An estimation of distribution algorithm for combinatorial optimization problems

This paper considers solving more than one combinatorial problem considered some of the most difficult to solve in the combinatorial optimization field, such as the job shop scheduling problem (JSSP), the vehicle routing problem with time windows (VRPTW), and the quay crane scheduling problem (QCSP). A hybrid metaheuristic algorithm that integrates the Mallows model and the Moth-flame algorithm solves these problems. Through an exponential function, the Mallows model emulates the solution space distribution for the problems; meanwhile, the Moth-flame algorithm is in charge of determining how to produce the offspring by a geometric function that helps identify the new solutions. The proposed metaheuristic, called HEDAMMF (Hybrid Estimation of Distribution Algorithm with Mallows model and Moth-Flame algorithm), improves the performance of recent algorithms. Although knowing the algebra of permutations is required to understand the proposed metaheuristic, utilizing the HEDAMMF is justified because certain problems are fixed differently under different circumstances. These problems do not share the same objective function (fitness) and/or the same constraints. Therefore, it is not possible to use a single model problem. The aforementioned approach is able to outperform recent algorithms under different metrics for these three combinatorial problems. Finally, it is possible to conclude that the hybrid metaheuristics have a better performance, or equal in effectiveness than recent algorithms

Particle Swarm Optimization

Particle swarm optimization (PSO) is a population based stochastic optimization technique influenced by the social behavior of bird flocking or fish schooling.PSO shares many similarities with evolutionary computation techniques such as Genetic Algorithms (GA). The system is initialized with a population of random solutions and searches for optima by updating generations. However, unlike GA, PSO has no evolution operators such as crossover and mutation. In PSO, the potential solutions, called particles, fly through the problem space by following the current optimum particles. This book represents the contributions of the top researchers in this field and will serve as a valuable tool for professionals in this interdisciplinary field

Internet of Things in urban waste collection

Nowadays, the waste collection management has an important role in urban areas. This paper faces this issue and proposes the application of a metaheuristic for the optimization of a weekly schedule and routing of the waste collection activities in an urban area. Differently to several contributions in literature, fixed periodic routes are not imposed. The results significantly improve the performance of the company involved, both in terms of resources used and costs saving

A parameter tuned hybrid algorithm for solving flow shop scheduling problems with parallel assembly stages

In this paper, we study the scheduling problem for a customized production system consisting of a flow shop production line with a parallel assembly stage that produces various products in two stages. In the first stage of the production line, parts are produced using a flow shop production line, and in the second stage, products are assembled on one of the parallel assembly lines. The objective is to minimize the time required to complete all goods (makespan) using efficient scheduling. A mathematical model is developed; however, the model is NP-hard and cannot be solved in a reasonable amount of time. To solve this NP-hard problem, we propose two well-known metaheuristics and a hybrid algorithm. To calibrate and improve the performance of our algorithms, we employ the Taguchi method. We evaluate the performance of our hybrid algorithm with the two well-known methods of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) and demonstrate that our hybrid algorithm outperforms both the GA and PSO approaches in terms of efficiency

Rámec pro plánování problémy

Import 22/07/2015Scheduling problems form an important subclass of combinatorial optimisation problems with many applications in manufacturing and logistics. Predominately these problems are NP-complete (decision based) and NP-hard (optimisation based), hence the main course of research in solving them concentrates on the design of efficient heuristic algorithms. Two main categories of these algorithms exist: deterministic algorithms and evolutionary metaheuristics. The deterministic algorithms comprise local improvement techniques, such as k-opt algorithm, which try to improve existing feasible solution, and constructive heuristics, such as NEH, which build a solution starting from scratch, adding one job at a time. Evolutionary metaheuristics have prospered in the past decades, owing to their efficiency and flexibility. Drawing inspiration from the theory of natural evolution or swarm behavioural patterns, the most popular of these algorithms in practice include for instance Genetic Algorithms, Differential Evolution, Particle Swarm Optimisation, amongst others. However, even though these heuristics provide in most cases close to optimal solution at reasonable execution time, this time is still impractically long for many applications. Therefore much effort has been dedicated to accelerating these algorithms. Since the development of hardware turns away from increasing the clock speed towards the parallel processing units, owing to reaching the limits of technology due to the increased power consumption and heat dissipation, this effort goes into parallelisation of the existing algorithms, to enable exploitation of the computing power of multi-core or many-core platforms. This is the goal of the first part of the thesis, accelerating two of the deterministic algorithms, NEH and 2-opt, with interesting results. Another approach has been taken in the second part, with the core premise of exploring the influence of stochasticity on the performance of an evolutionary algorithm, selecting the relatively recent and promising Discrete Artificial Bee Colony algorithm. The pseudo-random number generator has been replaced with the different types of dissipative chaos maps, with some of them improving the algorithm significantly. It has been shown that the population based evolutionary algorithms often form complex networks, taken from the point of view of the information exchange between individual solutions during the course of population development. The final part of this thesis puts this observation into practice by embedding the complex network analysis based self-adaptive mechanism into the ABC algorithm, a continuous optimisation problems solving evolutionary algorithm, which is however the basis for the afore mentioned DABC algorithm, and proving the effectiveness for some of the developed versions, currently on the standard continuous optimisation test functions, with the possibility to extend this modification to the combinatorial optimisations problems in the future being discussed in the conclusion.Rozvrhovací problémy jsou důležitou podtřídou úloh kombinatorické optimalizace s řadou aplikací ve výrobě a logistice. Většina těchto problémů je NP-úplných (rozhodovací forma) a NP-těžkých (optimalizační forma), proto se výzkum zaměřuje na návrh efektivních heuristických algoritmů. Dvě hlavní kategorie těchto algoritmů jsou deterministické algoritmy a evoluční metaheuristiky. Deterministické algoritmy zahrnují techniky lokálního prohledávání, například algoritmus k-opt, jejichž cílem je zlepšení existujícího přípustného řešení problému, dále pak konstruktivní heuristiky, jejichž příkladem je algoritmus NEH, které hledané řešení vytvářejí inkrementálně, bez potřeby znalosti vstupního bodu v prohledávaném prostoru řešení. Evoluční metaheuristiky mají za sebou historii úspěšného vývoje v posledních desetiletích, zejména díky jejich efektivitě a flexibilitě. Jejich inspirací jsou poznatky převzaté z biologie, teorie evoluce a inteligence hejna. Mezi nejpopulárnějšími z těchto algoritmů jsou, mimo jiné, genetické algoritmy, diferenciální evoluce, rojení částic (Particle Swarm Optimisation). Ačkoli tyto heuristiky nalézají ve většině případů řešení blížící se globálnímu optimu v přípustném výpočetním čase, pro řadu aplikací mohou být stále ještě nepřijatelně pomalé. Velké úsilí bylo věnováno zrychlení těchto algoritmů. Protože se vývoj hardware díky dosažení technologických limitů, vzhledem ke zvyšující se spotřebě energie a tepelnému vyzařování, obrací od zvyšování frekvence jednojádrového procesoru k vícejádrovým procesorům a paralelnímu zpracování, je tato snaha většinou orientovaná na paralelizaci existujících algoritmů, aby bylo umožněno využití výpočetní síly vícejádrových platforem (multi-core a many-core). Prvním cílem této práce je tudíž akcelerace dvou deterministických algoritmů, NEH a 2-opt, přičemž bylo dosaženo zajímavých výsledků. Jiný přístup byl zvolen ve druhé části, s hlavní myšlenkou prozkoumání vlivu náhodnosti na výkon evolučního algoritmu. Za tímto účelem byl zvolen relativně nový a slibný algoritmus Discrete Artificial Bee Colony. Generátor pseudonáhodných čísel byl nahrazen několika různými chaotickými mapami, z nichž některé znatelně zlepšily výsledky algoritmu. Bylo ukázáno, že evoluční algoritmy založené na populaci často formují komplexní sítě, vzato z pohledu výměny informací mezi jednotlivými řešeními v populaci během jejího vývoje. Závěrečná část práce aplikuje toto pozorování vložením samo přizpůsobivého mechanismu založeném na analýze komplexní sítě do algoritmu ABC, který je evolučním algoritmem pro spojitou optimalizaci a zároveň základem dříve zmíněného DABC algoritmu. Efektivita několika verzí algoritmu založeném na této myšlence je dokázána na standardní sadě testovacích funkcí pro spojitou optimalizaci. Možnost rozšíření této modifikace na kombinatorické optimalizační problémy je diskutována v závěru práce.460 - Katedra informatikyvýborn

On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

A Hybrid Estimation of Distribution Algorithm for Simulation-Based Scheduling in a Stochastic Permutation Flowshop

The permutation flowshop scheduling problem (PFSP) is NP-complete and tends to be more complicated when considering stochastic uncertainties in the real-world manufacturing environments. In this paper, a two-stage simulation-based hybrid estimation of distribution algorithm (TSSB-HEDA) is presented to schedule the permutation flowshop under stochastic processing times. To deal with processing time uncertainty, TSSB-HEDA evaluates candidate solutions using a novel two-stage simulation model (TSSM). This model first adopts the regression-based meta-modelling technique to determine a number of promising candidate solutions with less computation cost, and then uses a more accurate but time-consuming simulator to evaluate the performance of these selected ones. In addition, to avoid getting trapped into premature convergence, TSSB-HEDA employs both the probabilistic model of EDA and genetic operators of genetic algorithm (GA) to generate the offspring individuals. Enlightened by the weight training process of neural networks, a self-adaptive learning mechanism (SALM) is employed to dynamically adjust the ratio of offspring individuals generated by the probabilistic model. Computational experiments on Taillard’s benchmarks show that TSSB-HEDA is competitive in terms of both solution quality and computational performance