171 research outputs found
An evolutionary variable neighbourhood search for the unrelated parallel machine scheduling problem
This article addresses a challenging industrial problem known as the unrelated parallel machine scheduling problem (UPMSP) with sequence-dependent setup times. In UPMSP, we have a set of machines and a group of jobs. The goal is to find the optimal way to schedule jobs for execution by one of the several available machines. UPMSP has been classified as an NP-hard optimisation problem and, thus, cannot be solved by exact methods. Meta-heuristic algorithms are commonly used to find sub-optimal solutions. However, large-scale UPMSP instances pose a significant challenge to meta-heuristic algorithms. To effectively solve a large-scale UPMSP, this article introduces a two-stage evolutionary variable neighbourhood search (EVNS) methodology. The proposed EVNS integrates a variable neighbourhood search algorithm and an evolutionary descent framework in an adaptive manner. The proposed evolutionary framework is employed in the first stage. It uses a mix of crossover and mutation operators to generate diverse solutions. In the second stage, we propose an adaptive variable neighbourhood search to exploit the area around the solutions generated in the first stage. A dynamic strategy is developed to determine the switching time between these two stages. To guide the search towards promising areas, a diversity-based fitness function is proposed to explore different locations in the search landscape. We demonstrate the competitiveness of the proposed EVNS by presenting the computational results and comparisons on the 1640 UPMSP benchmark instances, which have been commonly used in the literature. The experiment results show that our EVNS obtains better results than the compared algorithms on several UPMSP instances
Efficient Algorithms for Unrelated Parallel Machine Scheduling Considering Time of Use Pricing and Demand Charges
There is an ever-increasing focus on sustainability and energy consumption worldwide. Manufacturing is one of the major areas where energy reduction is not only environmentally beneficial, but also incredibly financially beneficial. These industrial consumers pay for their electricity according to prices that fluctuate throughout the day. These price fluctuations are in place to shift consumption away from “peak” times, when electricity is in the highest demand. In addition to this consumption cost, industrial consumers are charged according to their highest level of demand in a given window of time in the form of demand charges. This paper presents multiple solution methods to solve a parallel machine shop scheduling problem to minimize the total energy cost of the production schedule under Time of Use (TOU) and demand charge pricing. The greedy heuristic and genetic algorithm developed are designed to provide efficient solutions to this problem. The results of these methods are compared to a previously developed integer program (IP) solved using CPLEX with respect to the quality of the solution and the computational time required to solve it. Findings of these tests show that the greedy heuristic handles the test problems with only a small optimality gap to the genetic algorithm and optimal IP solution. The largest test problems could not be solved by the genetic algorithm in the provided time period due to difficulty generating an initial solution population. However, when successful the genetic algorithm performed comparably to the CPLEX solver in terms solution quality yet provided faster solve times
Enabling the “Easy Button” for Broad, Parallel Optimization of Functions Evaluated by Simulation
Java Optimization by Simulation (JOBS) is presented: an open-source, object-oriented Java library designed to enable the study, research, and use of optimization for models evaluated by simulation. JOBS includes several novel design features that make it easy for a simulation modeler, without extensive expertise in optimization or parallel computation, to define an optimization model with deterministic and/or stochastic constraints, choose one or more metaheuristics to solve it and run, using massively parallel function evaluation to reduce wall-clock times.
JOBS is supported by a new language independent, application programming interface (API) for remote simulation model evaluation and a serverless computing environment to provide massively parallel function evaluation, on demand. Dynamic loop scheduling methods are evaluated in the serverless environment with the opportunity for significant resource contention for master node computing power and network bandwidth.
JOBS implements several population-based and single-solution improvement metaheuristics (solvers) for real, discrete, and mixed problems. The object-oriented design is extendible with classes that drastically reduce the amount of code required to implement a new solver and encourage re-use of solvers as building blocks for creating new multi-stage solvers or memetic algorithms
Hyper-heuristic decision tree induction
A hyper-heuristic is any algorithm that searches or operates in the space of
heuristics as opposed to the space of solutions. Hyper-heuristics are
increasingly used in function and combinatorial optimization. Rather than
attempt to solve a problem using a fixed heuristic, a hyper-heuristic
approach attempts to find a combination of heuristics that solve a problem
(and in turn may be directly suitable for a class of problem instances).
Hyper-heuristics have been little explored in data mining. This work presents
novel hyper-heuristic approaches to data mining, by searching a space of
attribute selection criteria for decision tree building algorithm. The search is
conducted by a genetic algorithm. The result of the hyper-heuristic search in
this case is a strategy for selecting attributes while building decision trees.
Most hyper-heuristics work by trying to adapt the heuristic to the state of
the problem being solved. Our hyper-heuristic is no different. It employs a
strategy for adapting the heuristic used to build decision tree nodes
according to some set of features of the training set it is working on. We
introduce, explore and evaluate five different ways in which this problem
state can be represented for a hyper-heuristic that operates within a decisiontree
building algorithm. In each case, the hyper-heuristic is guided by a rule
set that tries to map features of the data set to be split by the decision tree
building algorithm to a heuristic to be used for splitting the same data set.
We also explore and evaluate three different sets of low-level heuristics that
could be employed by such a hyper-heuristic.
This work also makes a distinction between specialist hyper-heuristics and
generalist hyper-heuristics. The main difference between these two hyperheuristcs
is the number of training sets used by the hyper-heuristic genetic
algorithm. Specialist hyper-heuristics are created using a single data set from
a particular domain for evolving the hyper-heurisic rule set. Such algorithms
are expected to outperform standard algorithms on the kind of data set used
by the hyper-heuristic genetic algorithm. Generalist hyper-heuristics are
trained on multiple data sets from different domains and are expected to
deliver a robust and competitive performance over these data sets when
compared to standard algorithms.
We evaluate both approaches for each kind of hyper-heuristic presented in
this thesis. We use both real data sets as well as synthetic data sets. Our
results suggest that none of the hyper-heuristics presented in this work are
suited for specialization – in most cases, the hyper-heuristic’s performance on
the data set it was specialized for was not significantly better than that of
the best performing standard algorithm. On the other hand, the generalist
hyper-heuristics delivered results that were very competitive to the best
standard methods. In some cases we even achieved a significantly better
overall performance than all of the standard methods
A new hybrid meta-heuristic algorithm for solving single machine scheduling problems
A dissertation submitted in partial ful lment of the
degree of Master of Science in Engineering (Electrical) (50/50)
in the
Faculty of Engineering and the Built Environment
Department of Electrical and Information Engineering
May 2017Numerous applications in a wide variety of elds has resulted in a rich history of research
into optimisation for scheduling. Although it is a fundamental form of the problem, the
single machine scheduling problem with two or more objectives is known to be NP-hard.
For this reason we consider the single machine problem a good test bed for solution
algorithms. While there is a plethora of research into various aspects of scheduling
problems, little has been done in evaluating the performance of the Simulated Annealing
algorithm for the fundamental problem, or using it in combination with other techniques.
Speci cally, this has not been done for minimising total weighted earliness and tardiness,
which is the optimisation objective of this work.
If we consider a mere ten jobs for scheduling, this results in over 3.6 million possible
solution schedules. It is thus of de nite practical necessity to reduce the search space in
order to nd an optimal or acceptable suboptimal solution in a shorter time, especially
when scaling up the problem size. This is of particular importance in the application
area of packet scheduling in wireless communications networks where the tolerance for
computational delays is very low. The main contribution of this work is to investigate
the hypothesis that inserting a step of pre-sampling by Markov Chain Monte Carlo
methods before running the Simulated Annealing algorithm on the pruned search space
can result in overall reduced running times.
The search space is divided into a number of sections and Metropolis-Hastings Markov
Chain Monte Carlo is performed over the sections in order to reduce the search space for
Simulated Annealing by a factor of 20 to 100. Trade-o s are found between the run time
and number of sections of the pre-sampling algorithm, and the run time of Simulated
Annealing for minimising the percentage deviation of the nal result from the optimal
solution cost. Algorithm performance is determined both by computational complexity
and the quality of the solution (i.e. the percentage deviation from the optimal). We
nd that the running time can be reduced by a factor of 4.5 to ensure a 2% deviation
from the optimal, as compared to the basic Simulated Annealing algorithm on the full
search space. More importantly, we are able to reduce the complexity of nding the
optimal from O(n:n!) for a complete search to O(nNS) for Simulated Annealing to
O(n(NMr +NS)+m) for the input variables n jobs, NS SA iterations, NM Metropolis-
Hastings iterations, r inner samples and m sections.MT 201
Theoretical and Computational Research in Various Scheduling Models
Nine manuscripts were published in this Special Issue on “Theoretical and Computational Research in Various Scheduling Models, 2021” of the MDPI Mathematics journal, covering a wide range of topics connected to the theory and applications of various scheduling models and their extensions/generalizations. These topics include a road network maintenance project, cost reduction of the subcontracted resources, a variant of the relocation problem, a network of activities with generally distributed durations through a Markov chain, idea on how to improve the return loading rate problem by integrating the sub-tour reversal approach with the method of the theory of constraints, an extended solution method for optimizing the bi-objective no-idle permutation flowshop scheduling problem, the burn-in (B/I) procedure, the Pareto-scheduling problem with two competing agents, and three preemptive Pareto-scheduling problems with two competing agents, among others. We hope that the book will be of interest to those working in the area of various scheduling problems and provide a bridge to facilitate the interaction between researchers and practitioners in scheduling questions. Although discrete mathematics is a common method to solve scheduling problems, the further development of this method is limited due to the lack of general principles, which poses a major challenge in this research field
An investigation of changeover sensitive heuristics in an industrial job shop environment
EThOS - Electronic Theses Online ServiceGBUnited Kingdo
Variable neighborhood search for the multi-level capacitated lotsizing problem
Das dynamische mehrstufige kapazitierte Losgrößenproblem (MLCLSP) behandelt im Rahmen der Produktionsplanung die wichtige Entscheidung über die optimalen Losgrößen, angefangen bei Endprodukten über Komponenten bis hin zu Rohstoffen, bei gleichzeitiger Berücksichtigung beschränkter Kapazitäten der zur Produktion benötigten Ressourcen. Da es sich um ein NP-schweres Problem handelt, stoßen exakte Lösungsverfahren an ihre Grenzen, sobald die Problemdimensionen ein größeres – man könnte durchaus sagen realistisches – Ausmaß erreichen. In der Praxis dominieren deshalb Methoden, die die Losgrößen der einzelnen Produkte sequenziell festlegen und überdies etwaige Kapazitätsbeschränkungen im Nachhinein, falls überhaupt, berücksichtigen. In der Literatur finden sich zahlreiche approximative Ansätze zur Lösung dieses komplexen betriebswirtschaftlichen Problems. Lokale Suche und auf ihr basierende Metaheuristiken stellen vielversprechende Werkzeuge dar, um die Defizite der aktuell eingesetzten Trial-and-Error Ansätze zu beheben und letzten Endes zulässige sowie kostenoptimale Produktionspläne zu erstellen.
Die in dieser Diplomarbeit vorgestellte Studie beschäftigt sich mit lokalen Suchverfahren für das MLCLSP. Acht Nachbarschaftsstrukturen, die sich aus einer Veränderung der Rüstvariablen ergeben, werden präsentiert und evaluiert. Grundlegende Optionen bei der Gestaltung eines iterativen Verbesserungsverfahrens, wie beispielsweise unterschiedliche Schrittfunktionen oder die temporäre Berücksichtigung unzulässiger Lösungen, werden getestet und verglichen.
Obwohl nur die Switch Nachbarschaft, die durch das Ändern einer einzigen Rüstvariable definiert wird, wirklich überzeugende Resultate liefert, können die übrigen Nachbarschaftsstrukturen durchaus als Perturbationsmechanismen im Rahmen einer Variablen Nachbarschaftssuche (VNS) zum Einsatz kommen. Die Implementierung dieser Metaheuristik, geprägt von den Ergebnissen der einfachen lokalen Suchverfahren, kann allerdings nicht vollkommen überzeugen. Die entwickelte VNS Variante kann die Lösungsgüte anderer zum Vergleich herangezogener Lösungsverfahren nicht erreichen und benötigt relativ lange Laufzeiten. Andererseits sind die Ergebnisse mit einer durchschnittlichen Abweichung zur besten bekannten Lösung von etwa vier Prozent über sämtliche untersuchte Problemklassen weit entfernt von einem Totalversagen. Es überwiegt der Eindruck, dass es sich um eine robuste Methode handelt, die in der Lage ist, Lösungen von hoher, teils sehr hoher Qualität nicht nur in Ausnahmefällen zu liefern. Etwaige Nachjustierungen könnten das Verfahren durchaus zu einem ernstzunehmenden Konkurrenten für bereits existierende Lösungsmethoden für das MLCLSP machen.The Multi-Level Capacitated Lotsizing Problem (MLCLSP) depicts the important decision in production planning of determining adequate lot sizes from final products onward, to subassemblies, parts and raw materials, all the while assuming limited capacities of the resources employed for manufacture. It is an NP-hard problem where exact methods fail in solving larger – one could say realistic – problem instances. Sequential approaches that tackle the problem item by item and postpone capacity considerations dominate current practice; approximate solution methods abound throughout the literature. Local search and metaheuristics based on it constitute a class of approximate methods well-equipped to take on the challenge of eventually replacing the trial-and-error process that impedes manufacturing companies in establishing feasible and cost-minimal production plans.
This thesis presents a study of local search based procedures for solving the MLCLSP. Eight different neighborhood structures, resulting from manipulations of the setup variables, are devised and evaluated. Fundamental options when designing an iterative improvement algorithm, such as best-improvement versus first-improvement step functions or the inclusion of infeasible solutions during the search are explored and compared.
Although only the Switch move, which alters the value of a single setup value, is convincing as a stand-alone neighborhood structure, the other neighborhoods can in any case be employed for the perturbation of solutions during the shaking step of a Variable Neighborhood Search (VNS). The implementation of this metaheuristic, shaped by the findings from testing the basic local search variants, led to mixed results. The procedure designed to tackle the MLCLSP cannot outperform the compared heuristics. Neither does it produce results that are terribly off – the average gap to the best known solutions settles around four percent over all problem classes tested. Nonetheless, the impression is supported that the VNS procedure is a robust method leading to good, sometimes even very good solutions at a regular basis that is amenable to further adjustments and thus eventually becoming a serious competitor for existing methods dealing with multi-level capacitated lotsizing decisions
- …