Grasp with memory-based mechanisms for minimizing total tardiness in single machine scheduling with setup times

This paper addresses the problem of scheduling jobs in a single machine with sequence dependent setup times in order to minimize the total tardiness with respect to job due dates. We propose variants of the GRASP metaheuristic that incorporate memory-based mechanisms for solving this problem. There are two mechanisms proposed in the literature that utilize a long-term memory composed of an elite set of high quality and sufficiently distant solutions. The first mechanism consists of extracting attributes from the elite solutions in order to influence the construction of an initial solution. The second one makes use of path relinking to connect a GRASP local minimum with a solution of the elite set, and also to connect solutions from the elite set. Reactive GRASP, which probabilistically determines the degree of randomness in the GRASP construction throughout the iterations, is also investigated. Computational tests for instances involving up to 150 jobs are reported, and the proposed method is compared with heuristic and exact methods from the literature.     

Estimates of the absolute error and a scheme for an approximate solution to scheduling problems

An approach is proposed for estimating absolute errors and finding approximate solutions to classical NP-hard scheduling problems of minimizing the maximum lateness for one or many machines and makespan is minimized. The concept of a metric (distance) between instances of the problem is introduced. The idea behind the approach is, given the problem instance, to construct another instance for which an optimal or approximate solution can be found at the minimum distance from the initial instance in the metric introduced. Instead of solving the original problem (instance), a set of approximating polynomially/pseudopolynomially solvable problems (instances) are considered, an instance at the minimum distance from the given one is chosen, and the resulting schedule is then applied to the original instance.     

A heuristic algorithm based on multi-assignment procedures for nurse scheduling

This paper tackles a Nurse Scheduling Problem which consists of generating work schedules for a set of nurses while considering their shift preferences and other requirements. The objective is to maximize the satisfaction of nurses’ preferences and minimize the violation of soft constraints. This paper presents a new deterministic heuristic algorithm, called MAPA (multi-assignment problem-based algorithm), which is based on successive resolutions of the assignment problem. The algorithm has two phases: a constructive phase and an improvement phase. The constructive phase builds a full schedule by solving successive assignment problems, one for each day in the planning period. The improvement phase uses a couple of procedures that re-solve assignment problems to produce a better schedule. Given the deterministic nature of this algorithm, the same schedule is obtained each time that the algorithm is applied to the same problem instance. The performance of MAPA is benchmarked against published results for almost 250,000 instances from the NSPLib dataset. In most cases, particularly on large instances of the problem, the results produced by MAPA are better when compared to best-known solutions from the literature. The experiments reported here also show that the MAPA algorithm finds more feasible solutions compared with other algorithms in the literature, which suggest that this proposed approach is effective and robust.     

An estimation of distribution algorithm for nurse scheduling

Schedules can be built in a similar way to a human scheduler by using a set of rules that involve domain knowledge. This paper presents an Estimation of Distribution Algorithm (EDA) for the nurse scheduling problem, which involves choosing a suitable scheduling rule from a set for the assignment of each nurse. Unlike previous work that used Genetic Algorithms (GAs) to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. we identify and mix building blocks directly. The EDA is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems.     

On the computation of all supported efficient solutions in multi-objective integer network flow problems

This paper presents a new algorithm for identifying all supported non-dominated vectors (or outcomes) in the objective space, as well as the corresponding efficient solutions in the decision space, for multi-objective integer network flow problems. Identifying the set of supported non-dominated vectors is of the utmost importance for obtaining a first approximation of the whole set of non-dominated vectors. This approximation is crucial, for example, in two-phase methods that first compute the supported non-dominated vectors and then the unsupported non-dominated ones. Our approach is based on a negative-cycle algorithm used in single objective minimum cost flow problems, applied to a sequence of parametric problems. The proposed approach uses the connectedness property of the set of supported non-dominated vectors/efficient solutions to find all integer solutions in maximal non-dominated/efficient facets.     

Helper-objectives: Using multi-objective evolutionary algorithms for single-objective optimisation

This paper investigates the use of multi-objective methods to guide the search when solving single-objective optimisation problems with genetic algorithms. Using the job shop scheduling and travelling salesman problems as examples, experiments demonstrate that the use of helper-objectives (additional objectives guiding the search) significantly improves the average performance of a standard GA. The helper-objectives guide the search towards solutions containing good building blocks and help the algorithm escape local optima. The experiments reveal that the approach works if the number of simultaneously used helper-objectives is low. However, a high number of helper-objectives can be used in the same run by changing the helper-objectives dynamically. The experiments reveal that for the majority of problem instances studied, the proposed approach significantly outperforms a traditional GA.The experiments also demonstrate that controlling the proportion of non-dominated solutions in the population is very important when using helper-objectives, since the presence of too many non-dominated solutions removes the selection pressure in the algorithm.     

Algorithms for common due-date assignment and sequencing on a single machine with sequence-dependent setup times

This paper focuses on the single machine sequencing and common due-date assignment problem for the objective of minimizing the sum of the penalties associated with earliness, tardiness and due-date assignment. Unlike the previous research articles on this class of scheduling problem, we consider sequence-dependent setup times that make the problem much more difficult. To solve the problem, a branch and bound algorithm, which incorporates the method to obtain lower and upper bounds as well as a dominance property to reduce the search space, is suggested that gives the optimal solutions for small-sized instances. Heuristic algorithms are suggested to obtain solutions for large-sized problems within a reasonable computation time. The performances of both the optimal and heuristic algorithms, in computational experiments on randomly generated test instances, are reported.     

A survey of the state-of-the-art of common due date assignment and scheduling research

We aim at providing a unified framework of the common due date assignment and scheduling problems in the deterministic case by surveying the literature concerning the models involving single machine and parallel machines. The problems with due date determination have received considerable attention in the last 15 years due to the introduction of new methods of inventory management such as just-in-time (JIT) concepts. The common due date model corresponds, for instance, to an assembly system in which the components of the product should be ready at the same time, or to a shop where several jobs constitute a single customer's order. In the problems under consideration, the objective is to find an optimal value of the common due date and the related optimal schedule in order to optimize a given criterion based on the due date and the completion times of jobs. The results on the algorithms and complexity of the common due date assignment and scheduling problems are summarized.     

PSPLIB - A project scheduling problem library: OR Software - ORSEP Operations Research Software Exchange Program

We present a set of benchmark instances for the evaluation of solution procedures for single- and multi-mode resource-constrained project scheduling problems. The instances have been systematically generated by the standard project generator ProGen. They are characterized by the input-parameters of ProGen. The entire benchmark set including its detailed characterization and the best solutions known so-far are available on a public ftp-site. Hence, researchers can download the benchmark sets they need for the evaluation of their algorithms. Additionally, they can make available new results. Depending on the progress made in the field, the instance library will be continuously enlarged and new results will be made accessible. This should be a valuable and driving source for further improvements in the area of project type scheduling.     

Scheduling interfering job sets on parallel machines

We consider bicriteria scheduling on identical parallel machines in a nontraditional context: jobs belong to two disjoint sets, and each set has a different criterion to be minimized. The jobs are all available at time zero and have to be scheduled (non-preemptively) on m parallel machines. The goal is to generate the set of all non-dominated solutions, so the decision maker can evaluate the tradeoffs and choose the schedule to be implemented. We consider the case where, for one of the two sets, the criterion to be minimized is makespan while for the other the total completion time needs to be minimized. Given that the problem is NP-hard, we propose an iterative SPT–LPT–SPT heuristic and a bicriteria genetic algorithm for the problem. Both approaches are designed to exploit the problem structure and generate a set of non-dominated solutions. In the genetic algorithm we use a special encoding scheme and also a unique strategy – based on the properties of a non-dominated solution – to ensure that all parts of the non-dominated front are explored. The heuristic and the genetic algorithm are compared with a time-indexed integer programming formulation for small and large instances. Results indicate that the both the heuristic and the genetic algorithm provide high solution quality and are computationally efficient. The heuristics proposed also have the potential to be generalized for the problem of interfering job sets involving other bicriteria pairs.     

Multicriteria scheduling optimization using an elitist multiobjective population heuristic: the h-NSDE algorithm

In today’s manufacturing industry more than one performance criteria are considered for optimization to various degrees simultaneously. To deal with such hard competitive environments it is essential to develop appropriate multicriteria scheduling approaches. In this paper consideration is given to the problem of scheduling n independent jobs on a single machine with due dates and objective to simultaneously minimize three performance criteria namely, total weighted tardiness (TWT), maximum tardiness and maximum earliness. In the single machine scheduling literature no previous studies have been performed on test problems examining these criteria simultaneously. After positioning the problem within the relevant research field, we present a new heuristic algorithm for its solution. The developed algorithm termed the hybrid non-dominated sorting differential evolution (h-NSDE) is an extension of the author’s previous algorithm for the single-machine mono-criterion TWT problem. h-NSDE is devoted to the search for Pareto-optimal solutions. To enable the decision maker for evaluating a greater number of alternative non-dominated solutions, three multiobjective optimization approaches have been implemented and tested within the context of h-NSDE: including a weighted-sum based approach, a fuzzy-measures based approach which takes into account the interaction among the criteria as well as a Pareto-based approach. Experiments conducted on existing data set benchmarks problems show the effect of these approaches on the performance of the h-NSDE algorithm. Moreover, comparative results between h-NSDE and some of the most popular multiobjective metaheuristics including SPEA2 and NSGA-II show clear superiority for h-NSDE in terms of both solution quality and solution diversity.     

Solving multi-objective multicast routing problems by evolutionary multi-objective simulated annealing algorithms with variable neighbourhoods

This paper presents the investigation of an evolutionary multi-objective simulated annealing (EMOSA) algorithm with variable neighbourhoods to solve the multi-objective multicast routing problems in telecommunications. The hybrid algorithm aims to carry out a more flexible and adaptive exploration in the complex search space by using features of the variable neighbourhood search to find more non-dominated solutions in the Pareto front. Different neighbourhood strictures have been designed with regard to the set of objectives, aiming to drive the search towards optimising all objectives simultaneously. A large number of simulations have been carried out on benchmark instances and random networks with real world features including cost, delay and link utilisations. Experimental results demonstrate that the proposed EMOSA algorithm with variable neighbourhoods is able to find high-quality non-dominated solutions for the problems tested. In particular, the neighbourhood structures that are specifically designed for each objective significantly improved the performance of the proposed algorithm compared with variants of the algorithm with a single neighbourhood.     

A scatter search method for bi-criteria {0, 1}-knapsack problems

This paper presents a scatter search (SS) based method for finding a good approximation of the non-dominated frontier for large size bi-criteria {0, 1}-knapsack instances. The method follows the usual structure of SS: (1) diversification, (2) improvement, (3) reference set update, (4) subset generation, and (5) solution combination. For each component specific procedures were built which strongly benefit from the single criterion problem, and also from the characteristics of the neighbourhood of bi-criteria non-dominated solutions. These aspects permit the guidance and restriction of the exploration of the decision space. Experiments were carried out on a large set of instances and the computational results are presented. The approach seems to be very efficient and the quality of the approximation is quite good. These points are also discussed in the paper.     

Multi-mode resource-constrained project scheduling using RCPSP and SAT solvers

This paper reports on a new solution approach for the well-known multi-mode resource-constrained project scheduling problem (MRCPSP). This problem type aims at the selection of a single activity mode from a set of available modes in order to construct a precedence and a (renewable and non-renewable) resource feasible project schedule with a minimal makespan. The problem type is known to be NP-hard and has been solved using various exact as well as (meta-)heuristic procedures.The new algorithm splits the problem type into a mode assignment and a single mode project scheduling step. The mode assignment step is solved by a satisfiability (SAT) problem solver and returns a feasible mode selection to the project scheduling step. The project scheduling step is solved using an efficient meta-heuristic procedure from literature to solve the resource-constrained project scheduling problem (RCPSP). However, unlike many traditional meta-heuristic methods in literature to solve the MRCPSP, the new approach executes these two steps in one run, relying on a single priority list. Straightforward adaptations to the pure SAT solver by using pseudo boolean non-renewable resource constraints has led to a high quality solution approach in a reasonable computational time. Computational results show that the procedure can report similar or sometimes even better solutions than found by other procedures in literature, although it often requires a higher CPU time.     

A discrete artificial bee colony algorithm for the multi-objective flexible job-shop scheduling problem with maintenance activities

This paper presents a novel discrete artificial bee colony (DABC) algorithm for solving the multi-objective flexible job shop scheduling problem with maintenance activities. Performance criteria considered are the maximum completion time so called makespan, the total workload of machines and the workload of the critical machine. Unlike the original ABC algorithm, the proposed DABC algorithm presents a unique solution representation where a food source is represented by two discrete vectors and tabu search (TS) is applied to each food source to generate neighboring food sources for the employed bees, onlooker bees, and scout bees. An efficient initialization scheme is introduced to construct the initial population with a certain level of quality and diversity. A self-adaptive strategy is adopted to enable the DABC algorithm with learning ability for producing neighboring solutions in different promising regions whereas an external Pareto archive set is designed to record the non-dominated solutions found so far. Furthermore, a novel decoding method is also presented to tackle maintenance activities in schedules generated. The proposed DABC algorithm is tested on a set of the well-known benchmark instances from the existing literature. Through a detailed analysis of experimental results, the highly effective and efficient performance of the proposed DABC algorithm is shown against the best performing algorithms from the literature.     

Random assignment problems

Analysis of random instances of optimization problems provides valuable insights into the behavior and properties of problem’s solutions, feasible region, and optimal values, especially in large-scale cases. A class of problems that have been studied extensively in the literature using the methods of probabilistic analysis is represented by the assignment problems, and many important problems in operations research and computer science can be formulated as assignment problems. This paper presents an overview of the recent results and developments in the area of probabilistic assignment problems, including the linear and multidimensional assignment problems, quadratic assignment problem, etc.     

Behavioral measures and their correlation with IPM iteration counts on semi-definite programming problems

We study four measures of problem instance behavior that might account for the observed differences in interior-point method (IPM) iterations when these methods are used to solve semidefinite programming (SDP) problem instances: (i) an aggregate geometry measure related to the primal and dual feasible regions (aspect ratios) and norms of the optimal solutions, (ii) the (Renegar-) condition measure C(d) of the data instance, (iii) a measure of the near-absence of strict complementarity of the optimal solution, and (iv) the level of degeneracy of the optimal solution. We compute these measures for the SDPLIB suite problem instances and measure the sample correlation (CORR) between these measures and IPM iteration counts (solved using the software SDPT3) when these measures have finite values. Our conclusions are roughly as follows: the aggregate geometry measure is highly correlated with IPM iterations (CORR = 0.901), and provides a very good explanation of IPM iterations, particularly for problem instances with solutions of small norm and aspect ratio. The condition measure C(d) is also correlated with IPM iterations, but less so than the aggregate geometry measure (CORR = 0.630). The near-absence of strict complementarity is weakly correlated with IPM iterations (CORR = 0.423). The level of degeneracy of the optimal solution is essentially uncorrelated with IPM iterations. This research has been partially supported through the MIT-Singapore Alliance.     

Transfer weight functions for injecting problem information in the multi-objective CMA-ES

The covariance matrix adaptation evolution strategy (CMA-ES) is one of the state-of-the-art evolutionary algorithms for optimization problems with continuous representation. It has been extensively applied to single-objective optimization problems, and different variants of CMA-ES have also been proposed for multi-objective optimization problems (MOPs). When applied to MOPs, the traditional steps of CMA-ES have to be modified to accommodate for multiple objectives. This fact is particularly evident when the number of objectives is higher than 3 and, with a high probability, all the solutions produced become non-dominated. An open question is to what extent information about the objective values of the non-dominated solutions can be injected in the CMA-ES model for a more effective search. In this paper, we investigate this general question using several metrics that describe the quality of the solutions already evaluated, different transfer weight functions, and a set of difficult benchmark instances including many-objective problems. We introduce a number of new strategies that modify how the probabilistic model is learned in CMA-ES. By conducting an exhaustive empirical analysis on two difficult benchmarks of many-objective functions we show that the proposed strategies to infuse information about the quality indicators into the learned models can achieve consistent improvements in the quality of the Pareto fronts obtained and enhance the convergence rate of the algorithm. Moreover, we conducted a comparison with a state-of-the-art algorithm from the literature, and achieved competitive results in problems with irregular Pareto fronts.     

Minimizing shifts for personnel task scheduling problems: A three-phase algorithm

The personnel task scheduling problem is a subject of commercial interest which has been investigated since the 1950s. This paper proposes an effective and efficient three-phase algorithm for solving the shift minimization personnel task scheduling problem (SMPTSP). To illustrate the increased efficacy of the proposed algorithm over an existing algorithm, computational experiments are performed on a test problem set with characteristics motivated by employee scheduling applications. Experimental results show that the proposed algorithm outperforms the existing algorithm in terms of providing optimal solutions, improving upon most of the best-known solutions and revealing high-quality feasible solutions for those unsolved test instances in the literature.