Average-weight-controlled bin-oriented heuristics for the one-dimensional bin-packing problem

Bin-oriented heuristics for one-dimensional bin-packing problem construct solutions by packing one bin at a time. Several such heuristics consider two or more subsets for each bin and pack the one with the largest total weight. These heuristics sometimes generate poor solutions, due to a tendency to use many small items early in the process. To address this problem, we propose a method of controlling the average weight of items packed by bin-oriented heuristics. Constructive heuristics and an improvement heuristic based on this approach are introduced. Additionally, reduction methods for bin-oriented heuristics are presented. The results of an extensive computational study show that: (1) controlling average weight significantly improves solutions and reduces computation time of bin-oriented heuristics; (2) reduction methods improve solutions and processing times of some bin-oriented heuristics; and (3) the new improvement heuristic outperforms all other known complex heuristics, in terms of both average solution quality and computation time.     

On the Significance of the Initial Solution in Travelling Salesman Heuristics

The quality requirements set by edge exchange heuristics on their initial solutions are evaluated in connection with the travelling salesman problem. The performance of the heuristics is measured using the expected value of the best solution achievable in a certain computing time. The computational results show that the use of initial solutions generated by applying a construction heuristic, instead of random initial solutions, typically improves the performance of edge exchange heuristics. The improvement, however, is dependent on the edge exchange heuristic to be used, the properties of the problem, and the computing time available.     

A GRASP + ILP-based metaheuristic for the capacitated location-routing problem

In this paper we present a three-phase heuristic for the Capacitated Location-Routing Problem. In the first stage, we apply a GRASP followed by local search procedures to construct a bundle of solutions. In the second stage, an integer-linear program (ILP) is solved taking as input the different routes belonging to the solutions of the bundle, with the objective of constructing a new solution as a combination of these routes. In the third and final stage, the same ILP is iteratively solved by column generation to improve the solutions found during the first two stages. The last two stages are based on a new model, the location-reallocation model, which generalizes the capacitated facility location problem and the reallocation model by simultaneously locating facilities and reallocating customers to routes assigned to these facilities. Extensive computational experiments show that our method is competitive with the other heuristics found in the literature, yielding the tightest average gaps on several sets of instances and being able to improve the best known feasible solutions for some of them.     

An empirical study of hyperheuristics for managing very large sets of low level heuristics

Hyperheuristics give us the appealing possibility of abstracting the solution method from the problem, since our hyperheuristic, at each decision point, chooses between different low level heuristics rather than different solutions as is usually the case for metaheuristics. By assembling low level heuristics from parameterised components we may create hundreds or thousands of low level heuristics, and there is increasing evidence that this is effective in dealing with every eventuality that may arise when solving different combinatorial optimisation problem instances since at each iteration the solution landscape is amenable to at least one of the low level heuristics. However, the large number of low level heuristics means that the hyperheuristic has to intelligently select the correct low level heuristic to use, to make best use of available CPU time. This paper empirically investigates several hyperheuristics designed for large collections of low level heuristics and adapts other hyperheuristics from the literature to cope with these large sets of low level heuristics on a difficult real-world workforce scheduling problem. In the process we empirically investigate a wide range of approaches for setting tabu tenure in hyperheuristic methods, for a complex real-world problem. The results show that the hyperheuristic methods described provide a good way to trade off CPU time and solution quality.     

Worst case analysis of Max-Regret,Greedy and other heuristics for Multidimensional Assignment and Traveling Salesman Problems

Optimization heuristics are often compared with each other to determine which one performs best by means of worst-case performance ratio reflecting the quality of returned solution in the worst case. The domination number is a complement parameter indicating the quality of the heuristic in hand by determining how many feasible solutions are dominated by the heuristic solution. We prove that the Max-Regret heuristic introduced by Balas and Saltzman (Oper. Res. 39:150–161, 1991) finds the unique worst possible solution for some instances of the s-dimensional (s≥3) assignment and asymmetric traveling salesman problems of each possible size. We show that the Triple Interchange heuristic (for s=3) also introduced by Balas and Saltzman and two new heuristics (Part and Recursive Opt Matching) have factorial domination numbers for the s-dimensional (s≥3) assignment problem.     

Adaptive automated construction of hybrid heuristics for exam timetabling and graph colouring problems

In this paper, we present a random iterative graph based hyper-heuristic to produce a collection of heuristic sequences to construct solutions of different quality. These heuristic sequences can be seen as dynamic hybridisations of different graph colouring heuristics that construct solutions step by step. Based on these sequences, we statistically analyse the way in which graph colouring heuristics are automatically hybridised. This, to our knowledge, represents a new direction in hyper-heuristic research. It is observed that spending the search effort on hybridising Largest Weighted Degree with Saturation Degree at the early stage of solution construction tends to generate high quality solutions. Based on these observations, an iterative hybrid approach is developed to adaptively hybridise these two graph colouring heuristics at different stages of solution construction. The overall aim here is to automate the heuristic design process, which draws upon an emerging research theme on developing computer methods to design and adapt heuristics automatically. Experimental results on benchmark exam timetabling and graph colouring problems demonstrate the effectiveness and generality of this adaptive hybrid approach compared with previous methods on automatically generating and adapting heuristics. Indeed, we also show that the approach is competitive with the state of the art human produced methods.     

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.     

Enhancing Stochastic Search Performance by Value-Biased Randomization of Heuristics

This paper investigates the utility of introducing randomization as a means of boosting the performance of search heuristics. We introduce a particular approach to randomization, called Value-biased stochastic sampling (VBSS), which emphasizes the use of heuristic value in determining stochastic bias. We offer an empirical study of the performance of value-biased and rank-biased approaches to randomizing search heuristics. We also consider the use of these stochastic sampling techniques in conjunction with local hill-climbing. Finally, we contrast the performance of stochastic sampling search with more systematic search procedures as a means of amplifying the performance of search heuristics.     

Exact and heuristic methods for placing ships in locks

The ship placement problem constitutes a daily challenge for planners in tide river harbours. In essence, it entails positioning a set of ships into as few lock chambers as possible while satisfying a number of general and specific placement constraints. These constraints make the ship placement problem different from traditional 2D bin packing. A mathematical formulation for the problem is presented. In addition, a decomposition model is developed which allows for computing optimal solutions in a reasonable time. A multi-order best fit heuristic for the ship placement problem is introduced, and its performance is compared with that of the left-right-left-back heuristic. Experiments on simulated and real-life instances show that the multi-order best fit heuristic beats the other heuristics by a landslide, while maintaining comparable calculation times. Finally, the new heuristic’s optimality gap is small, while it clearly outperforms the exact approach with respect to calculation time.     

A repeated matching heuristic for the single-source capacitated facility location problem

Facility location models form an important class of integer programming problems, with application in many areas such as the distribution and transportation industries. An important class of solution methods for these problems are so-called Lagrangean heuristics which have been shown to produce high quality solutions and which are at the same time robust. The general facility location problem can be divided into a number of special problems depending on the properties assumed. In the capacitated location problem each facility has a specific capacity on the service it provides. We describe a new solution approach for the capacitated facility location problem when each customer is served by a single facility. The approach is based on a repeated matching algorithm which essentially solves a series of matching problems until certain convergence criteria are satisfied. The method generates feasible solutions in each iteration in contrast to Lagrangean heuristics where problem dependent heuristics must be used to construct a feasible solution. Numerical results show that the approach produces solutions which are of similar and often better than those produced using the best Lagrangean heuristics.     

Cooperative Strategies for Solving the Bicriteria Sparse Multiple Knapsack Problem

For hard optimization problems, it is difficult to design heuristic algorithms which exhibit uniformly superior performance for all problem instances. As a result it becomes necessary to tailor the algorithms based on the problem instance. In this paper, we introduce the use of a cooperative problem solving team of heuristics that evolves algorithms for a given problem instance. The efficacy of this method is examined by solving six difficult instances of a bicriteria sparse multiple knapsack problem. Results indicate that such tailored algorithms uniformly improve solutions as compared to using predesigned heuristic algorithms.     

Greedy heuristics for the diameter-constrained minimum spanning tree problem

The diameter-constrained minimum spanning tree problem is an NP-hard combinatorial optimization problem that seeks a minimum cost spanning tree with a limit D imposed upon the length of any path in the tree. We begin by presenting four constructive greedy heuristics and, secondly, we present some second-order heuristics, performing some improvements on feasible solutions, hopefully leading to better objective function values. We present a heuristic with an edge exchange mechanism, another that transforms a feasible spanning tree solution into a feasible diameter-constrained spanning tree solution, and finally another with a repetitive mechanism. Computational results show that repetitive heuristics can improve considerably over the results of the greedy constructive heuristics, but using a huge amount of computation time. To obtain computational results, we use instances of the problem corresponding to complete graphs with a number of nodes between 20 and 60 and with the value of D varying between 4 and 9.     

A single-resource revenue management problem with random resource consumptions

We study a single-resource multi-class revenue management problem where the resource consumption for each class is random and only revealed at departure. The model is motivated by cargo revenue management problems in the airline and other shipping industries. We study how random resource consumption distribution affects the optimal expected profit and identify a preference acceptance order on classes. For a special case where the resource consumption for each class follows the same distribution, we fully characterize the optimal control policy. We then propose two easily computable heuristics: (i) a class-independent heuristic through parameter scaling, and (ii) a decomposition heuristic that decomposes the dynamic programming formulation into a collection of one-dimensional problems. We conduct extensive numerical experiments to investigate the performance of the two heuristics and compared them with several widely studied heuristic policies. Our results show that both heuristics work very well, with class-independent heuristic slightly better between the two. In particular, they consistently outperform heuristics that ignore demand and/or resource consumption uncertainty. Our results demonstrate the importance of considering random resource consumption as another problem dimension in revenue management applications.     

Time lag size in multiple operations flow shop scheduling heuristics

This paper considers a multistage flow shop where jobs require multiple operations at each stage and a finish-to-start time lag between any two consecutive operations of a job: the next operation of a job cannot start until the time lag after the former operation of that job has elapsed. The effect of the size of this time lag is considered when studying the effectiveness of solution approaches for this problem. Since the problem of minimizing the makespan is shown to be NP-hard even for the two-stage case, we present a lower bound based heuristic approach that is used to construct several heuristic procedures. These heuristics use lower bounds on the minimum makespan to solve the problem. The effectiveness of these heuristics is empirically evaluated for various time lag sizes by solving a large number of randomly generated problems. We show that the relative performance of the heuristics depends on the size of the time lag. If the ratio of mean time lag and mean processing time is 20% or more, heuristics that construct an active schedule perform less well than heuristics that construct a non-delay schedule. The opposite holds true if this ratio is smaller. The performance of the widely used Shortest Processing Time heuristic (SPT) deteriorates quickly if the size of the time lags increases. We propose instead to use the Earliest Finish Time heuristic (EFT) in case time lags are present. EFT performs much better in this case and is identical to SPT if all time lags are zero. The use of the lower bound based heuristics results in an improvement of the makespan performance of up to 50% as compared with the performance of some simple dispatching heuristics that take the presence of multiple operations and time lags into account. This effect increases with the size of the time lags.     

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.     

Adaptive linear combination of heuristic orderings in constructing examination timetables

In this paper, we investigate adaptive linear combinations of graph coloring heuristics with a heuristic modifier to address the examination timetabling problem. We invoke a normalisation strategy for each parameter in order to generalise the specific problem data. Two graph coloring heuristics were used in this study (largest degree and saturation degree). A score for the difficulty of assigning each examination was obtained from an adaptive linear combination of these two heuristics and examinations in the list were ordered based on this value. The examinations with the score value representing the higher difficulty were chosen for scheduling based on two strategies. We tested for single and multiple heuristics with and without a heuristic modifier with different combinations of weight values for each parameter on the Toronto and ITC2007 benchmark data sets. We observed that the combination of multiple heuristics with a heuristic modifier offers an effective way to obtain good solution quality. Experimental results demonstrate that our approach delivers promising results. We conclude that this adaptive linear combination of heuristics is a highly effective method and simple to implement.     

Pareto optimality and a class of set covering heuristics

The set covering problem has many diverse applications to problems arising in crew scheduling, facility location and other business areas. Since the problem is known to be hard to solve optimally, a number of approximate (heuristic) approaches have been designed for it. These approaches (with one exception) divide into two main groups, greedy heuristics and dual saturation heuristics. We use the concept of a Pareto optimal dual solution to show that an arbitrary dual saturation heuristic has the same worst-case performance guarantee as the two best known heuristics of that type. Moreover, this poor performance level is always attainable by those two heuristics.     

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.     

Multi-Path Approach for Reliability-Redundancy Allocation Using a Scaling Method

The reliability-redundancy allocation problem is an optimization problem that achieves better system reliability by determining levels of component redundancies and reliabilities simultaneously. The problem is classified with the hardest problems in the reliability optimization field because the decision variables are mixed-integer and the system reliability function is nonlinear, non-separable, and non-convex. Thus, iterative heuristics are highly recommended for solving the problem due to their reasonable solution quality and relatively short computation time. At present, most iterative heuristics use sensitivity factors to select an appropriate variable which significantly improves the system reliability. The sensitivity factor represents the impact amount of each variable to the system reliability at a designated iteration. However, these heuristics are inefficient in terms of solution quality and computation time because the sensitivity factor calculations are performed only at integer variables. It results in degradation of the exploration and growth in the number of subsequent continuous nonlinear programming (NLP) subproblems. To overcome the drawbacks of existing iterative heuristics, we propose a new scaling method based on the multi-path iterative heuristics introduced by Ha (2004). The scaling method is able to compute sensitivity factors for all decision variables and results in a decreased number of NLP subproblems. In addition, the approximation heuristic for NLP subproblems helps to avoid redundant computation of NLP subproblems caused by outlined solution candidates. Numerical experimental results show that the proposed heuristic is superior to the best existing heuristic in terms of solution quality and computation time.     

A Two Stage Search Heuristic for Scheduling Payments in Projects

When the Net Present Value (NPV) of a project is used as a measure of its financial performance, effective management of cash flows over the duration of the project is critical for improved profitability. Progress payments are a major component of project cash flows. In many project environments, the contractor can negotiate payment terms. Payments are typically tied to completion of project activities and therefore have significant impact on the schedule of activities and the timing of the payments. In this paper, we consider the problem of simultaneously determining the amount, timing and location of progress payments in projects to maximize NPV. Due to the combinatorial nature of the problem, heuristics are a practical approach to solving the problem. We propose a two-stage heuristic where simulated annealing is used in the first stage to determine a set of payments. In the second stage, activities are rescheduled to improve project NPV. We compare the performance of this general purpose heuristic with other problem-dependent heuristics from the literature. Our results indicate that the simulated annealing heuristic significantly outperforms the parameter-based heuristics. Although rescheduling in the second stage improves NPV, increases are relatively small in magnitude. While the specific parameters settings suggested by the simulated annealing heuristic in this study may have limited generalizability at this time due to the narrow range of problems tested, our analysis suggests that a pure simulated annealing approach is a very attractive alternative for obtaining good heuristic solutions to the complex problem of scheduling payments in projects.