ADEPT: A Heuristic Program for Proving Theorems of Group Theory

A computer program, named ADEPT (A Distinctly Empirical Prover of Theorems), has been written which proves theorems taken from the abstract theory of groups. Its operation is basically heuristic, incorporating many of the techniques of the human mathematician in a "natural" way. This program has proved almost 100 theorems, as well as serving as a vehicle for testing and evaluating special-purpose heuristics. A detailed description of the program is supplemented by accounts of its performance on a number of theorems, thus providing many insights into the particular problems inherent in the design of a procedure capable of proving a variety of theorems from this domain. Suggestions have been formulated for further efforts along these lines, and comparisons with related work previously reported in the literature have been made.

A hyper-heuristic ensemble method for static job-shop scheduling.

We describe a new hyper-heuristic method NELLI-GP for solving job-shop scheduling problems (JSSP) that evolves an ensemble of heuristics. The ensemble adopts a divide-and-conquer approach in which each heuristic solves a unique subset of the instance set considered. NELLI-GP extends an existing ensemble method called NELLI by introducing a novel heuristic generator that evolves heuristics composed of linear sequences of dispatching rules: each rule is represented using a tree structure and is itself evolved. Following a training period, the ensemble is shown to outperform both existing dispatching rules and a standard genetic programming algorithm on a large set of new test instances. In addition, it obtains superior results on a set of 210 benchmark problems from the literature when compared to two state-of-the-art hyperheuristic approaches. Further analysis of the relationship between heuristics in the evolved ensemble and the instances each solves provides new insights into features that might describe similar instances.

Evaluation of tumor response, disease control, progression-free survival, and time to progression as potential surrogate end points in metastatic breast cancer.

PURPOSE: Overall survival (OS) can be observed only after prolonged follow-up, and any potential effect of first-line therapies on OS may be confounded by the effects of subsequent therapy. We investigated whether tumor response, disease control, progression-free survival (PFS), or time to progression (TTP) could be considered a valid surrogate for OS to assess the benefits of first-line therapies for patients with metastatic breast cancer. PATIENTS AND METHODS: Individual patient data were collected on 3,953 patients in 11 randomized trials that compared an anthracycline (alone or in combination) with a taxane (alone or in combination with an anthracycline). Surrogacy was assessed through the correlation between the end points as well as through the correlation between the treatment effects on the end points. RESULTS: Tumor response (survival odds ratio [OR], 6.2; 95% CI, 5.3 to 7.0) and disease control (survival OR, 5.5; 95% CI, 4.8 to 6.3) were strongly associated with OS. PFS (rank correlation coefficient, 0.688; 95% CI, 0.686 to 0.690) and TTP (rank correlation coefficient, 0.682; 95% CI, 0.680 to 0.684) were moderately associated with OS. Response log ORs were strongly correlated with PFS log hazard ratios (linear coefficient [rho], 0.96; 95% CI, 0.73 to 1.19). Response and disease control log ORs and PFS and TTP log hazard ratios were poorly correlated with log hazard ratios for OS, but the confidence limits of rho were too wide to be informative. CONCLUSION: No end point could be demonstrated as a good surrogate for OS in these trials. Tumor response may be an acceptable surrogate for PFS.

Real-Time Decision Making and Aggressive Behavior in Youth: A Heuristic Model of Response Evaluation and Decision (RED).

Considerable scientific and intervention attention has been paid to judgment and decision-making systems associated with aggressive behavior in youth. However, most empirical studies have investigated social-cognitive correlates of stable child and adolescent aggressiveness, and less is known about real-time decision making to engage in aggressive behavior. A model of real-time decision making must incorporate both impulsive actions and rational thought. The present paper advances a process model (response evaluation and decision; RED) of real-time behavioral judgments and decision making in aggressive youths with mathematic representations that may be used to quantify response strength. These components are a heuristic to describe decision making, though it is doubtful that individuals always mentally complete these steps. RED represents an organization of social-cognitive operations believed to be active during the response decision step of social information processing. The model posits that RED processes can be circumvented through impulsive responding. This article provides a description and integration of thoughtful, rational decision making and nonrational impulsivity in aggressive behavioral interactions.

Analyzing and selecting tasks for mathematics teaching: a heuristic

In planning units and lessons every day, teachers face the problem of designing a sequence of activities to promote learning. In particular, they are expected to foster the development of learning goals in their students. Based on the idea of learning path of a task, we describe a heuristic procedure to enable teachers to characterize a learning goal in terms of its cognitive requirements and to analyze and select tasks based on this characterization. We then present an example of how a group of future teachers used this heuristic in a preservice teachers training course and discuss its contributions and constraints.

A new heuristic for three-machine flow shop scheduling

This paper considers the problem of sequencing n jobs in a three-machine flow shop with the objective of minimizing the makespan, which is the completion time of the last job. An O(n log n) time heuristic that is based on Johnson's algorithm is presented. It is shown to generate a schedule with length at most 5/3 times that of an optimal schedule, thereby reducing the previous best available worst-case performance ratio of 2. An application to the general flow shop is also discussed.

A nested location-routing heuristic using route length estimation

A nested heuristic approach that uses route length approximation is proposed to solve the location-routing problem. A new estimation formula for route length approximation is also developed. The heuristic is evaluated empirically against the sequential method and a recently developed nested method for location routing problems. This testing is carried out on a set of problems of 400 customers and around 15 to 25 depots with good results.

Intelligent technologies for nuclear power systems: heuristic and neural tools

The consecutive, partly overlapping emergence of expert systems and then neural computation methods among intelligent technologies, is reflected in the evolving scene of their application to nuclear engineering. This paper provides a bird's eye view of the state of the application in the domain, along with a review of a particular task, the one perhaps economically more important: refueling design in nuclear power reactors.

Nested heuristic methods for the location-routeing problem

The concept of 'nested methods' is adopted to solve the location-routeing problem. Unlike the sequential and iterative approaches, in this method we treat the routeing element as a sub-problem within the larger problem of location. Efficient techniques that take into account the above concept and which use a neighbourhood structure inspired from computational geometry are presented. A simple version of tabu search is also embedded into our methods to improve the solutions further. Computational testing is carried out on five sets of problems of 400 customers with five levels of depot fixed costs, and the results obtained are encouraging.

A greedy open shop heuristic with job priorities

The paper presents an improved version of the greedy open shop approximation algorithm with pre-ordering of jobs. It is shown that the algorithm compares favorably with the greedy algorithm with no pre-ordering by reducing either its absolute or relative error. In the case of three machines, the new algorithm creates a schedule with the makespan that is at most 3/2 times the optimal value.

A heuristic algorithm for two-machine re-entrant shop scheduling

This paper considers the problem of sequencing n jobs in a two‐machine re‐entrant shopwith the objective of minimizing the maximum completion time. The shop consists of twomachines, M1 and M2 , and each job has the processing route (M1 , M2 , M1 ). An O(n log n)time heuristic is presented which generates a schedule with length at most 4/3 times that ofan optimal schedule, thereby improving the best previously available worst‐case performanceratio of 3/2.

The use of a biased heuristic by a genetic algorithm applied to the design of multipoint connections in a local access network

This paper presents a genetic algorithm for finding a constrained minimum spanning tree. The problem is of relevance in the design of minimum cost communication networks, where there is a need to connect all the terminals at a user site to a terminal concentrator in a multipoint (tree) configuration, while ensuring that link capacity constraints are not violated. The approach used maintains a distinction between genotype and phenotype, which produces superior results to those found using a direct representation in a previous study.

A heuristic for the two-machine open-shop scheduling problem with transportation times

The paper considers a problem of scheduling n jobs in a two-machine open shop to minimize the makespan, provided that preemption is not allowed and the interstage transportation times are involved. This problem is known to be unary NP-hard. We present an algorithm that requires O (n log n) time and provides a worst-case performance ratio of 3/2.