Scheduling Problems

Scheduling is defined as the process of assigning operations to resources over time to optimize a criterion. Problems with scheduling comprise both a set of resources and a set of a consumers. As such, managing scheduling problems involves managing the use of resources by several consumers. This book presents some new applications and trends related to task and data scheduling. In particular, chapters focus on data science, big data, high-performance computing, and Cloud computing environments. In addition, this book presents novel algorithms and literature reviews that will guide current and new researchers who work with load balancing, scheduling, and allocation problems

Performance Analyses of Graph Heuristics and Selected Trajectory Metaheuristics on Examination Timetable Problem

Examination timetabling problem is hard to solve due to its NP-hard nature, with a large number of constraints having to be accommodated. To deal with the problem effectually, frequently heuristics are used for constructing feasible examination timetable while meta-heuristics are applied for improving the solution quality. This paper presents the performances of graph heuristics and major trajectory metaheuristics or S-metaheuristics for addressing both capacitated and un-capacitated examination timetabling problem. For constructing the feasible solution, six graph heuristics are used. They are largest degree (LD), largest weighted degree (LWD), largest enrolment degree (LE), and three hybrid heuristic with saturation degree (SD) such as SD-LD, SD-LE, and SD-LWD. Five trajectory algorithms comprising of tabu search (TS), simulated annealing (SA), late acceptance hill climbing (LAHC), great deluge algorithm (GDA), and variable neighborhood search (VNS) are employed for improving the solution quality. Experiments have been tested on several instances of un-capacitated and capacitated benchmark datasets, which are Toronto and ITC2007 dataset respectively. Experimental results indicate that, in terms of construction of solution of datasets, hybridizing of SD produces the best initial solutions. The study also reveals that, during improvement, GDA, SA, and LAHC can produce better quality solutions compared to TS and VNS for solving both benchmark examination timetabling datasets

Swarm Intelligent in Bio-Inspired Perspective: A Summary

This paper summarizes the research performed in the field of swarm intelligent in recent years. The classification of swarm intelligence based on behavior is introduced.  The principles of each behaviors, i.e. foraging, aggregating, gathering, preying, echolocation, growth, mating, clustering, climbing, brooding, herding, and jumping are described. 3 algorithms commonly used in swarm intelligent are discussed.  At the end of summary, the applications of the SI algorithms are presented

Swarm Intelligent in Bio-Inspired Perspective: A Summary

This paper summarizes the research performed in the field of swarm intelligent in recent years. The classification of swarm intelligence based on behavior is introduced. The principles of each behaviors, i.e. foraging, aggregating, gathering, preying, echolocation, growth, mating, clustering, climbing, brooding, herding, and jumping are described. 3 algorithms commonly used in swarm intelligent are discussed. At the end of summary, the applications of the SI algorithms are presented

Investigating evolutionary computation with smart mutation for three types of Economic Load Dispatch optimisation problem

The Economic Load Dispatch (ELD) problem is an optimisation task concerned with how electricity generating stations can meet their customers’ demands while minimising under/over-generation, and minimising the operational costs of running the generating units. In the conventional or Static Economic Load Dispatch (SELD), an optimal solution is sought in terms of how much power to produce from each of the individual generating units at the power station, while meeting (predicted) customers’ load demands. With the inclusion of a more realistic dynamic view of demand over time and associated constraints, the Dynamic Economic Load Dispatch (DELD) problem is an extension of the SELD, and aims at determining the optimal power generation schedule on a regular basis, revising the power system configuration (subject to constraints) at intervals during the day as demand patterns change. Both the SELD and DELD have been investigated in the recent literature with modern heuristic optimisation approaches providing excellent results in comparison with classical techniques. However, these problems are defined under the assumption of a regulated electricity market, where utilities tend to share their generating resources so as to minimise the total cost of supplying the demanded load. Currently, the electricity distribution scene is progressing towards a restructured, liberalised and competitive market. In this market the utility companies are privatised, and naturally compete with each other to increase their profits, while they also engage in bidding transactions with their customers. This formulation is referred to as: Bid-Based Dynamic Economic Load Dispatch (BBDELD). This thesis proposes a Smart Evolutionary Algorithm (SEA), which combines a standard evolutionary algorithm with a “smart mutation” approach. The so-called ‘smart’ mutation operator focuses mutation on genes contributing most to costs and penalty violations, while obeying operational constraints. We develop specialised versions of SEA for each of the SELD, DELD and BBDELD problems, and show that this approach is superior to previously published approaches in each case. The thesis also applies the approach to a new case study relevant to Nigerian electricity deregulation. Results on this case study indicate that our SEA is able to deal with larger scale energy optimisation tasks

A meta-heurística por colônia de formigas pelo algoritmo minmaxant system aplicada ao problema de quadro de horários escolar

Trabalho de Conclusão de Curso, apresentado para obtenção do grau de Bacharel no Curso de Ciência da Computação da Universidade do Extremo Sul Catarinense, UNESC.A geração de quadro de horários nas escolas é um problema clássico de otimização combinatória que se constitui em um fator crítico de qualidade para qualquer instituição de ensino. O software de gestão escolar i-Educar é um projeto feito em comunidade, utilizado por diversos municípios em todo o Brasil para auxílio na gestão de escolas públicas. Considerando a complexidade na elaboração de grade horária de forma manual e a dificuldade de obtenção de soluções ótimas tem tempo computacional aceitável, o presente trabalho propõe o uso da meta-heurística de otimização por colônia de formigas para gerar quadros de horários com dados do software de gestão escolar i-Educar. Para isto, foi implementada uma API que permite ler os dados do i-Educar, e importar estes para a base de dados do protótipo. Dentre os métodos de colônia de formigas, empregou-se o algoritmo Min-Max Ant System para geração da grade horária. Os resultados foram positivos, podendo ser gerado grade horária de qualidade com tempo satisfatório, afirmando então, que método MMAS com busca local é um bom candidato para resolução de problemas de otimização combinatória, podendo gerar bons resultados e com poucas violações das restrições difíceis

Memetički algoritmi

Na početku ovog rada opisali smo evolucijske algoritme i njihove značajke. Evolucijski algoritmi najčešće se koriste za rješavanje problema optimizacije, a baziraju se na principima Darwinove teorije o prirodnoj selekciji. Temeljni način evolucijskog rješavanja problema oslanja se na metodu pokušaja i pogreške. Ideja je jedinke što bolje prilagoditi nekoj danoj okolini s obzirom na određene karakteristike. Intuitivno, želimo izvesti analogiju između evolucije u stvarnom svijetu i evolucijskog programiranja na način da okolina predstavlja zadani problem koji treba riješiti, jedinke predstavljaju rješenja, a podobnost jedinki (eng. fitness) predstavlja koliko je to rješenje dobro. Do boljeg rješenja u svakoj generaciji dolazimo pomoću operatora varijacije: mutacije i rekombinacije. Njih primjenjujemo na roditelje u svrhu dobivanja podobnijih potomaka, odnosno boljih rješenja. Memetički algoritmi zapravo su evolucijski algoritmi kombinirani s drugim tehnikama ili pak nadograđeni nekim metodama ili strukturama podataka. Ono što najčešće želimo implementirati jesu podaci o samom problemu koji želimo riješiti. Važan dio memetičkog programiranja je lokalno pretraživanje. U najopćenitijim crtama to je iterativni proces koji ispituje skup točaka oko trenutnog rješenja, i ukoliko nađe bolje rješenje u tom skupu, onda ga postavi za novo trenutno rješenje. Također, operatori koji se koriste u evolucijskom programiranju mogu se nadograditi stečenim znanjima ili pak možemo odmah u inicijalizaciju umetnuti informacije koje bi nam pomogle pri rješavanju problema. Time automatski dobivamo bolji i efikasniji algoritam. Na kraju smo teoriju demonstrirali praktičnim primjerom u MATLAB-u i to algoritmom skakutanja žaba (eng. Shuffled Frog Leaping Algorithm- SFLA). Gledali smo populaciju od 500 žaba na području $[-10,10] \times [-10,10]$ s funkcijom podobnosti $f(x,y)=x^2+y^2$, gdje je $(x,y)$ pozicija svake žabe. Primjer nam je dao očekivane rezultate s obzirom na teorijsku podlogu koju smo obradili u prva dva poglavlja. Pokazalo se da je upotreba memetičkih algoritama izrazito korisna u praksi i čini istraživačko područje koje posjeduje veliki potencijal za daljnja istraživanja.At the beginning of this graduate thesis we have described evolutionary algorithms and their features. They are most commonly used for solving optimization problems and they form a class of algorithms that are based on the Darwinian principles of natural selection. The fundamental way of evolutionary computing relates to a particular style of problem solving– that of trial and error. The idea is to adapt individuals to better suit the given environment. Intuitively, we want to link the evolution in ‘real world’ to the evolutionary computing and we do that in a way that environment represents a given problem, individuals represent solutions, and fitness of every individual represents a measure of how good solution solves a given problem. In every generation we make new (better) solutions by using variation operators: mutation and recombination. They are applied to the so-called parents, producing one or more children (new solutions). Memetic algorithms are actually evolutionary algorithms combined with other techniques or have other methods or data structures incorporated within them. In most cases we want to include information about the problem we are solving into the evolutionary algorithm. The important phase of memetic algorithm is local search. Briefly described, local search is an iterative process of examining the set of points in the neighbourhood of the current solution, and replacing it with a better neighbour if one exists. Variation operators that are used in evolutionary algorithms can also be upgraded by incorporating problem-specific knowledge, or we can just incorporate that information in initialization phase as well. By making these changes we instantly get a better and more efficient algorithm. In the end, we demonstrated the theory with a practical example in MATLAB. The example we have described is called Shuffled Frog Leaping Algorithm (SFLA). We observed the population of 500 frogs in the $[-10,10] \times [-10,10]$ environment with fitness function $f(x,y)=x^2+y^2$, in which $(x,y)$ represents position of each frog. The example yielded the expected results considering the theory we have explained in the first two chapters. It turned out that memetic algorithms are very successful in practice and they form a rapidly growing research area with great potential

Offline Learning for Sequence-based Selection Hyper-heuristics

This thesis is concerned with finding solutions to discrete NP-hard problems. Such problems occur in a wide range of real-world applications, such as bin packing, industrial flow shop problems, determining Boolean satisfiability, the traveling salesman and vehicle routing problems, course timetabling, personnel scheduling, and the optimisation of water distribution networks. They are typically represented as optimisation problems where the goal is to find a ``best'' solution from a given space of feasible solutions. As no known polynomial-time algorithmic solution exists for NP-hard problems, they are usually solved by applying heuristic methods. Selection hyper-heuristics are algorithms that organise and combine a number of individual low level heuristics into a higher level framework with the objective of improving optimisation performance. Many selection hyper-heuristics employ learning algorithms in order to enhance optimisation performance by improving the selection of single heuristics, and this learning may be classified as either online or offline. This thesis presents a novel statistical framework for the offline learning of subsequences of low level heuristics in order to improve the optimisation performance of sequenced-based selection hyper-heuristics. A selection hyper-heuristic is used to optimise the HyFlex set of discrete benchmark problems. The resulting sequences of low level heuristic selections and objective function values are used to generate an offline learning database of heuristic selections. The sequences in the database are broken down into subsequences and the mathematical concept of a logarithmic return is used to discriminate between ``effective'' subsequences, that tend to lead to improvements in optimisation performance, and ``disruptive'' subsequences that tend to lead to worsening performance. Effective subsequences are used to improve hyper-heuristics performance directly, by embedding them in a simple hyper-heuristic design, and indirectly as the inputs to an appropriate hyper-heuristic learning algorithm. Furthermore, by comparing effective subsequences across different problem domains it is possible to investigate the potential for cross-domain learning. The results presented here demonstrates that the use of well chosen subsequences of heuristics can lead to small, but statistically significant, improvements in optimisation performance

Enhancement of bees algorithm for global optimisation

This research focuses on the improvement of the Bees Algorithm, a swarm-based nature-inspired optimisation algorithm that mimics the foraging behaviour of honeybees. The algorithm consists of exploitation and exploration, the two key elements of optimisation techniques that help to find the global optimum in optimisation problems. This thesis presents three new approaches to the Bees Algorithm in a pursuit to improve its convergence speed and accuracy. The first proposed algorithm focuses on intensifying the local search area by incorporating Hooke and Jeeves’ method in its exploitation mechanism. This direct search method contains a pattern move that works well in the new variant named “Bees Algorithm with Hooke and Jeeves” (BA-HJ). The second proposed algorithm replaces the randomly generated recruited bees deployment method with chaotic sequences using a well-known logistic map. This new variant called “Bees Algorithm with Chaos” (ChaosBA) was intended to use the characteristic of chaotic sequences to escape from local optima and at the same time maintain the diversity of the population. The third improvement uses the information of the current best solutions to create new candidate solutions probabilistically using the Estimation Distribution Algorithm (EDA) approach. This new version is called Bees Algorithm with Estimation Distribution (BAED). Simulation results show that these proposed algorithms perform better than the standard BA, SPSO2011 and qABC in terms of convergence for the majority of the tested benchmark functions. The BA-HJ outperformed the standard BA in thirteen out of fifteen benchmark functions and is more effective in eleven out of fifteen benchmark functions when compared to SPSO2011 and qABC. In the case of the ChaosBA, the algorithm outperformed the standard BA in twelve out of fifteen benchmark functions and significantly better in eleven out of fifteen test functions compared to qABC and SPSO2011. BAED discovered the optimal solution with the least number of evaluations in fourteen out of fifteen cases compared to the standard BA, and eleven out of fifteen functions compared to SPSO2011 and qABC. Furthermore, the results on a set of constrained mechanical design problems also show that the performance of the proposed algorithms is comparable to those of the standard BA and other swarm-based algorithms from the literature