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In this paper, a set of stylized numerical benchmark problems is developed. These problems are based on the Oak Ridge National Laboratory preconceptual design of a fluoride-salt-cooled small modula...

This paper deals with a set of geometrical problems for mathematical problem-solving at different difficulty levels. All of these are presented as national flags and one has to investigate invarian...

This study addresses the single-machine scheduling problem with a common due window (CDW) that has a constant size and position. The objective is to minimise the total weighted earliness–tardiness penalties for jobs completed out of the CDW. To determine a schedule as close to optimum as possible, this study develops a dynamic dispatching rule and an effective constructive heuristic. The better performance of the proposed heuristic is demonstrated by comparing the results of it with those of a state-of-the-art greedy heuristic on a well-known benchmark problem set. In addition, we incorporate the constructive heuristic into a best-so-far meta-heuristic to examine the benefit of the proposed heuristic. The results show that the best known solutions in 144 out of the 250 benchmark instances are improved.

This work proposes a high-performance algorithm for solving the multi-objective unrelated parallel machine scheduling problem. The proposed approach is based on the iterated Pareto greedy (IPG) algorithm but exploits the accessible Tabu list (TL) to enhance its performance. To demonstrate the superior performance of the proposed Tabu-enhanced iterated Pareto greedy (TIPG) algorithm, its computational results are compared with IPG and existing algorithms on the same benchmark problem set. Experimental results reveal that incorporating the accessible TL can eliminate ineffective job moves, causing the TIPG algorithm to outperform state-of-the-art approaches in the light of five multi-objective performance metrics. This work contributes a useful theoretical and practical optimisation method for solving this problem.

Minimizing makespan in permutation flowshops is one of the most frequently investigated problems in scheduling theory. The NEH heuristic is commonly regarded as the best current constructive heuristic for solving this NP-hard problem. In this paper, we propose a novel constructive heuristic with an effective tie-breaking strategy to improve the scheduling quality of this problem. Experimental results reveal that the proposed approach outperforms NEH for all problem sizes on the standard benchmark problem set of Taillard. This study thus appears to successfully demonstrate a high-performing constructive heuristic that can serve as a new foundation for future research on this extremely challenging scheduling problem.

The distributed permutation flowshop scheduling problem (DPFSP) is a newly proposed topic in the shop scheduling field, which has important application in globalised and multi-plant environments. This study presents a modified iterated greedy (MIG) algorithm for this problem to minimise the maximum completion time among all the factories. Compared with previous approaches, the proposed algorithm is simpler yet more effective, more efficient, and more robust in solving the DPFSP. To validate the performance of the proposed MIG algorithm, computational experiments and comparisons are conducted on an extended benchmark problem set of Taillard. Despite its simplicity, the computational results show that the proposed MIG algorithm outperforms all existing algorithms, and the best-known solutions for almost half of instances are updated. This study can be offered as a contribution to the growing body of work on both theoretically and practically useful approaches to the DPFSP.

This paper presents a hybrid discrete differential evolution HDDE algorithm to solve the Pm// problem. The coding and decoding scheme based on job permutation is applied in the algorithm. The algorithm employs several efficient heuristics in the initialisation phase and incorporates an insertion-based local search. To validate the proposed algorithm, computational experiments are conducted on a benchmark problem set from the literature. Computational results show that the HDDE algorithm outperforms the existing state-of-the-art algorithms for the Pm// problem.

In this paper, two evolutionary heuristics are proposed to determine the cutting parameters in multipass turning operations. Optimal selection of cutting speed, feed rate, and depth of cut is important in machining operations due to significant influence of these parameters on machining quality and machining economics. This paper is about optimising these three parameters using heuristic methods. The first heuristic implemented in the paper is a simple Particle Swarm Optimisation (PSO) algorithm, and the second heuristic implemented is a hybrid of Genetic Algorithm and Artificial Immune System (GA-AIS). A multipass turning operation with rough machining and then finish machining is considered in this paper. The objective function considered is minimisation of unit production cost that optimises the machining parameters. The performance of the PSO and GA-AIS are evaluated by comparing with the heuristics reported in the literature using a problem set used by other researchers for this problem. The results ...

The purpose of the study was to examine the role of problem sets on student learning and satisfaction in university microeconomics. 126 students participated in the study in consecutive years. Independent samples t-test shows that students who were not given answer keys outperformed students who were given answer keys. Multiple regression analysis demonstrates that, along with high school percentiles and student major, problem set with or without answer key significantly explains student learning in economics. The authors discuss the role of answer keys and their implications for teaching university economics courses.

Imagine a typical student taking an average set of courses. She has to complete a laboratory write-up for chemistry, write a research paper for linguistics, finish a problem set for mathematics, cr...

This study considers the scheduling problem of multistage hybrid flowshops with multiprocessor tasks, which is a core topic for numerous industrial applications. An effective and efficient heuristic, namely the heuristic of multistage hybrid flowshops (HMHF) is proposed to solve this problem. To verify the developed heuristic, computational experiments are conducted on a well-known benchmark problem set. The results are compared with 10 constructive heuristics and a tabu search (TS) based meta-heuristic from the relevant literature. These computational results show that the proposed HMHF heuristic is highly effective when compared to these algorithms for this problem on the same benchmark instances.

The emergence of metamodels as approximate objective function representations offers the ability to ‘design’ metamodels with favourable optimization characteristics without compromising the accurate representational capabilities of arbitrary function topologies and modalities. With non-uniform rational B-splines (NURBs) as a metamodel basis, favourable optimization properties can be obtained which allow the intelligent selection of starting points for multistart optimization algorithms and which constrain optimization searches to metamodel regions containing the global metamodel optimum. In this article NURBs-based metamodels are used to define an optimization algorithm (HyPerOp) which guarantees the discovery of the global metamodel optimum with known computational effort. Emphasis is placed on demonstrating how NURBs’ properties contribute to a favourable objective function approximation. Through a large non-linear optimization trial problem set, the claim that HyPerOp is guaranteed to find the global m...

Most homework sets in statistics courses are constructed so that students concentrate or “mass” their practice on a certain topic in one problem set. Distributed practice homework sets include review problems in each set so that practice on a topic is distributed across problem sets. There is a body of research that points to the efficacy of distributed practice for developing a variety of skills from word recall to surgical techniques. A trial was conducted in several sections of a business statistics course where students were randomly assigned to either have massed practice homework sets or distributed practice homework sets. The two groups were then compared on the course assessments. The results show some evidence for the efficacy of distributed practice homework sets, although this effect may be modified significantly by the instructor or by a Hawthorne effect.

This paper reports four experiments investigating whether model construction of linear reasoning problems is open to strategic decisions. A reversed choice/nochoice paradigm was used in which reasoners first had to apply two model construction strategies (acronym and rehearsal strategy) to two problem sets. Next, they could choose freely among the two strategies to apply to a new problem set. Experiment 1 showed that reasoners selected the strategy that they experienced as the most accurate one in the no-choice phase. Moreover, in Experiment 2, it was found that reasoners adapted their strategy choice to changing problem features, to use the most suitable strategy for premise encoding. Experiments 3 and 4 generalised these findings to more complex linear reasoning problems with a mixed sentence frame and a semi-continuous presentation of the premises, and to two-model problems. On the basis of these results, we argue that strategic decisions influence model construction in linear reasoning.

Over the past 50 years, researchers have developed many simple constructive heuristics for the scheduling problem. A major defect of these heuristics is the non-robustness of their solutions. An ant colony system (ACS) approach is presented to continuously improve the constructive heuristics. To verify the developed ACS approach, a computational study is conducted on the single machine total weighted tardiness problem. The results show that the proposed approach can effectively improve the robustness of various constructive heuristics, and outperform the existing heuristics for a well-known benchmark problem set. From the viewpoints of both the solution quality and computational expenses, the proposed ACS approach is an efficient and effective method for scheduling problems.

In many solution methods for resource-constrained project scheduling, it is assumed that both the duration of each activity and its resource requirements are known and fixed. In real-life projects, however, it often occurs that only one renewable bottleneck resource is available and that the activities have a total work content which indicates how much work (expressed in man-periods) has to be performed. The objective then is to schedule each activity in one of its possible execution modes, subject to the precedence and resource constraints, in order to minimize the project makespan. We present a branch-and-bound procedure and report computational results, obtained using a full factorial experiment on a randomly generated problem set.

In this article, we investigate whether assigning problem sets to students in economic principles classes increases their learning. Two classes taught by the same instructor using the same textbook and examinations, in the mornings of the same days of the week, provided the setting. One class was assigned problems, whereas the other was not. At the end of the semester, the class that received problem sets did not score significantly higher than the control group on either the TUCE or a comprehensive multiple-choice final examination, ceteris paribus. However, the experimental group did have significantly better attendance, and the increased attendance had a significantly positive effect on learning, according to both measures.

Validation of new products during the design and early life stages is vital to successful product introduction to the marketplace. Frequently the duration of validation is either too short (due to schedule compression) or too long (due to minimal correc..

Regarding the cattle industry in Greece, the main concern is to promote self-sufficiency, in the context of minimizing imports, by increasing the output. Since in multi-product farms, there is a close interdependence regarding production response and changes in relative profitability, the problem set is to determine the optimal price policy for attaining some pro-assigned levels of production without reducing the stocks. In this context an optimal control problem has been formulated for the purpose of deriving the optimum structure of the relative farm prices. The control problem has been solved by applying a procedure which utilizes some useful properties of the generalized inverse. The method has been found to be quite efficient, for a certain class of optimal control problems, when compared with other routine methods.

SUMMARY CAE has enabled vibrational problems, which were regarded as intractable 20 years ago, to be solvable by students using computational support. The paper describes a problem set to final year undergraduates which concerns the torsional vibrational response of a three degrees of freedom system which is subjected simultaneously to three different arbitrarily varying torques. The solution involves the use of standard library routines for matrix multiplication and eigensolutions, a Runge-Kutta routine to solve a second order differential equation and general competence in writing software.

Summary Thirty-seven graduate students in nursing were given the problem set, used by Tversky and Kahneman in their study on the “law of small numbers,” as an extra credit part of a final examination for a statistics course. While some conservativism was noted, the major Tversky and Kahneman postulates were supported. These incidentally obtained replication data provide support for the contention that the tendency, induced by representativeness, to confidently make inferences is only slightly, if at all, determined by factors such as statistical and empirical sophistication, availability of normative criteria, knowledge about the shortcomings of human judgment, and the conditions under which inferences are to be made.