Heuristic Decomposition Research Articles

A strong integer linear optimization model to the compartmentalized knapsack problem

AbstractThe compartmentalized knapsack problem (CKP) is a relatively new type of problem with a wide application in industrial processes, arising, for instance, in the case of cutting steel coils in two phases in the metallurgical industry.In the literature, there are two mathematical formulations for the CKP: a classical formulation, which is a nonlinear integer programming (IP) model, and a recent (linear) IP formulation, obtained by discretizing the compartments that can be built for each class of items; the latter is an important contribution, because it makes the problem amenable to solution by mixed‐integer linear programming tools. Combinatorial enumeration algorithms and several pseudo‐polynomial decomposition heuristics were also developed for the CKP.This paper presents a new model for the exact solution of the CKP, denoted as the strong integer linear model, derived from the (linear) IP formulation by strengthening data, reducing symmetry, and lifting, and also a new pseudo‐polynomial heuristic, the heuristic of the strong capacities. Computational experiments are presented with a large set of instances that show the advantage of the new approaches. The strong model solves the CKP exactly more than seven times faster, and the new heuristic is more efficient, presenting a good balance in the terms of effectiveness.

Heuristic Topological Decomposition Algorithm for Optimal Energy-Resource-Efficient Routing of Complex Process Pipeline Systems

A heuristic topological decomposition algorithm for optimal energy-resource-efficient routing of complex process pipeline systems was developed. The algorithm is distinguished by using an automated procedure for constructing a topological model of a hydraulic circuit as a hydraulic structural graph, a modified algorithm for finding the shortest spanning tree of the initial structural graph, and a set of heuristic rules. The developed algorithm enables one to determine the optimal energy-resource-efficient route with minimum reduced cost.

A heuristic procedure to solve the project staffing problem with discrete time/resource trade-offs and personnel scheduling constraints

When scheduling projects under resource constraints, assumptions are typically made with respect to the resource availability and activities are planned each with its own duration and resource requirements. In resource scheduling, important assumptions are made with respect to the staffing requirements. Both problems are typically solved in a sequential manner leading to a suboptimal outcome. We integrate these two interrelated scheduling problems to determine the optimal personnel budget that minimises the overall cost. Integrating these problems increases the scheduling flexibility, which improves the overall performance. In addition, we consider some resource demand flexibility in this research as an activity can be performed in multiple modes. In this paper, we present an iterated local search procedure for the integrated multi-mode project scheduling and personnel staffing problem. Detailed computational experiments are presented to evaluate different decomposition heuristics and comparison is made with alternative optimisation techniques.

A biobjective feature selection algorithm for large omics datasets

AbstractFeature selection is one of the most important concepts in data mining when dimensionality reduction is needed. The performance measures of feature selection encompass predictive accuracy and result comprehensibility. Consistency‐based methods are a significant category of feature selection research that substantially improves the comprehensibility of the result using the parsimony principle. In this work, the biobjective version of the algorithm logical analysis of inconsistent data is applied to large volumes of data. In order to deal with hundreds of thousands of attributes, heuristic decomposition uses parallel processing to solve a set covering problem and a cross‐validation technique. The biobjective solutions contain the number of reduced features and the accuracy. The algorithm is applied to omics datasets with genome‐like characteristics of patients with rare diseases.

An integer linear optimization model to the compartmentalized knapsack problem

AbstractThe compartmentalized knapsack problem arose from two‐phased cutting stock problems, especially with steel roll cutting. In its original formulation, it refers to an integer nonlinear optimization model, which, up to now, has been solved through decomposition heuristics. The objective of this article is to show that the constrained compartmentalized knapsack problem has a linear optimization model. Therefore, we have considered the original nonlinear model and propose a linear model for the problem, demonstrating their equivalence. We also propose a new decomposition heuristic and perform numerical tests to verify the limits of the proposed model and the quality of the heuristic solutions.

Mixed integer linear programming for quality of service optimization in Clouds

The analysis of the Quality of Service (QoS) level in a Cloud Computing environment becomes an attractive research domain as the utilization rate is daily higher and higher. Its management has a huge impact on the performance of both services and global Cloud infrastructures. Thus, in order to find a good trade-off, a Cloud provider has to take into account many QoS objectives, and also the manner to optimize them during the virtual machines allocation process. To tackle this complex challenge, this article proposed a multiobjective optimization of four relevant Cloud QoS objectives, using two different optimization methods: a Genetic Algorithm (GA) and a Mixed Integer Linear Programming (MILP) approach. The complexity of the virtual machine allocation problem is increased by the modeling of Dynamic Voltage and Frequency Scaling (DVFS) for energy saving on hosts. A global mixed-integer non linear programming formulation is presented and a MILP formulation is derived by linearization. A heuristic decomposition method, which uses the MILP to optimize intermediate objectives, is proposed. Numerous experimental results show the complementarity of the two heuristics to obtain various trade-offs between the different QoS objectives.

A matheuristic for the Cargo Mix Problem with Block Stowage

The cargo-mix problem aims at selecting the amount of containers of a given type to load on a vessel. In this article we present an extended definition that includes the analysis of a circular route with draft restrictions, limitations on expected cargo and the use of a block stowage strategy. A compact formulation of the problem based on the state-of-the-art heuristic decomposition is shown not to be able to solve the extended problem, thus a matheuristic approach is presented that can achieve high quality results in a matter of seconds.

A decomposition approach to dual shuttle automated storage and retrieval systems

Automated Storage and Retrieval Systems (AS/RS) have become vital in today’s distribution and production environments, however it remains necessary to equip them with more efficient operational control policies. Motivated by real situations encountered by companies employing AS/RS, the present paper studies a miniload AS/RS system, with a dual shuttle crane in which a set of storage and retrieval requests must be scheduled such that the prioritized waiting time is minimized. Dual shuttle cranes have received minimal academic attention and thus continue to pose new problems that must be solved. The miniload AS/RS problem is addressed by decomposing it into a location assignment and sequencing problem. Different heuristic strategies are introduced for making the assignments, while a general mathematical model and efficient branch and bound procedure are proposed for optimizing the sequence. Additionally, a fast metaheuristic capable of solving larger instances is also developed. A set of real-world based benchmarks with varying characteristics is generated to evaluate the proposed methods. Very small instances prove the only for which optimal sequences are found in reasonable calculation time. Experimental results demonstrate the effectiveness of the heuristic decomposition method.

A GRASP algorithm for the container stowage slot planning problem

This work presents a generalization of the Slot Planning Problem which raises when the liner shipping industry needs to plan the placement of containers within a vessel (stowage planning). State-of-the-art stowage planning relies on a heuristic decomposition where containers are first distributed in clusters along the vessel. For each of those clusters a specific position for each container must be found. Compared to previous studies, we have introduced two new features: the explicit handling of rolled out containers and the inclusion of separations rules for dangerous cargo. We present a novel integer programming formulation and a Greedy Randomized Adaptive Search Procedure (GRASP) to solve the problem. The approach is able to find high-quality solution within 1s. We also provide comparison with the state-of-the-art on an existing and a new set of benchmark instances.

A two-dimensional heuristic decomposition approach to a three-dimensional multiple container loading problem

Efficient container loading has the potential to considerably reduce logistics and transportation costs. The container loading problem is computationally complex and, despite extensive academic effort, there remains room for algorithm improvement. Real-world problems are not always addressed satisfactorily primarily due to the large number of complex constraints and objectives. The problem addressed by this work is an unsolved multiple container loading problem introduced by Renault on the occasion of the 2014/2015 ESICUP challenge, organized by the EURO Special Interest Group on Cutting and Packing (ESICUP). Renault’s problem requires a large number of different items to be packed into containers of different types and sizes. Items must be grouped into stacks and respect the ‘this side up’ constraint. The primary objective is to minimize the volume of shipped containers. The smallest volume container may be left behind for the next shipment and is excluded from the main objective. Nevertheless, only a limited percentage of each product may be packed into this container. Additionally, a set of secondary objectives is considered. This work presents a decomposition approach embedded in a multi-phase heuristic for the problem. Feasible solutions are generated quickly, and subsequently improved by local search and post-processing procedures. Experiments revealed that the approach generates optimal solutions for two instances, in addition to good quality solutions for those remaining from the Renault set. The algorithmic contribution is, however, not restricted to the Renault instances. Experiments on less constrained container loading instances from the literature demonstrate the approach’s general applicability and competitiveness.

Heuristic decomposition approaches for an integrated task scheduling and personnel rostering problem

Real world combinatorial optimisation problems do not often reduce to neatly delineated theoretical problems. Rather, they combine characteristics of various subproblems which then appear to be strongly intertwined. The present contribution introduces a challenging integration of task and personnel scheduling in which both tasks and shifts must be assigned to a set of multi-skilled employees. Three constructive heuristics, based on column generation and other decomposition schemes, are presented, as well as a very large-scale neighbourhood search algorithm to further decrease the schedule's cost. The performance of these algorithms is evaluated on a large set of diverse instances. Computational results illustrate the effectiveness of the proposed approaches, and provide insight into their behaviour. The initial benchmarks are published so as to encourage further research.

When road trains supply freight trains: scheduling the container loading process by gantry crane between multi-trailer trucks and freight trains

An efficient integration of rail transport into the hinterland traffic is an important topic for ports all around the world. In this context, we treat a scheduling problem where multi-trailer trucks (denoted as road trains) deliver containers to some gantry crane, which successively loads the boxes onto freight trains. A road train carries up to a dozen containers, so that a lot of energy is consumed especially when setting a road train in motion. Thus, there is a basic trade-off between the effort of road train and gantry crane. The more often a road train is relocated, the higher its own demand for energy, but the lower that for moving the crane when processing containers rather from nearby holding positions and vice versa. This paper formalizes the novel problem setting and suggests a heuristic decomposition approach, which determines the stop locations of the road train and schedules the gantry crane during the loading process.

Tree decompositions and social graphs

AbstractRecent work has established that large informatics graphs such as social and information networks have non-trivial tree-like structure when viewed at moderate size scales. Here, we present results from the first detailed empirical evaluation of the use of tree decomposition (TD) heuristics for structure identification and extraction in social graphs. Although TDs have historically been used in structural graph theory and scientific computing, we show that—even with existing TD heuristics developed for those very different areas—TD methods can identify interesting structure in a wide range of realistic informatics graphs. Our main contributions are the following: we show that TD methods can identify structures that correlate strongly with the core-periphery structure of realistic networks, even when using simple greedy heuristics; we show that the peripheral bags of these TDs correlate well with low-conductance communities (when they exist) found using local spectral computations; and we show that ...

An Improved Energy-Awareness Formulation for General Precedence Continuous-Time Scheduling Models

Efficient frameworks for scheduling of energy-intensive industries are important enablers for the industrial implementation of the demand-side management concept (DSM). DSM enables enterprises to cut their energy cost as well as to support the grid in dealing with fluctuating availability of energy. In this work, we present an improvement of the energy-aware production scheduling strategy reported in Hadera et al.,1 which is based upon a continuous-time scheduling formulation. The improvement concerns the modeling of the coupling between the scheduling problem and the computation of the energy bill. The resulting optimization problem is solved by the heuristic bilevel decomposition from Hadera et al.2 Numerical studies showed that although the proposed formulation and heuristic decomposition does not guarantee to obtain the global minimum it does provide good quality solutions within reasonable solution times. The new energy-awareness formulation reduces the number of binary variables and constraints and ...

Modeling and optimizing the evacuation of hospitals based on the MRCPSP with resource transfers

In this paper, we consider the problem of hospital evacuation and model it as a multi-mode resource-constrained project scheduling problem (MRCPSP) with additional resource transfers and blockings. Based on this model two heuristic decomposition approaches are proposed. The first uses a tabu search algorithm for the mode assignment problem, the scheduling subproblem is solved by adapted serial and parallel schedule generation schemes using priority rules. The second is based on a decomposition into an evacuation and a routing subproblem where solutions are represented by resource flows. Computational experiments were performed for both approaches using randomly generated instances based on real-world scenarios.

Эффективное применение пакетов дискретной оптимизации в облачной инфраструктуре на основе эвристической декомпозиции исходной задачи в системе оптимизационного моделирования AMPL

Эффективное применение пакетов дискретной оптимизации в облачной инфраструктуре на основе эвристической декомпозиции исходной задачи в системе оптимизационного моделирования AMPL

Criteria and Heuristics for Business Process Model Decomposition

It is generally agreed that large process models should be decomposed into sub-processes in order to enhance understandability and maintainability. Accordingly, a number of process decomposition criteria and heuristics have been proposed in the literature. This paper presents a review of the field revealing distinct classes of criteria and heuristics. The study raises the question of how different decomposition heuristics affect process model understandability and maintainability. To address this question, an experiment is conducted where two different heuristics, one based on breakpoints and the other on data objects, were used to decompose a flat process model. The results of the experiment show that, although there are minor differences, the heuristics cause very similar results in regard to understandability and maintainability as measured by various process model metrics.

A decomposition heuristics based on multi-bottleneck machines for large-scale job shop scheduling problems

Design/methodology/approach: In the algorithm, a number of sub-problems are constructed by iteratively decomposing the large-scale JSP according to the process route of each job. And then the solution of the large-scale JSP can be obtained by iteratively solving the sub-problems. In order to improve the sub-problems' solving efficiency and the solution quality, a detection method for multi-bottleneck machines based on critical path is proposed. Therewith the unscheduled operations can be decomposed into bottleneck operations and non-bottleneck operations. According to the principle of “Bottleneck leads the performance of the whole manufacturing system” in TOC (Theory Of Constraints), the bottleneck operations are scheduled by genetic algorithm for high solution quality, and the non-bottleneck operations are scheduled by dispatching rules for the improvement of the solving efficiency.

Scheduling the part supply of mixed-model assembly lines in line-integrated supermarkets

Line-integrated supermarkets constitute a novel in-house parts logistics concept for feeding mixed-model assembly lines. In this context, supermarkets are decentralized logistics areas located directly in each station. Here, parts are withdrawn from their containers by a dedicated logistics worker and sorted just-in-sequence (JIS) into a JIS-bin. From this bin, assembly workers fetch the parts required by the current workpiece and mount them during the respective production cycle. This paper treats the scheduling of the part supply processes within line-integrated supermarkets. The scheduling problem for refilling the JIS-bins is formalized and a complexity analysis is provided. Furthermore, a heuristic decomposition approach is presented and important managerial aspects are investigated.

Optimum packing of rectangles based on heuristic dynamic decomposition algorithm

To solve the optimum packing of two-dimensional rectangle layout problem,a heuristic dynamic decomposition algorithm was proposed,which can be used in the three-dimensional rectangule layout and global optimization problems.The container was orthogonally decomposed according to the emission rectangles,and the best sub-container was selected according to the degree of place coupling,then the state of all containers was updated by the interference relationship,so the large-scale and complex problem can be solved quickly and efficiently.The experimental results of the Bench-mark cases internationally recognized show that the proposed algorithm has better performance compared with similar algorithms,in which the layout utilization efficiency is increased by 9.4% and the calculating efficiency is improved up to 95.7%.Finally the algorithm has been applied to the commercialized packing software AutoCUT,and it has good application prospects.