An electromagnetic meta-heuristic for the nurse scheduling problem

In this paper, we present a novel meta-heuristic technique for the nurse scheduling problem (NSP). This well-known scheduling problem assigns nurses to shifts per day maximizing the overall quality of the roster while taking various constraints into account. The problem is known to be NP-hard. Due to its complexity and relevance, many algorithms have been developed to solve practical and often case-specific models of the NSP. The huge variety of constraints and the several objective function possibilities have led to exact and meta-heuristic procedures in various guises, and hence comparison and state-of-the-art reporting of standard results seem to be a utopian idea. We present a meta-heuristic procedure for the NSP based on the framework proposed by Birbil and Fang (J. Glob. Opt. 25, 263–282, 2003). The Electromagnetic (EM) approach is based on the theory of physics, and simulates attraction and repulsion of sample points in order to move towards a promising solution. Moreover, we present computational experiments on a standard benchmark dataset, and solve problem instances under different assumptions. We show that the proposed procedure performs consistently well under many different circumstances, and hence, can be considered as robust against case-specific constraints.     

Comparison and hybridization of crossover operators for the nurse scheduling problem

In this paper, we present a hybrid genetic algorithm for the well-known nurse scheduling problem (NSP). The NSP involves the construction of roster schedules for nursing staff in order to maximize the quality of the roster schedule subject to various hard constraints. In the literature, several genetic algorithms have been proposed to solve the NSP under various assumptions. The contribution of this paper is twofold. First, we extensively compare the various crossover operators and test them on a standard dataset in a solitary approach. Second, we propose several options to hybridize the various crossover operators.     

罚转向网络最短路径算法及其复杂性研究

本文建立和研究了具有转向惩罚值的网络模型．论文首先引入了罚转向网络符号及规则，对所建立的罚转向网络模型的性质进行了讨论，在证明了路径与子路径关系的三个定理之后，提出了求解其最短路径的算法并证明了算法的复杂性结论，论文最后给出了一个用该算法求解项转向网络的最短路径实例．     

A global optimization method for nonconvex separable programming problems

Conventional methods of solving nonconvex separable programming (NSP) problems by mixed integer programming methods requires adding numerous 0–1 variables. In this work, we present a new method of deriving the global optimum of a NSP program using less number of 0–1 variables. A separable function is initially expressed by a piecewise linear function with summation of absolute terms. Linearizing these absolute terms allows us to convert a NSP problem into a linearly mixed 0–1 program solvable for reaching a solution which is extremely close to the global optimum.     

Quadratic Hamilton–Poisson Systems on $\mathfrak{se}(1,1)^{*}_{-}$: The Inhomogeneous Case

The blow-up of smooth solution to the isentropic compressible Navier-Stokes-Poisson (NSP) system on \(\mathbb{R}^{d}\) is studied in this paper. We obtain that if the initial density is compactly supported, the spherically symmetric smooth solution to the NSP system on \(\mathbb{R}^{d}\ (d\geq 2)\) blows up in finite time. In the case \(d=1\), if \(2\mu +\lambda >0\), then the NSP system only exits a zero smooth solution on ? for the compactly supported initial density.     

Iteratively reweighted algorithm for signals recovery with coherent tight frame

We consider the problem of compressed sensing with a coherent tight frame and design an iteratively reweighted least squares algorithm to solve it. To analyze the problem, we propose a sufficient null space property under a tight frame (sufficient D‐NSP). We show that, if a measurement matrix A satisfies the sufficient D‐NSP of order s, then an s‐sparse signal under the tight frame can be exactly recovered. Furthermore, if A satisfies the restricted isometric property with tight frame D of order 2bs, then it also satisfies the sufficient D‐NSP of order as with a < b and b sufficiently large. We prove the convergence of the algorithm based on the sufficient D‐NSP and give the upper error bounds. In numerical experiments, we use the discrete cosine transform, discrete Fourier transform, and Haar wavelets to verify the effectiveness of this algorithm. With increasing measurement number, the signal‐to‐noise ratio increases monotonically.     

Genetic algorithm-based subproblem solution procedures for a modified shifting bottleneck heuristic for complex job shops

In this paper, we consider a modified shifting bottleneck heuristic for complex job shops. The considered job shop environment contains parallel batching machines, machines with sequence-dependent setup times and reentrant process flows. Semiconductor wafer fabrication facilities (Wafer Fabs) are typical examples for manufacturing systems with these characteristics. Our primary performance measure is total weighted tardiness (TWT). The shifting bottleneck heuristic uses a disjunctive graph to decompose the overall scheduling into scheduling problems for single tool groups. The scheduling algorithms for these scheduling problems are called subproblem solution procedures (SSPs). In previous research, only subproblem solution procedures based on dispatching rules have been considered. In this paper, we are interested in how much we can gain in terms of TWT if we apply more sophisticated subproblem solution procedures like genetic algorithms for parallel machine scheduling. We conduct simulation experiments in a dynamic job shop environment in order to assess the performance of the suggested subproblem solution procedures. It turns out that using near to optimal subproblem solution procedures leads in many situations to improved results compared to dispatching-based subproblem solution procedures.     

Short-Term Forecasting: A Review of Procedures in the Electricity Supply Industry

A review of forecasting procedures which have been developed in the electricity supply industry to serve the short-term needs of load dispatching is presented. The procedures are broadly categorised into whether or not use is made of a standard load concept. From the point of view of comparative research in applied forecasting, some comments are proposed on the wide variety of methods which have been developed for basically similar problems.     

A survey of solution techniques for the partially observed Markov decision process

We survey several computational procedures for the partially observed Markov decision process (POMDP) that have been developed since the Monahan survey was published in 1982. The POMDP generalizes the standard, completely observed Markov decision process by permitting the possibility that state observations may be noise-corrupted and/or costly. Several computational procedures presented are convergence accelerating variants of, or approximations to, the Smallwood-Sondik algorithm. Finite-memory suboptimal design results are reported, and new research directions involving heuristic search are discussed.This research was supported by NSF Grant ECS-8708183 and ARO Contract DAAG-29-85-K0089.     

Optimal Biopsy Protocols for Prostate Cancer

Prostate cancer is the second leading cause of cancer-related death among American men. Biopsy for prostate cancer is a procedure known as transrectal ultrasound-guided needle biopsy. Because of the low resolution of ultrasound, the urologist cannot usually distinguish between cancerous and healthy tissue. For this reason, most biopsies follow standard protocols based on long-term experience of physicians. Recent studies indicate that these protocols have a significant rate of false negative diagnoses. In this research we use real prostate specimens removed by prostatectomy to develop a 3-D distribution map of cancer in the prostate, and use this to develop optimized biopsy procedures. The new procedures have detection rates that are significantly higher than those of current procedures, and thus have the potential to increase the rate of early detection of prostate cancer.     

A sequential integer programming method for discontinuous labor tour scheduling

General set-covering formulations (GSCFs) of labor tour scheduling problems have recently received substantial attention in the research literature. The most successful heuristic approaches to these problems have used the linear programming (LP) solution to the GSCF as a starting point and subsequently applied heuristic augmentation and improvement procedures to obtain feasible integer solutions. Integer programming (IP) methods eliminate the need for augmentation and improvement procedures, but have generally been considered intractable for large GSCFs. In this paper we present a sequential mixed-integer programming (SMIP) heuristic for discontinuous (< 24 hours/day) tour-scheduling problems which takes advantage of the structure of the GSCF. The new heuristic substantially outperformed two prominent LP-based methods across 432 full-time workforce test problems, yielding optimal solutions for 429 of the problems. For a set of 36 test problems associated with a mixed-workforce scheduling environment that allowed both full-time and part-time employees with varying levels of cost and productivity, the SMIP heuristic yielded solution costs that were significantly better than previously published costs obtained with competitive methods.     

Zero duality gap in surrogate constraint optimization: A concise review of models

Surrogate constraint relaxation was proposed in the 1960s as an alternative to the Lagrangian relaxation for solving difficult optimization problems. The duality gap in the surrogate relaxation is always as good as the duality gap in the Lagrangian relaxation. Over the years researchers have proposed procedures to reduce the gap in the surrogate constraint. Our aim is to review models that close the surrogate duality gap. Five research streams that provide procedures with zero duality gap are identified and discussed. In each research stream, we will review major results, discuss limitations, and suggest possible future research opportunities. In addition, relationships between models if they exist, are also discussed.     

Lifting and separation procedures for the cut polytope

The max-cut problem and the associated cut polytope on complete graphs have been extensively studied over the last 25 years. However, in comparison, only little research has been conducted for the cut polytope on arbitrary graphs, in particular separation algorithms have received only little attention. In this study we describe new separation and lifting procedures for the cut polytope on general graphs. These procedures exploit algorithmic and structural results known for the cut polytope on complete graphs to generate valid, and sometimes facet defining, inequalities for the cut polytope on arbitrary graphs in a cutting plane framework. We report computational results on a set of well-established benchmark problems.     

Flowshop scheduling research after five decades

Since Johnson’s seminal paper in 1954, flowshop scheduling problems have received considerable research attention over the last fifty years. As a result, several optimization and heuristic solution procedures are available to solve a variety of flowshop scheduling problems. This paper provides a brief glimpse into the evolution of flowshop scheduling problems and possible approaches for their solution over the last fifty years. It briefly introduces the current flowshop problems being solved and the approaches being taken to solve (optimally or approximately) them. The paper concludes with some fruitful directions for future research.     

Branch and win: OR tree search algorithms for solving combinatorial optimisation problems

Currently, most combinatorial optimisation problems have to be solved, if the optimum solution is sought, using general techniques to explore the space of feasible solutions and, more specifically, through exploratory enumerative procedures in trees and search graphs. We propose Branch and Win, a general formulation for understanding and synthesising the different tree search procedures that have been presented in the literature of operations research as well as in that of artificial intelligence. Several general ideas are also presented, whose application allows designing new hybrid search algorithms, in order to implement the procedure.     

Strategies of node selection in search procedures for solving combinatorial optimization problems: A survey and a general formalization

Currently, most combinatorial optimization problems have to be solved, if the optimum solution is sought, using general techniques to explore the space of feasible solutions and, more specifically, through exploratory enumerative procedures in trees and search graphs. The objective of this work is to propose a survey and a general formalization of the selection strategy of the next node to explore, a feature that is common to all these optimization procedures. This research has been partially supported by TAP98-0494 project     

A common framework and taxonomy for multicriteria scheduling problems with interfering and competing jobs: Multi-agent scheduling problems

Most classical scheduling research assumes that the objectives sought are common to all jobs to be scheduled. However, many real-life applications can be modeled by considering different sets of jobs, each one with its own objective(s), and an increasing number of papers addressing these problems has appeared over the last few years. Since so far the area lacks a unified view, the studied problems have received different names (such as interfering jobs, multi-agent scheduling, and mixed-criteria), some authors do not seem to be aware of important contributions in related problems, and solution procedures are often developed without taking into account existing ones. Therefore, the topic is in need of a common framework that allows for a systematic recollection of existing contributions, as well as a clear definition of the main research avenues. In this paper we review multicriteria scheduling problems involving two or more sets of jobs and propose an unified framework providing a common definition, name and notation for these problems. Moreover, we systematically review and classify the existing contributions in terms of the complexity of the problems and the proposed solution procedures, discuss the main advances, and point out future research lines in the topic.     

Choosing the Operational Research Programme for B.I.S.R.A

This paper examines some important problems in the evaluation and selection of research projects, with particular reference to operational research projects in a central industry research organization. A method for project evaluation is suggested which provides data suitable for use in a powerful and flexible formal procedure for project selection. In evaluating a project, the assessment of resource requirements is based on a probabilistic network plan of the project, and the estimates of benefits are derived from the marginal effects on the industry of performing or not performing the project, using discounted cash flow techniques. The procedure for project selection chooses not only the projects to be undertaken, but also the team sizes that should be used. A wide variety of constraints can be imposed on the system to reflect different aspects of management policy or other special factors. The procedures described have been implemented, and have proved well worth while.     

On the stability of finite numerical procedures

Summary Many procedures, for example Gaussian elimination with partial pivoting, have been shown to be stable in the following sense. The effect of round-off errors is to produce a computed solution which is the exact solution for slightly different data. Sometimes that is equivalent to the computed solution being close to the exact solution. In this paper we study this equivalence.Our research was supported in part by NSF grant GJ-797.     

Collusive game solutions via optimization

A Nash-based collusive game among a finite set of players is one in which the players coordinate in order for each to gain higher payoffs than those prescribed by the Nash equilibrium solution. In this paper, we study the optimization problem of such a collusive game in which the players collectively maximize the Nash bargaining objective subject to a set of incentive compatibility constraints. We present a smooth reformulation of this optimization problem in terms of a nonlinear complementarity problem. We establish the convexity of the optimization problem in the case where each player's strategy set is unidimensional. In the multivariate case, we propose upper and lower bounding procedures for the collusive optimization problem and establish convergence properties of these procedures. Computational results with these procedures for solving some test problems are reported. It is with great honor that we dedicate this paper to Professor Terry Rockafellar on the occasion of his 70th birthday. Our work provides another example showing how Terry's fundamental contributions to convex and variational analysis have impacted the computational solution of applied game problems. This author's research was partially supported by the National Science Foundation under grant ECS-0080577. This author's research was partially supported by the National Science Foundation under grant CCR-0098013.