664 research outputs found
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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (âefficientâ) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find âquicklyâ (reasonable run-times), with âhighâ probability, provable âgoodâ solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
Applying the big bang-big crunch metaheuristic to large-sized operational problems
In this study, we present an investigation of comparing the capability of a big bang-big crunch metaheuristic (BBBC) for managing operational problems including combinatorial optimization problems. The BBBC is a product of the evolution theory of the universe in physics and astronomy. Two main phases of BBBC are the big bang and the big crunch. The big bang phase involves the creation of a population of random initial solutions, while in the big crunch phase these solutions are shrunk into one elite solution exhibited by a mass center. This study looks into the BBBCâs effectiveness in assignment and scheduling problems. Where it was enhanced by incorporating an elite pool of diverse and high quality solutions; a simple descent heuristic as a local search method; implicit recombination; Euclidean distance; dynamic population size; and elitism strategies. Those strategies provide a balanced search of diverse and good quality population. The investigation is conducted by comparing the proposed BBBC with similar metaheuristics. The BBBC is tested on three different classes of combinatorial optimization problems; namely, quadratic assignment, bin packing, and job shop scheduling problems. Where the incorporated strategies have a greater impact on the BBBC's performance. Experiments showed that the BBBC maintains a good balance between diversity and quality which produces high-quality solutions, and outperforms other identical metaheuristics (e.g. swarm intelligence and evolutionary algorithms) reported in the literature
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HEDCOS: High Efficiency Dynamic Combinatorial Optimization System using Ant Colony Optimization algorithm
This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonDynamic combinatorial optimization is gaining popularity among industrial practitioners due to the ever-increasing scale of their optimization problems and efforts to solve them to remain competitive. Larger optimization problems are not only more computationally intense to optimize but also have more uncertainty within problem inputs. If some aspects of the problem are subject to dynamic change, it becomes a Dynamic Optimization Problem (DOP).
In this thesis, a High Efficiency Dynamic Combinatorial Optimization System is built to solve challenging DOPs with high-quality solutions. The system is created using Ant Colony Optimization (ACO) baseline algorithm with three novel developments.
First, introduced an extension method for ACO algorithm called Dynamic Impact. Dynamic Impact is designed to improve convergence and solution quality by solving challenging optimization problems with a non-linear relationship between resource consumption and fitness. This proposed method is tested against the real-world Microchip Manufacturing Plant Production Floor Optimization (MMPPFO) problem and the theoretical benchmark Multidimensional Knapsack Problem (MKP).
Second, a non-stochastic dataset generation method was introduced to solve the dynamic optimization research replicability problem. This method uses a static benchmark dataset as a starting point and source of entropy to generate a sequence of dynamic states. Then using this method, 1405 Dynamic Multidimensional Knapsack Problem (DMKP) benchmark datasets were generated and published using famous static MKP benchmark instances as the initial state.
Third, introduced a nature-inspired discrete dynamic optimization strategy for ACO by modelling real-world antsâ symbiotic relationship with aphids. ACO with Aphids strategy is designed to solve discrete domain DOPs with event-triggered discrete dynamism. The strategy improved inter-state convergence by allowing better solution recovery after dynamic environment changes. Aphids mediate the information from previous dynamic optimization states to maximize initial results performance and minimize the impact on convergence speed. This strategy is tested for DMKP and against identical ACO implementations using Full-Restart and Pheromone-Sharing strategies, with all other variables isolated.
Overall, Dynamic Impact and ACO with Aphids developments are compounding. Using Dynamic Impact on single objective optimization of MMPPFO, the fitness value was improved by 33.2% over the ACO algorithm without Dynamic Impact. MKP benchmark instances of low complexity have been solved to a 100% success rate even when a high degree of solution sparseness is observed, and large complexity instances have shown the average gap improved by 4.26 times. ACO with Aphids has also demonstrated superior performance over the Pheromone-Sharing strategy in every test on average gap reduced by 29.2% for a total compounded dynamic optimization performance improvement of 6.02 times. Also, ACO with Aphids has outperformed the Full-Restart strategy for large datasets groups, and the overall average gap is reduced by 52.5% for a total compounded dynamic optimization performance improvement of 8.99 times
A WOA-based optimization approach for task scheduling in cloud Computing systems
Task scheduling in cloud computing can directly
affect the resource usage and operational cost of a system. To
improve the efficiency of task executions in a cloud, various
metaheuristic algorithms, as well as their variations, have been
proposed to optimize the scheduling. In this work, for the
first time, we apply the latest metaheuristics WOA (the whale
optimization algorithm) for cloud task scheduling with a multiobjective optimization model, aiming at improving the performance of a cloud system with given computing resources. On that
basis, we propose an advanced approach called IWC (Improved
WOA for Cloud task scheduling) to further improve the optimal
solution search capability of the WOA-based method. We present
the detailed implementation of IWC and our simulation-based
experiments show that the proposed IWC has better convergence
speed and accuracy in searching for the optimal task scheduling
plans, compared to the current metaheuristic algorithms. Moreover, it can also achieve better performance on system resource
utilization, in the presence of both small and large-scale tasks
Reinforcement Learning-assisted Evolutionary Algorithm: A Survey and Research Opportunities
Evolutionary algorithms (EA), a class of stochastic search methods based on
the principles of natural evolution, have received widespread acclaim for their
exceptional performance in various real-world optimization problems. While
researchers worldwide have proposed a wide variety of EAs, certain limitations
remain, such as slow convergence speed and poor generalization capabilities.
Consequently, numerous scholars actively explore improvements to algorithmic
structures, operators, search patterns, etc., to enhance their optimization
performance. Reinforcement learning (RL) integrated as a component in the EA
framework has demonstrated superior performance in recent years. This paper
presents a comprehensive survey on integrating reinforcement learning into the
evolutionary algorithm, referred to as reinforcement learning-assisted
evolutionary algorithm (RL-EA). We begin with the conceptual outlines of
reinforcement learning and the evolutionary algorithm. We then provide a
taxonomy of RL-EA. Subsequently, we discuss the RL-EA integration method, the
RL-assisted strategy adopted by RL-EA, and its applications according to the
existing literature. The RL-assisted procedure is divided according to the
implemented functions including solution generation, learnable objective
function, algorithm/operator/sub-population selection, parameter adaptation,
and other strategies. Finally, we analyze potential directions for future
research. This survey serves as a rich resource for researchers interested in
RL-EA as it overviews the current state-of-the-art and highlights the
associated challenges. By leveraging this survey, readers can swiftly gain
insights into RL-EA to develop efficient algorithms, thereby fostering further
advancements in this emerging field.Comment: 26 pages, 16 figure
Hybrid ant colony system algorithm for static and dynamic job scheduling in grid computing
Grid computing is a distributed system with heterogeneous infrastructures. Resource
management system (RMS) is one of the most important components which has great influence on the grid computing performance. The main part of RMS is the scheduler algorithm which has the responsibility to map submitted tasks to available resources. The complexity of scheduling problem is considered as a nondeterministic polynomial complete (NP-complete) problem and therefore, an intelligent algorithm is required to achieve better scheduling solution. One of the prominent intelligent algorithms is ant colony system (ACS) which is implemented widely to solve various types of scheduling problems. However, ACS suffers from stagnation problem in medium and large size grid computing system. ACS is based on exploitation and exploration
mechanisms where the exploitation is sufficient but the exploration has a deficiency. The exploration in ACS is based on a random approach without any strategy. This study proposed four hybrid algorithms between ACS, Genetic Algorithm (GA), and Tabu Search (TS) algorithms to enhance the ACS performance. The algorithms are ACS(GA), ACS+GA, ACS(TS), and ACS+TS. These proposed hybrid algorithms
will enhance ACS in terms of exploration mechanism and solution refinement by
implementing low and high levels hybridization of ACS, GA, and TS algorithms. The proposed algorithms were evaluated against twelve metaheuristic algorithms in static (expected time to compute model) and dynamic (distribution pattern) grid computing
environments. A simulator called ExSim was developed to mimic the static and dynamic nature of the grid computing. Experimental results show that the proposed algorithms outperform ACS in terms of best makespan values. Performance of ACS(GA), ACS+GA, ACS(TS), and ACS+TS are better than ACS by 0.35%, 2.03%, 4.65% and 6.99% respectively for static environment. For dynamic environment,
performance of ACS(GA), ACS+GA, ACS+TS, and ACS(TS) are better than ACS by 0.01%, 0.56%, 1.16%, and 1.26% respectively. The proposed algorithms can be used to schedule tasks in grid computing with better performance in terms of makespan
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Metaheuristic approach for solving scheduling and financial derivative problems
This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonThe objective of this thesis is to implement metaheuristic approaches to solve di erent
types of combinatorial problems. The thesis is focused on neighborhood heuristic optimisation
techniques such as Variable Neighborhood Search (VNS) and Ant Colony Optimisation
(ACO) algorithms. The thesis will focus on two diverse combinatorial problems.
A job shop scheduling problem, and a nancial derivative matching problem. The rst
is a NP-hard 2-stage assembly problem, where we will be focussing on the rst stage. It
consists of sequencing a set of jobs having multiple components to be processed. Each job
has to be worked on independently on a speci c machine. We consider these jobs to form
a vector of tasks. Our objective is to schedule jobs on the particular machines in order
to minimise the completion time before the second stage starts. In this thesis, we have
constructed a new hybrid metaheuristic approach to solve this unique job shop scheduling
problem.
The second problem has arisen in the nancial sector, where the nancial regulators collects
transaction data across regulated assets classes. Our focus is to identify any unhedged
derivative, Contract for Di erence (CFD), with its corresponding underlying asset that
has been reported to the corresponding component authorities. The underlying asset
and CFD transaction contain di erent variables, like volume and price. Therefore, we are
looking for a combination of underlying asset variables that may hedge the equivalent CFD
variables. Our aim is to identify unhedged or unmatched CFD's with their corresponding
underlying asset. This problem closely relates to the goal programming problem with
variable parameters. We have developed two new local search methods and embedded the
newly constructed local search methods with basic VNS, to attain a new modi ed variant
of the VNS algorithm. We then used these newly constructed VNS variants to solve this
nancial matching problem.
In tackling the Vector Job Scheduling problem, we developed a new hybrid optimisation
heuristic algorithm by combining VNS and ACO. We then compared the results of this hybrid algorithm with VNS and ACO on their own. We found that the hybrid algorithm
performance is better than the other two independent heuristic algorithms. In tackling
the nancial derivative problem, our objective is to match the CFD trades with their
corresponding underlying equity trades. Our goal is to identify the mismatched CFD
trades while optimising the search process. We have developed two new local search
techniques and we have implemented a VNS algorithm with the newly developed local
search techniques to attain better solutions
The design and applications of the african buffalo algorithm for general optimization problems
Optimization, basically, is the economics of science. It is concerned with the need to maximize profit and minimize cost in terms of time and resources needed to execute a given project in any field of human endeavor. There have been several scientific investigations in the past several decades on discovering effective and efficient algorithms to providing solutions to the optimization needs of mankind leading to the development
of deterministic algorithms that provide exact solutions to optimization problems. In the past five decades, however, the attention of scientists has shifted from the deterministic algorithms to the stochastic ones since the latter have proven to be more robust and efficient, even though they do not guarantee exact solutions. Some of the successfully designed stochastic algorithms include Simulated Annealing, Genetic Algorithm, Ant Colony Optimization, Particle Swarm Optimization, Bee Colony Optimization, Artificial Bee Colony Optimization, Firefly Optimization etc. A critical look at these âefficientâ
stochastic algorithms reveals the need for improvements in the areas of effectiveness, the number of several parameters used, premature convergence, ability to search diverse landscapes and complex implementation strategies. The African Buffalo Optimization (ABO), which is inspired by the herd management, communication and successful
grazing cultures of the African buffalos, is designed to attempt solutions to the observed shortcomings of the existing stochastic optimization algorithms. Through several experimental procedures, the ABO was used to successfully solve benchmark optimization problems in mono-modal and multimodal, constrained and unconstrained,
separable and non-separable search landscapes with competitive outcomes. Moreover, the ABO algorithm was applied to solve over 100 out of the 118 benchmark symmetric and all the asymmetric travelling salesmanâs problems available in TSPLIB95. Based on the
successful experimentation with the novel algorithm, it is safe to conclude that the ABO is a worthy contribution to the scientific literature
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