A Weight-coded Evolutionary Algorithm for the Multidimensional Knapsack Problem

A revised weight-coded evolutionary algorithm (RWCEA) is proposed for solving multidimensional knapsack problems. This RWCEA uses a new decoding method and incorporates a heuristic method in initialization. Computational results show that the RWCEA performs better than a weight-coded evolutionary algorithm proposed by Raidl (1999) and to some existing benchmarks, it can yield better results than the ones reported in the OR-library.Comment: Submitted to Applied Mathematics and Computation on April 8, 201

Optimal QoS aware multiple paths web service composition using heuristic algorithms and data mining techniques

The goal of QoS-aware service composition is to generate optimal composite services that satisfy the QoS requirements defined by clients. However, when compositions contain more than one execution path (i.e., multiple path's compositions), it is difficult to generate a composite service that simultaneously optimizes all the execution paths involved in the composite service at the same time while meeting the QoS requirements. This issue brings us to the challenge of solving the QoS-aware service composition problem, so called an optimization problem. A further research challenge is the determination of the QoS characteristics that can be considered as selection criteria. In this thesis, a smart QoS-aware service composition approach is proposed. The aim is to solve the above-mentioned problems via an optimization mechanism based upon the combination between runtime path prediction method and heuristic algorithms. This mechanism is performed in two steps. First, the runtime path prediction method predicts, at runtime, and just before the actual composition, execution, the execution path that will potentially be executed. Second, both the constructive procedure (CP) and the complementary procedure (CCP) heuristic algorithms computed the optimization considering only the execution path that has been predicted by the runtime path prediction method for criteria selection, eight QoS characteristics are suggested after investigating related works on the area of web service and web service composition. Furthermore, prioritizing the selected QoS criteria is suggested in order to assist clients when choosing the right criteria. Experiments via WEKA tool and simulation prototype were conducted to evaluate the methods used. For the runtime path prediction method, the results showed that the path prediction method achieved promising prediction accuracy, and the number of paths involved in the prediction did not affect the accuracy. For the optimization mechanism, the evaluation was conducted by comparing the mechanism with relevant optimization techniques. The simulation results showed that the proposed optimization mechanism outperforms the relevant optimization techniques by (1) generating the highest overall QoS ratio solutions, (2) consuming the smallest computation time, and (3) producing the lowest percentage of constraints violated number

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 ants’ 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

Indicator Based Ant Colony Optimization for Multi-objective Knapsack Problem

AbstractThe use of metaheuristics to solve multi-objective optimization problems (MOP) is a very active research topic. Ant Colony Optimization (ACO) has received a growing interest in the last years for such problems. Many algorithms have been proposed in the literature to solve different MOP. This paper presents an indicator-based ant colony optimization algorithm called IBACO for the multi-objective knapsack problem (MOKP). The IBACO algorithm proposes a new idea that uses binary quality indicators to guide the search of artificial ants. These indicators were initially used by Zitzler and Künzli in the selection process of their evolutionary algorithm IBEA. In this paper, we use the indicator optimization principle to reinforce the best solutions by rewarding pheromone trails. We carry out a set of experiments on MOKP benchmark instances by applying the two binary indicators: epsilon indicator and hypervolume indicator. The comparison of the proposed algorithm with IBEA, ACO and other state-of-the-art evolutionary algorithms shows that IBACO is significantly better on most instances

Application of Pigeon Inspired Optimization for Multidimensional Knapsack Problem

The multidimensional knapsack problem (MKP) is a generalization of the classical knapsack problem, a problem for allocating a resource by selecting a subset of objects that seek for the highest profit while satisfying the capacity of knapsack constraint. The MKP have many practical applications in different areas and classified as a NP-hard problem. An exact method like branch and bound and dynamic programming can solve the problem, but its time computation increases exponentially with the size of the problem. Whereas some approximation method has been developed to produce a near-optimal solution within reasonable computational times. In this paper a pigeon inspired optimization (PIO) is proposed for solving MKP. PIO is one of the metaheuristic algorithms that is classified in population-based swarm intelligent that is developed based on the behavior of the pigeon to find its home although it had gone far away from it home. In this paper, PIO implementation to solve MKP is applied to two different characteristic cases in total 10 cases. The result of the implementation of the two-best combination of parameter values for 10 cases compared to particle swarm optimization, intelligent water drop algorithm and the genetic algorithm gives satisfactory results

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 (“efficient”) 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 “quickly” (reasonable run-times), with “high” probability, provable “good” 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

Submodular memetic approximation for multiobjective parallel test paper generation

Parallel test paper generation is a biobjective distributed resource optimization problem, which aims to generate multiple similarly optimal test papers automatically according to multiple user-specified assessment criteria. Generating high-quality parallel test papers is challenging due to its NP-hardness in both of the collective objective functions. In this paper, we propose a submodular memetic approximation algorithm for solving this problem. The proposed algorithm is an adaptive memetic algorithm (MA), which exploits the submodular property of the collective objective functions to design greedy-based approximation algorithms for enhancing steps of the multiobjective MA. Synergizing the intensification of submodular local search mechanism with the diversification of the population-based submodular crossover operator, our algorithm can jointly optimize the total quality maximization objective and the fairness quality maximization objective. Our MA can achieve provable near-optimal solutions in a huge search space of large datasets in efficient polynomial runtime. Performance results on various datasets have shown that our algorithm has drastically outperformed the current techniques in terms of paper quality and runtime efficiency

An Expandable Machine Learning-Optimization Framework to Sequential Decision-Making

We present an integrated prediction-optimization (PredOpt) framework to efficiently solve sequential decision-making problems by predicting the values of binary decision variables in an optimal solution. We address the key issues of sequential dependence, infeasibility, and generalization in machine learning (ML) to make predictions for optimal solutions to combinatorial problems. The sequential nature of the combinatorial optimization problems considered is captured with recurrent neural networks and a sliding-attention window. We integrate an attention-based encoder-decoder neural network architecture with an infeasibility-elimination and generalization framework to learn high-quality feasible solutions to time-dependent optimization problems. In this framework, the required level of predictions is optimized to eliminate the infeasibility of the ML predictions. These predictions are then fixed in mixed-integer programming (MIP) problems to solve them quickly with the aid of a commercial solver. We demonstrate our approach to tackling the two well-known dynamic NP-Hard optimization problems: multi-item capacitated lot-sizing (MCLSP) and multi-dimensional knapsack (MSMK). Our results show that models trained on shorter and smaller-dimensional instances can be successfully used to predict longer and larger-dimensional problems. The solution time can be reduced by three orders of magnitude with an average optimality gap below 0.1%. We compare PredOpt with various specially designed heuristics and show that our framework outperforms them. PredOpt can be advantageous for solving dynamic MIP problems that need to be solved instantly and repetitively