John Silberholz

The Generalized Traveling Salesman Problem: A New Genetic Algorithm Approach

The Generalized Traveling Salesman Problem (GTSP) is a modification of the Traveling Salesman Problem in which nodes are partitioned into clusters and exactly one node from each cluster is visited in a cycle. It has numerous applications, including airplane routing, computer file sequencing, and postal delivery. To produce solutions to this problem, a genetic algorithm (GA) heuristic mimicking natural selection was coded with several new features including isolated initial populations and a new reproduction mechanism. During modeling runs, the proposed GA outperformed other published heuristics in terms of solution quality while maintaining comparable runtimes.

Comparison of Metaheuristics

Metaheuristics are truly diverse in nature—under the overarching theme of performing operations to escape local optima, algorithms as different as ant colony optimization, tabu search, harmony search, and genetic algorithms have emerged. Due to the unique functionality of each type of metaheuristic, comparison of metaheuristics is in many ways more difficult than other algorithmic comparisons. In this chapter, we discuss techniques for meaningful comparison of metaheuristics. We discuss how to create and classify instances in a new testbed and how to make sure other researchers have access to the problems for future metaheuristic comparisons. Further, we discuss the disadvantages of large parameter sets and how to measure complicating parameter interactions in a metaheuristic’s parameter space. Last, we discuss how to compare metaheuristics in terms of both solution quality and runtime.

The effective application of a new approach to the generalized orienteering problem

The Orienteering Problem (OP) is an important problem in network optimization in which each city in a network is assigned a score and a maximum-score path from a designated start city to a designated end city is sought that is shorter than a pre-specified length limit. The Generalized Orienteering Problem (GOP) is a generalized version of the OP in which each city is assigned a number of scores for different attributes and the overall function to optimize is a function of these attribute scores. In this paper, the function used was a non-linear combination of attribute scores, making the problem difficult to solve. The GOP has a number of applications, largely in the field of routing. We designed a two-parameter iterative algorithm for the GOP, and computational experiments suggest that this algorithm performs as well as or better than other heuristics for the GOP in terms of solution quality while running faster. Further computational experiments suggest that our algorithm also outperforms the leading algorithm for solving the OP in terms of solution quality while maintaining a comparable solution speed.

An Analytics Approach to Designing Combination Chemotherapy Regimens for Cancer

Cancer is a leading cause of death worldwide, and advanced cancer is often treated with combinations of multiple chemotherapy drugs. In this work, we develop models to predict the outcomes of clinical trials testing combination chemotherapy regimens before they are run and to select the combination chemotherapy regimens to be tested in new phase II and phase III clinical trials, with the primary objective of improving the quality of regimens tested in phase III trials compared to current practice. We built a database of 414 clinical trials for advanced gastric cancer and use it to build statistical models that attain an out-of-sample R 2 of 0.56 when predicting a trial’s median overall survival (OS) and an out-of-sample area under the curve (AUC) of 0.83 when predicting if a trial has unacceptably high toxicity. We propose models that use machine learning and optimization to suggest regimens to be tested in phase II and phase III trials. Though it is inherently challenging to evaluate the performance of such models without actually running clinical trials, we use two techniques to obtain estimates for the quality of regimens selected by our models compared with those actually tested in current clinical practice. Both techniques indicate that the models might improve the efficacy of the regimens selected for testing in phase III clinical trials without changing toxicity outcomes. This evaluation of the proposed models suggests that they merit further testing in a clinical trial setting. This paper was accepted by Noah Gans, stochastic models and systems .

Integrating post-Newtonian equations on graphics processing units

We report on early results of a numerical and statistical study of binary black hole inspirals. The two black holes are evolved using post-Newtonian approximations starting with initially randomly distributed spin vectors. We characterize certain aspects of the distribution shortly before merger. In particular we note the uniform distribution of black hole spin vector dot products shortly before merger and a high correlation between the initial and final black hole spin vector dot products in the equal-mass, maximally spinning case. These simulations were performed on Graphics Processing Units, and we demonstrate a speed-up of a factor 50 over a more conventional CPU implementation.

Comparison of Heuristics for Solving the Gmlst Problem

Given a graph G whose edges are labeled with one or more labels, the Generalized Minimum Label Spanning Tree problem seeks the spanning tree over this graph that uses the least number of labels. We provide a mathematical model for this problem and propose effective greedy heuristics and metaheuristics. We finally compare the results of these algorithms with benchmark heuristics for the related Minimum Label Spanning Tree problem.

Comparison of heuristics for the colourful travelling salesman problem

In the colourful travelling salesman problem CTSP, given a graph G with a not necessarily distinct label colour assigned to each edge, a Hamiltonian tour with the minimum number of different labels is sought. The problem is a variant of the well-known Hamiltonian cycle problem and has potential applications in telecommunication networks, optical networks, and multimodal transportation networks, in which one aims to ensure connectivity or other properties by means of a limited number of connection types. We propose two new heuristics based on the deconstruction of a Hamiltonian tour into subpaths and their reconstruction into a new tour, as well as an adaptation of an existing approach. Extensive experimentation shows the effectiveness of the proposed approaches.

Moneyball for Academics: Network Analysis for Predicting Research Impact

How are scholars ranked for promotion, tenure and honors? How can we improve the quantitative tools available for decision makers when making such decisions? Can we predict the academic impact of scholars and papers at early stages using quantitative tools?Current academic decisions (hiring, tenure, prizes) are mostly very subjective. In the era of “Big Data,” a solid quantitative set of measurements should be used to support this decision process.This paper presents a method for predicting the probability of a paper being in the most cited papers using only data available at the time of publication. We find that highly cited papers have different structural properties and that these centrality measures are associated with increased odds of being in the top percentile of citation count.The paper also presents a method for predicting the future impact of researchers, using information available early in their careers. This model integrates information about changes in a young researcher’s role in the citation network and co-authorship network and demonstrates how this improves predictions of their future impact.These results show that the use of quantitative methods can complement the qualitative decision-making process in academia and improve the prediction of academic impact.

Statistical constraints on binary black hole inspiral dynamics

We perform a statistical analysis of binary black holes in the post-Newtonian approximation by systematically sampling and evolving the parameter space of initial configurations for quasi-circular inspirals. Through a principal component analysis of spin and orbital angular momentum variables, we systematically look for uncorrelated quantities and find three of them which are highly conserved in a statistical sense, both as functions of time and with respect to variations in initial spin orientations. For example, we find a combination of spin scalar products, , that is exactly conserved in time at the considered post-Newtonian order (including spin–spin and radiative effects) for binaries with equal masses and spin magnitudes evolving in a quasi-circular inspiral. We also look for and find the variables that account for the largest variations in the problem. We present binary black hole simulations of the full Einstein equations analyzing to what extent these results might carry over to the full theory in the inspiral and merger regimes. Among other applications these results should be useful both in semi-analytical and numerical building of templates of gravitational waves for gravitational wave detectors.

OR Forum—Tenure Analytics: Models for Predicting Research Impact

Tenure decisions, key decisions in academic institutions, are primarily based on subjective assessments of candidates. Using a large-scale bibliometric database containing 198,310 papers published 1975–2012 in the field of operations research (OR), we propose prediction models of whether a scholar would perform well on a number of future success metrics using statistical models trained with data from the scholar’s first five years of publication, a subset of the information available to tenure committees. These models, which use network centrality of the citation network, coauthorship network, and a dual network combining the two, significantly outperform simple predictive models based on citation counts alone. Using a data set of the 54 scholars who obtained a Ph.D. after 1995 and held an assistant professorship at a top-10 OR program in 2003 or earlier, these statistical models, using data up to five years after the scholar became an assistant professor and constrained to tenure the same number of candidates as tenure committees did, made a different decision than the tenure committees for 16 (30%) of the candidates. This resulted in a set of scholars with significantly better future A-journal paper counts, citation counts, and h -indexes than the scholars actually selected by tenure committees. These results show that analytics can complement the tenure decision-making process in academia and improve the prediction of academic impact.