spijkers' (1989) study, the different movement time pairings did not modify the effect of movement velocity on response programming time. Moreover, the same pattern of results was observed whether or not the subjects were permitted to visually guide their ongoing movement. Thus, Spijkers' proposition, that the type of control one may use to guide an aiming movement needs to be determined before movement initiation can take place, was not confirmed.