Merging Nodes in Search Trees: an Exact Exponential Algorithm for the Single Machine Total Tardiness Scheduling Problem

This paper proposes an exact exponential algorithm for the problem of minimizing the total tardiness of jobs on a single machine. It exploits the structure of a basic branch-and-reduce framework based on the well known Lawler\u27s decomposition property. The proposed algorithm, called branch-and-merge, is an improvement of the branch-and-reduce technique with the embedding of a node merging operation. Its time complexity is O*(2.247^n) keeping the space complexity polynomial. The branch-and-merge technique is likely to be generalized to other sequencing problems with similar decomposition properties

Exact and Heuristic Hybrid Approaches for Scheduling and Clustering Problems

This thesis deals with the design of exact and heuristic algorithms for scheduling and clustering combinatorial optimization problems. All the works are linked by the fact that all the presented methods arebasically hybrid algorithms, that mix techniques used in the world of combinatorial optimization. The algorithms are all efficient in practice, but the one presented in Chapter 4, that has mostly theoretical interest. Chapter 2 presents practical solution algorithms based on an ILP model for an energy scheduling combinatorial problem that arises in a smart building context. Chapter 3 presents a new cutting stock problem and introduce a mathematical formulation and a heuristic solution approach based on a heuristic column generation scheme. Chapter 4 provides an exact exponential algorithm, whose importance is only theoretical so far, for a classical scheduling problem: the Single Machine Total Tardiness Problem. The relevant aspect is that the designed algorithm has the best worst case complexity for the problem, that has been studied for several decades. Furthermore, such result is based on a new technique, called Branch and Merge, that avoids the solution of several equivalent sub-problems in a branching algorithm that requires polynomial space. As a consequence, such technique embeds in a branching algorithm ideas coming from other traditional computer science techniques such as dynamic programming and memorization, but keeping the space requirement polynomial. Chapter 5 provides an exact approach based on semidefinite programming and a matheuristic approach based on a quadratic solver for a fractional clustering combinatorial optimization problem, called Max-Mean Dispersion Problem. The matheuristic approach has the peculiarity of using a non-linear MIP solver. The proposed exact approach uses a general semidefinite programming relaxation and it is likely to be extended to other combinatorial problems with a fractional formulation. Chapter 6 proposes practical solution methods for a real world clustering problem arising in a smart city context. The solution algorithm is based on the solution of a Set Cover model via a commercial ILP solver. As a conclusion, the main contribution of this thesis is given by several approaches of practical or theoretical interest, for two classes of important combinatorial problems: clustering and scheduling. All the practical methods presented in the thesis are validated by extensive computational experiments, that compare the proposed methods with the ones available in the state of the art

Data-driven Algorithm for Scheduling with Total Tardiness

In this paper, we investigate the use of deep learning for solving a classical NP-Hard single machine scheduling problem where the criterion is to minimize the total tardiness. Instead of designing an end-to-end machine learning model, we utilize well known decomposition of the problem and we enhance it with a data-driven approach. We have designed a regressor containing a deep neural network that learns and predicts the criterion of a given set of jobs. The network acts as a polynomial-time estimator of the criterion that is used in a single-pass scheduling algorithm based on Lawler's decomposition theorem. Essentially, the regressor guides the algorithm to select the best position for each job. The experimental results show that our data-driven approach can efficiently generalize information from the training phase to significantly larger instances (up to 350 jobs) where it achieves an optimality gap of about 0.5%, which is four times less than the gap of the state-of-the-art NBR heuristic

Data-driven algorithm for single machine scheduling problem

V této práci představuje metodu pro řešení problému Single machine total tardiness problem. Analyzovali jsme užití Deep learning metod, pro Single machine total tardiness problem. Využili jsme rozděl a panuj algoritmu a odvodili z něj data-driven přístup. Vytvořili jsme hlubokou neuronovou síť se schopností predikovat hodnotu kritéria problému. Tato neuronová síť jedná jako optimální orákulum s polynomiální dobou běhu. Orákulum řídí rozděl a panuj metodu v každém kroku. Náš data-driven přístup překonává state-of-the-art heuristiku ve kvalitě řešení.In this thesis, we present a method for solving a single machine total tardiness problem a classical NP-hard scheduling problem. We investigate the use of deep learning method for this problem. We utilize known decomposition method from operation research, and we derive data-driven method. We introduce a deep neural network that predicts the objective value and acts as a polynomial-time oracle. Oracle drive decomposition method in each step. Our data-driven method outperforms the state-of-the-art heuristic in terms of optimality gap

Energy-Efficient Flexible Flow Shop Scheduling With Due Date and Total Flow Time

One of the most significant optimization issues facing a manufacturing company is the flexible flow shop scheduling problem (FFSS). However, FFSS with uncertainty and energy-related elements has received little investigation. Additionally, in order to reduce overall waiting times and earliness/tardiness issues, the topic of flexible flow shop scheduling with shared due dates is researched. Using transmission line loadings and bus voltage magnitude variations, an unique severity function is formulated in this research. Optimize total energy consumption, total agreement index, and make span all at once. Many different meta-heuristics have been presented in the past to find near-optimal answers in an acceptable amount of computation time. To explore the potential for energy saving in shop floor management, a multi-level optimization technique for flexible flow shop scheduling and integrates power models for individual machines with cutting parameters optimisation into energy-efficient scheduling issues is proposed. However, it can be difficult and time-consuming to fine-tune algorithm-specific parameters for solving FFSP

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe