Heuristic solutions to the long-term unit commitment problem with cogeneration plants

We consider a long-term version of the unit commitment problem that spans over one year divided into hourly time intervals. It includes constraints on electricity and heating production as well as on biomass consumption. The problem is of interest for scenario analysis in long-term strategic planning. We model the problem as a large mixed integer programming problem. Two solutions to this problem are of interest but computationally intractable: the optimal solution and the solution derived by market simulation. To achieve good and fast approximations to these two solutions, we design heuristic algorithms, including mixed integer programming heuristics, construction heuristics and local search procedures. Two setups are the best: a relax and fix mixed integer programming approach with an objective function reformulation and a combination of a dispatching heuristic with stochastic local search. The work is developed in the context of the Danish electricity market and the computational analysis is carried out on real-life data.     

MILP-based heuristics for the design of rural community electrification projects

Wind–photovoltaic systems are a suitable option to provide electricity to isolated communities autonomously. To design these systems, there are recent mathematical models that solve the location and type of each of the electrification components and the design of the possible distribution microgrids. When the amount of demand points to electrify increases, solving the mathematical model requires a computational time that becomes infeasible in practice. To speed up the solving process, three heuristic methods based on mixed integer linear programming (MILP) are presented in this paper: Relax and Fix heuristics, heuristics based on a Corridor Method and Increasing Radius heuristics. In all algorithms first a relaxed MILP is solved to obtain a base solution and then it is used as a starting point to find a feasible solution by searching in a reduced search space. For each type of heuristic several options to relax and to reduce the solution space are developed and tested. Extensive computational experiments based on real projects are carried out and results show that the best heuristic vary according to the size of instances.     

A note on a single-machine lot scheduling problem with indivisible orders

In this paper, a lot scheduling problem on a single machine with indivisible orders is studied. The objective is to minimize the total completion time of all orders. We show that the problem is NP-hard in the strong sense. Then, a binary integer programming approach and four simple heuristics are proposed to solve the problem. The binary integer programming approach with running time limit is considered as one heuristic method. As compared to a lower bound, the average performances of the heuristic method are really good and better than those of the four simple heuristics.     

Supplier selection and purchase problem for multi-echelon defective supply chain system with stochastic demand

In the real production process, some members in the supply chain system sometimes cannot effectively complete their production task because of defects involving the production or purchasing of components. A supply chain system that has defects in at least one echelon is called a multi-echelon defective supply chain (MDSC) system. Most supply chain systems are MDSC systems. Determining parts or components supply quota from different suppliers with limited suppliers, factories and distribution centers capacities in the supply chain system are becoming an important issue for businesses. In this study, we propose a new heuristic (H2) which is an extension of H1 heuristic that was previously presented. The MDSC system was formed with the mixed integer linear programming by LINDO software for calculation of the lower bound. The heuristics and MDSC system were modeled by using ProModel software. The heuristics were applied to a case from the Turkish furniture industry. The heuristics were compared with each other by considering different coefficients of variation, service levels, and deviation from lower bound. Simulation experiments showed that the proposed H2 heuristic outperformed the H1 heuristic.     

Intruder alert! Optimization models for solving the mobile robot graph-clear problem

We develop optimization approaches to the graph-clear problem, a pursuit-evasion problem where mobile robots must clear a facility of intruders. The objective is to minimize the number of robots required. We contribute new formal results on progressive and contiguous assumptions and their impact on algorithm completeness. We present mixed-integer linear programming and constraint programming models, as well as new heuristic variants for the problem, comparing them to previously proposed heuristics. Our empirical work indicates that our heuristic variants improve on those from the literature, that constraint programming finds better solutions than the heuristics in run-times reasonable for the application, and that mixed-integer linear programming is superior for proving optimality. Given their performance and the appeal of the model-and-solve framework, we conclude that the proposed optimization methods are currently the most suitable for the graph-clear problem.     

Automating the packing heuristic design process with genetic programming

The literature shows that one-, two-, and three-dimensional bin packing and knapsack packing are difficult problems in operational research. Many techniques, including exact, heuristic, and metaheuristic approaches, have been investigated to solve these problems and it is often not clear which method to use when presented with a new instance. This paper presents an approach which is motivated by the goal of building computer systems which can design heuristic methods. The overall aim is to explore the possibilities for automating the heuristic design process. We present a genetic programming system to automatically generate a good quality heuristic for each instance. It is not necessary to change the methodology depending on the problem type (one-, two-, or three-dimensional knapsack and bin packing problems), and it therefore has a level of generality unmatched by other systems in the literature. We carry out an extensive suite of experiments and compare with the best human designed heuristics in the literature. Note that our heuristic design methodology uses the same parameters for all the experiments. The contribution of this paper is to present a more general packing methodology than those currently available, and to show that, by using this methodology, it is possible for a computer system to design heuristics which are competitive with the human designed heuristics from the literature. This represents the first packing algorithm in the literature able to claim human competitive results in such a wide variety of packing domains.     

Adaptive selection of heuristics for assigning time slots and rooms in exam timetables

This paper presents an iterative adaptive approach which hybridises bin packing heuristics to assign exams to time slots and rooms. The approach combines a graph-colouring heuristic, to select an exam in every iteration, with bin-packing heuristics to automate the process of time slot and room allocation for exam timetabling problems. We start by analysing the quality of the solutions obtained by using one heuristic at a time. Depending on the individual performance of each heuristic, a random iterative hyper-heuristic is used to randomly hybridise the heuristics and produce a collection of heuristic sequences to construct solutions with different quality. Based on these sequences, we analyse the way in which the bin packing heuristics are automatically hybridised. It is observed that the performance of the heuristics used varies depending on the problem. Based on these observations, an iterative hybrid approach is developed to adaptively choose and hybridise the heuristics during solution construction. The overall aim here is to automate the heuristic design process, which draws upon an emerging research theme which is concerned with developing methods to design and adapt heuristics automatically. The approach is tested on the exam timetabling track of the second International Timetabling Competition, to evaluate its ability to generalise on instances with different features. The hyper-heuristic with low-level graph-colouring and bin-packing heuristics approach was found to generalise well over all the problem instances and performed comparably to the state of the art approaches.     

Heuristics for minimizing maximum lateness on a single machine with family-dependent set-up times

We address the problem of scheduling a single machine subject to family-dependent set-up times in order to minimize maximum lateness. We present a number of local improvement heuristics based on the work of previous researchers, a rolling horizon heuristic, and an incomplete dynamic programming heuristic. Extensive computational experiments on randomly generated test problems compare the performance of these heuristics. The rolling horizon procedures perform particularly well but require their parameters to be set based on problem characteristics to obtain their best performance.     

Grammar-based generation of variable-selection heuristics for constraint satisfaction problems

We propose a grammar-based genetic programming framework that generates variable-selection heuristics for solving constraint satisfaction problems. This approach can be considered as a generation hyper-heuristic. A grammar to express heuristics is extracted from successful human-designed variable-selection heuristics. The search is performed on the derivation sequences of this grammar using a strongly typed genetic programming framework. The approach brings two innovations to grammar-based hyper-heuristics in this domain: the incorporation of if-then-else rules to the function set, and the implementation of overloaded functions capable of handling different input dimensionality. Moreover, the heuristic search space is explored using not only evolutionary search, but also two alternative simpler strategies, namely, iterated local search and parallel hill climbing. We tested our approach on synthetic and real-world instances. The newly generated heuristics have an improved performance when compared against human-designed heuristics. Our results suggest that the constrained search space imposed by the proposed grammar is the main factor in the generation of good heuristics. However, to generate more general heuristics, the composition of the training set and the search methodology played an important role. We found that increasing the variability of the training set improved the generality of the evolved heuristics, and the evolutionary search strategy produced slightly better results.     

基于Rough集的启发式约简中启发式规则比较研究

采用属性的重要性作为启发式属性约简规则比较普遍。选择几种研究较多的属性重要性启发式规则,如属性依赖度、区分矩阵频率、信息熵等,进行简要介绍。通过编程实现规则和算法、采用经典数据集的运算比较作了汇总,从运算结果分析中获取了不同启发式规则对属性约简影响的几个基本结论。     

Parallel Heuristics for Improved, Balanced Graph Colorings

The computation of good, balanced graph colorings is an essential part of many algorithms required in scientific and engineering applications. Motivated by an effective sequential heuristic, we introduce a new parallel heuristic, PLF, and show that this heuristic has the same expected runtime under the PRAM computational model as the scalable coloring heuristic introduced by Jones and Plassmann. We present experimental results performed on the Intel DELTA that demonstrate that this new heuristic consistently generates better colorings and requires only slightly more time than the JP heuristic. In the second part of the paper we introduce two new parallel color-balancing heuristics, PDR(k) and PLF(k). We show that these heuristics have the desirable property that they do not increase the number of colors used by an initial coloring during the balancing process. We present experimental results that show that these heuristics are very effective in obtaining balanced colorings and, in addition, exhibit scalable performance.     

A performance comparison of heuristics for the total weighted tardiness problem

The single machine total weighted tardiness problem is an NP-hard problem that requires the use of heuristic solution procedures when more than 50 jobs are to be scheduled. In the literature, a well-tuned simulated annealing method and a descent heuristic with zero interchanges (DESO) both generated the best solutions for a large set of randomly generated problems. Due dates are generated by defining two parameters: the relative range of due dates (RDD) and the average tardiness factor (TF). In this paper, we define several heuristics based on dynamic programming and then use these and DESO heuristics to solve 50-job, 100-job, 200-job, and 500-job problems.     

A knowledge based system for flow shop scheduling

A technique is designed to integrate several solution methods to the problem of job sequencing in a flow shop. The solution methods integrated are linear programming, heuristics, and an expert system approach. The advantages to this integrated approach include reducing computation time and improving the solution as compared to the use of heuristic alone.     

Document image decoding by heuristic search

This correspondence describes an approach to reducing the computational cost of document image decoding by viewing it as a heuristic search problem. The kernel of the approach is a modified dynamic programming (DP) algorithm, called the iterated complete path (ICP) algorithm, that is intended for use with separable source models. A set of heuristic functions are presented for decoding formatted text with ICP. Speedups of 3-25 over DP have been observed when decoding text columns and telephone yellow pages using ICP and the proposed heuristics     

Decomposition heuristic to minimize total cost in a multi-level supply chain network

In this paper, the distribution planning model for the multi-level supply chain network is studied. Products which are manufactured at factory are delivered to customers through warehouses and distribution centers for the given customer demands. The objective function of suggested model is to minimize logistic costs such as replenishment cost, inventory holding cost and transportation cost. A mixed integer programming formulation and heuristics for practical use are suggested. Heuristics are composed of two steps: decomposition and post improving process. In the decomposition heuristics, the problems are solved optimally only considering the transportation route first by the minimum cost flow problem, and the replenishment plan is generated by applying the cost-saving heuristic which was originally suggested in the manufacturing assembly line operation, and integrating with the transportation plan. Another heuristic, in which the original model is segmented due to the time periods, and run on a rolling horizon based method, is suggested. With the post-improving process using tabu search method, the performances are evaluated, and it was shown that solutions can be computed within a reasonable computation time by the gap of about 10% in average from the lower bound of the optimal solutions.     

Evolving priority scheduling heuristics with genetic programming

This paper investigates the use of genetic programming in automated synthesis of scheduling heuristics for an arbitrary performance measure. Genetic programming is used to evolve the priority function, which determines the priority values of certain system elements (jobs, machines). The priority function is used within an appropriate meta-algorithm for a given environment, which forms the priority scheduling heuristic. The evolved solutions are compared with existing scheduling heuristics and found to perform similarly to or better than existing algorithms. We intend to show that this approach is particularly useful for combinations of scheduling environments and performance measures for which no adequate scheduling algorithms exist.     

A case-based approach to heuristic planning

Most of the great success of heuristic search as an approach to AI Planning is due to the right design of domain-independent heuristics. Although many heuristic planners perform reasonably well, the computational cost of computing the heuristic function in every search node is very high, causing the planner to scale poorly when increasing the size of the planning tasks. For tackling this problem, planners can incorporate additional domain-dependent heuristics in order to improve their performance. Learning-based planners try to automatically acquire these domain-dependent heuristics using previous solved problems. In this work, we present a case-based reasoning approach that learns abstracted state transitions that serve as domain control knowledge for improving the planning process. The recommendations from the retrieved cases are used as guidance for pruning or ordering nodes in different heuristic search algorithms applied to planning tasks. We show that the CBR guidance is appropriate for a considerable number of planning benchmarks.     

Grammatical evolution as a hyper-heuristic to evolve deterministic real-valued optimization algorithms

Hyper-heuristic methodologies have been extensively and successfully used to generate combinatorial optimization heuristics. On the other hand, there have been almost no attempts to build a hyper-heuristic to evolve an algorithm for solving real-valued optimization problems. In our previous research, we succeeded to evolve a Nelder–Mead-like real function minimization heuristic using genetic programming and the primitives extracted from the original Nelder–Mead algorithm. The resulting heuristic was better than the original Nelder–Mead method in the number of solved test problems but it was slower in that it needed considerably more cost function evaluations to solve the problems also solved by the original method. In this paper we exploit grammatical evolution as a hyper-heuristic to evolve heuristics that outperform the original Nelder–Mead method in all aspects. However, the main goal of the paper is not to build yet another real function optimization algorithm but to shed some light on the influence of different factors on the behavior of the evolution process as well as on the quality of the obtained heuristics. In particular, we investigate through extensive evolution runs the influence of the shape and dimensionality of the training function, and the impact of the size limit set to the evolving algorithms. At the end of this research we succeeded to evolve a number of heuristics that solved more test problems and in fewer cost function evaluations than the original Nelder–Mead method. Our solvers are also highly competitive with the improvements made to the original method based on rigorous mathematical convergence proofs found in the literature. Even more importantly, we identified some directions in which to continue the work in order to be able to construct a productive hyper-heuristic capable of evolving real function optimization heuristics that would outperform a human designer in all aspects.     

Constructing a unifying theory of dynamic programming DCOP algorithms via the generalized distributive law

In this paper we propose a novel message-passing algorithm, the so-called Action-GDL, as an extension to the generalized distributive law (GDL) to efficiently solve DCOPs. Action-GDL provides a unifying perspective of several dynamic programming DCOP algorithms that are based on GDL, such as DPOP and DCPOP algorithms. We empirically show how Action-GDL using a novel distributed post-processing heuristic can outperform DCPOP, and by extension DPOP, even when the latter uses the best arrangement provided by multiple state-of-the-art heuristics.     

On look-ahead heuristics in disjunctive logic programming

Disjunctive logic programming (DLP), also called answer set programming (ASP), is a convenient programming paradigm which allows for solving problems in a simple and highly declarative way. The language of DLP is very expressive and able to represent even problems of high complexity (every problem in the complexity class ${{\Sigma}_{2}^{P}} = {\rm NP}^{{\rm NP}}$ ). During the last decade, efficient systems supporting DLP have become available. Virtually all of these systems internally rely on variants of the Davis–Putnam procedure (for deciding propositional satisfiability [SAT]), combined with a suitable model checker. The heuristic for the selection of the branching literal (i.e., the criterion determining the literal to be assumed true at a given stage of the computation) dramatically affects the performance of a DLP system. While heuristics for SAT have received a fair deal of research, only little work on heuristics for DLP has been done so far. In this paper, we design, implement, optimize, and experiment with a number of heuristics for DLP. We focus on different look-ahead heuristics, also called “dynamic heuristics” (the DLP equivalent of unit propagation [UP] heuristics for SAT). These are branching rules where the heuristic value of a literal Q depends on the result of taking Q true and computing its consequences. We motivate and formally define a number of look-ahead heuristics for DLP programs. Furthermore, since look-ahead heuristics are computationally expensive, we design two techniques for optimizing the burden of their computation. We implement all the proposed heuristics and optimization techniques in DLV—the state-of-the-art implementation of disjunctive logic programming, and we carry out experiments, thoroughly comparing the heuristics and optimization techniques on a large number of instances of well-known benchmark problems. The results of these experiments are very interesting, showing that the proposed techniques significantly improve the performance of the DLV system.