Beam search heuristics for quadratic earliness and tardiness scheduling

In this paper, we present beam search heuristics for the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. These heuristics include classic beam search procedures, as well as filtered and recovering algorithms. We consider three dispatching heuristics as evaluation functions, in order to analyse the effect of different rules on the performance of the beam search procedures. The computational results show that using better dispatching heuristics improves the effectiveness of the beam search algorithms. The performance of the several heuristics is similar for instances with low variability. For high variability instances, however, the detailed, filtered and recovering beam search (RBS) procedures clearly outperform the best existing heuristic. The detailed beam search algorithm performs quite well, and is recommended for small- to medium-sized instances. For larger instances, however, this procedure requires excessive computation times, and the RBS algorithm then becomes the heuristic of choice.     

Local search intensified: Very large-scale variable neighborhood search for the multi-resource generalized assignment problem

We introduce a heuristic for the Multi-Resource Generalized Assignment Problem (MRGAP) based on the concepts of Very Large-Scale Neighborhood Search and Variable Neighborhood Search. The heuristic is a simplified version of the Very Large-Scale Variable Neighborhood Search for the Generalized Assignment Problem. Our algorithm can be viewed as a k-exchange heuristic; but unlike traditional k-exchange algorithms, we choose larger values of k resulting in neighborhoods of very large size with high probability. Searching this large neighborhood (approximately) amounts to solving a sequence of smaller MRGAPs either by exact algorithms or by heuristics. Computational results on benchmark test problems are presented. We obtained improved solutions for many instances compared to some of the best known heuristics for the MRGAP within reasonable running time. The central idea of our heuristic can be used to develop efficient heuristics for other hard combinatorial optimization problems as well.     

Solving multiobjective,multiconstraint knapsack problems using mathematical programming and evolutionary algorithms

In this paper, we solve instances of the multiobjective multiconstraint (or multidimensional) knapsack problem (MOMCKP) from the literature, with three objective functions and three constraints. We use exact as well as approximate algorithms. The exact algorithm is a properly modified version of the multicriteria branch and bound (MCBB) algorithm, which is further customized by suitable heuristics. Three branching heuristics and a more general purpose composite branching and construction heuristic are devised. Comparison is made to the published results from another exact algorithm, the adaptive ε-constraint method [Laumanns, M., Thiele, L., Zitzler, E., 2006. An efficient, adaptive parameter variation scheme for Metaheuristics based on the epsilon-constraint method. European Journal of Operational Research 169, 932–942], using the same data sets. Furthermore, the same problems are solved using standard multiobjective evolutionary algorithms (MOEA), namely, the SPEA2 and the NSGAII. The results from the exact case show that the branching heuristics greatly improve the performance of the MCBB algorithm, which becomes faster than the adaptive ε -constraint. Regarding the performance of the MOEA algorithms in the specific problems, SPEA2 outperforms NSGAII in the degree of approximation of the Pareto front, as measured by the coverage metric (especially for the largest instance).     

A hyper-heuristic approach to sequencing by hybridization of DNA sequences

In this paper we investigate the use of hyper-heuristic methodologies for predicting DNA sequences. In particular, we utilize Sequencing by Hybridization. We believe that this is the first time that hyper-heuristics have been investigated in this domain. A hyper-heuristic is provided with a set of low-level heuristics and the aim is to decide which heuristic to call at each decision point. We investigate three types of hyper-heuristics. Two of these (simulated annealing and tabu search) draw their inspiration from meta-heuristics. The choice function hyper-heuristic draws its inspiration from reinforcement learning. We utilize two independent sets of low-level heuristics. The first set is based on a previous tabu search method, with the second set being a significant extension to this basic set, including utilizing a different representation and introducing the definition of clusters. The datasets we use comprises two randomly generated datasets and also a publicly available biological dataset. In total, we carried out experiments using 70 different combinations of heuristics, using the three datasets mentioned above and investigating six different hyper-heuristic algorithms. Our results demonstrate the effectiveness of a hyper-heuristic approach to this problem domain. It is necessary to provide a good set of low-level heuristics, which are able to both intensify and diversify the search but this approach has demonstrated very encouraging results on this extremely difficult and important problem domain.     

A comparison of algorithm RS with algorithm OPTSOL70

In a very recent paper (Almiñana and Pastor (1997)) we proposed a new lagrangian surrogate heuristic, called RS, for solving the location (or unicost) set covering problem. In that paper we show that RS is more accurate than the pair of greedy type heuristics FMC/CMA and that RS outperforms the surrogate heuristic SH. Here we are going to compare algorithms RS with the best designed hybrid algorithm for the location set covering problem, known as OPTSOL70.     

A hybrid scatter search/electromagnetism meta-heuristic for project scheduling

In the last few decades, several effective algorithms for solving the resource-constrained project scheduling problem have been proposed. However, the challenging nature of this problem, summarised in its strongly NP-hard status, restricts the effectiveness of exact optimisation to relatively small instances. In this paper, we present a new meta-heuristic for this problem, able to provide near-optimal heuristic solutions for relatively large instances. The procedure combines elements from scatter search, a generic population-based evolutionary search method, and from a recently introduced heuristic method for the optimisation of unconstrained continuous functions based on an analogy with electromagnetism theory. We present computational experiments on standard benchmark datasets, compare the results with current state-of-the-art heuristics, and show that the procedure is capable of producing consistently good results for challenging instances of the resource-constrained project scheduling problem. We also demonstrate that the algorithm outperforms state-of-the-art existing heuristics.     

A Genetic Algorithm for the Multidimensional Knapsack Problem

In this paper we present a heuristic based upon genetic algorithms for the multidimensional knapsack problem. A heuristic operator which utilises problem-specific knowledge is incorporated into the standard genetic algorithm approach. Computational results show that the genetic algorithm heuristic is capable of obtaining high-quality solutions for problems of various characteristics, whilst requiring only a modest amount of computational effort. Computational results also show that the genetic algorithm heuristic gives superior quality solutions to a number of other heuristics.     

Improved and self-tuned occurrence heuristics

In this note we present three efficient variations of the occurrence heuristic, adopted by many exact string matching algorithms and first introduced in the well-known Boyer–Moore algorithm. Our first heuristic, called improved-occurrence heuristic, is a simple improvement of the rule introduced by Sunday in his Quick-Search algorithm. Our second heuristic, called worst-occurrence heuristic, achieves its speed-up by selecting the relative position which yields the largest average advancement. Finally, our third heuristic, called jumping-occurrence heuristic, uses two characters for computing the next shift. Setting the distance between these two characters optimally allows one to maximize the average advancement. The worst-occurrence and jumping-occurrence heuristics tune their parameters according to the distribution of the characters in the text. Experimental results show that the newly proposed heuristics achieve very good results on average, especially in the case of small alphabets.     

Reinforcement learning versus heuristics for order acceptance on a single resource

Order Acceptance (OA) is one of the main functions in business control. Accepting an order when capacity is available could disable the system to accept more profitable orders in the future with opportunity losses as a consequence. Uncertain information is also an important issue here. We use Markov decision models and learning methods from Artificial Intelligence to find decision policies under uncertainty. Reinforcement Learning (RL) is quite a new approach in OA. It is shown here that RL works well compared with heuristics. It is demonstrated that employing an RL trained agent is a robust, flexible approach that in addition can be used to support the detection of good heuristics.     

On branching heuristics for the bi-objective 0/1 unidimensional knapsack problem

This paper focuses on branching strategies that are involved in branch and bound algorithms when solving multi-objective optimization problems. The choice of the branching variable at each node of the search tree constitutes indeed an important component of these algorithms. In this work we focus on multi-objective knapsack problems. In the literature, branching heuristics used for these problems are static, i.e., the order on the variables is determined prior to the execution. This study investigates the benefit of defining more sophisticated branching strategies. We first analyze and compare a representative set of classic branching heuristics and conclude that none can be identified as the best overall heuristic. Using an oracle, we highlight that combining branching heuristics within the same branch and bound algorithm leads to considerably reduced search trees but induces high computational costs. Based on learning adaptive techniques, we propose then dynamic adaptive branching strategies that are able to select the suitable heuristic to apply at each node of the search tree. Experiments are conducted on the bi-objective 0/1 unidimensional knapsack problem.     

一种新的交通网络设计优化算法

交通网络设计问题是研究如何用定量的方法在已有交通网络上添加或扩容某些路段的问题.文章在回顾交通网络设计问题文献的基础上,提出了基于图论网络优化思想的解决该类问题的一种新思路,给出了启发式算法,并进行了算法复杂性分析,最后通过算例验证了其有效性.     

Routing and wavelength assignment in optical networks using bin packing based algorithms

This paper addresses the problem of routing and wavelength assignment (RWA) of static lightpath requests in wavelength routed optical networks. The objective is to minimize the number of wavelengths used. This problem has been shown to be NP-complete and several heuristic algorithms have been developed to solve it. We suggest very efficient, yet simple, heuristic algorithms for the RWA problem developed by applying classical bin packing algorithms. The heuristics were tested on a series of large random networks and compared with an efficient existing algorithm for the same problem. Results indicate that the proposed algorithms yield solutions significantly superior in quality, not only with respect to the number of wavelength used, but also with respect to the physical length of the established lightpaths. Comparison with lower bounds shows that the proposed heuristics obtain optimal or near optimal solutions in many cases.     

A Comparison of Heuristics for the Discrete Cost Multicommodity Network Optimization Problem

In this paper, approximate solutions algorithms for discrete cost multicommodity network optimization problems are presented and compared. Firstly, extensions of classical greedy heuristics, based on link-rerouting and flow-rerouting heuristics, are presented in details. Secondly, a new approximate solution algorithm, which basically consists of a heuristic implementation of the exact Benders-type cutting plane generation method, is proposed. All these algorithms are extensively compared on randomly generated graphs up to 50 nodes and 90 links. It clearly appears that this new Benders-type approach is very promising since it produces the best heuristic solutions.     

Learning heuristics for basic block instruction scheduling

Instruction scheduling is an important step for improving the performance of object code produced by a compiler. A fundamental problem that arises in instruction scheduling is to find a minimum length schedule for a basic block—a straight-line sequence of code with a single entry point and a single exit point—subject to precedence, latency, and resource constraints. Solving the problem exactly is known to be difficult, and most compilers use a greedy list scheduling algorithm coupled with a heuristic. The heuristic is usually hand-crafted, a potentially time-consuming process. In contrast, we present a study on automatically learning good heuristics using techniques from machine learning. In our study, a recently proposed optimal basic block scheduler was used to generate the machine learning training data. A decision tree learning algorithm was then used to induce a simple heuristic from the training data. The automatically constructed decision tree heuristic was compared against a popular critical-path heuristic on the SPEC 2000 benchmarks. On this benchmark suite, the decision tree heuristic reduced the number of basic blocks that were not optimally scheduled by up to 55% compared to the critical-path heuristic, and gave improved performance guarantees in terms of the worst-case factor from optimality.     

Some results of the worst-case analysis for flow shop scheduling with a learning effect

This article considers flow shop scheduling problems with a learning effect. By the learning effect, we mean that the processing time of a job is defined by a function of its position in a processing permutation. The objective is to minimize the total weighted completion time. Some heuristic algorithms by using the optimal permutations for the corresponding single machine scheduling problems are presented, and the worst-case bound of these heuristics are also analyzed.     

Heuristics for matrix bandwidth reduction

In this work, we provide two heuristic algorithms for the matrix bandwidth reduction problem. The first is a genetic algorithm and the second uses node label adjustments. Experiments show these heuristics improve solution quality when compared with the well-known GPS algorithm and recently-developed methods using tabu search and GRASP with Path Relinking. Further, the node adjustment approach obtains solutions at speeds comparable to the fast GPS algorithm.     

Multi-armed bandit-based hyper-heuristics for combinatorial optimization problems

There are significant research opportunities in the integration of Machine Learning (ML) methods and Combinatorial Optimization Problems (COPs). In this work, we focus on metaheuristics to solve COPs that have an important learning component. These algorithms must explore a solution space and learn from the information they obtain in order to find high-quality solutions. Among the metaheuristics, we study Hyper-Heuristics (HHs), algorithms that, given a number of low-level heuristics, iteratively select and apply heuristics to a solution. The HH we consider has a Markov model to produce sequences of low-level heuristics, which we combine with a Multi-Armed Bandit Problem (MAB)-based method to learn its parameters. This work proposes several improvements to the HH metaheuristic that yields a better learning for solving problem instances. Specifically, this is the first work in HHs to present Exponential Weights for Exploration and Exploitation (EXP3) as a learning method, an algorithm that is able to deal with adversarial settings. We also present a case study for the Vehicle Routing Problem with Time Windows (VRPTW), for which we include a list of low-level heuristics that have been proposed in the literature. We show that our algorithms can handle a large and diverse list of heuristics, illustrating that they can be easily configured to solve COPs of different nature. The computational results indicate that our algorithms are competitive methods for the VRPTW (2.16% gap on average with respect to the best known solutions), demonstrating the potential of these algorithms to solve COPs. Finally, we show how algorithms can even detect low-level heuristics that do not contribute to finding better solutions to the problem.     

Random backtracking in backtrack search algorithms for satisfiability

This paper proposes the utilization of randomized backtracking within complete backtrack search algorithms for propositional satisfiability (SAT). In recent years, randomization has become pervasive in SAT algorithms. Incomplete algorithms for SAT, for example the ones based on local search, often resort to randomization. Complete algorithms also resort to randomization. These include state-of-the-art backtrack search SAT algorithms that often randomize variable selection heuristics. Moreover, it is plain that the introduction of randomization in other components of backtrack search SAT algorithms can potentially yield new competitive search strategies. As a result, we propose a stochastic backtrack search algorithm for SAT, that randomizes both the variable selection and the backtrack steps of the algorithm. In addition, we relate randomized backtracking with a more general form of backtracking, referred to as unrestricted backtracking. Finally, experimental results for different organizations of randomized backtracking are described and compared, providing empirical evidence that the new search algorithm for SAT is a very competitive approach for solving hard real-world instances.     

Computation of general correlation coefficients for interval data

This paper provides a comprehensive analysis of computational problems concerning calculation of general correlation coefficients for interval data. Exact algorithms solving this task have unacceptable computational complexity for larger samples, therefore we concentrate on computational problems arising in approximate algorithms. General correlation coefficients for interval data are also given by intervals. We derive bounds on their lower and upper endpoints. Moreover, we propose a set of heuristic solutions and optimization methods for approximate computation. Extensive simulation experiments show that the heuristics yield very good solutions for strong dependencies. In other cases, global optimization using evolutionary algorithm performs best. A real data example of autocorrelation of cloud cover data confirms the applicability of the approach.     

A tree search method for the container loading problem with shipment priority

This paper addresses a special kind of container loading problem with shipment priority. We present a tree search method, which is based on a greedy heuristic. In the greedy heuristic, blocks made up of identical items with the same orientation are selected for packing into a container. Five evaluation functions are proposed for block selection, and the different blocks selected by each evaluation function constitute the branches of the search tree. A method of space splitting and merging is also embedded in the algorithm to facilitate efficient use of the container space. In addition, the proposed algorithm covers an important constraint called shipment priority to solve practical problems. The validity of the proposed algorithm is examined by comparing the present results with those of published algorithms using the same data.