Binary artificial algae algorithm for multidimensional knapsack problems

The multidimensional knapsack problem (MKP) is a well-known NP-hard optimization problem. Various meta-heuristic methods are dedicated to solve this problem in literature. Recently a new meta-heuristic algorithm, called artificial algae algorithm (AAA), was presented, which has been successfully applied to solve various continuous optimization problems. However, due to its continuous nature, AAA cannot settle the discrete problem straightforwardly such as MKP. In view of this, this paper proposes a binary artificial algae algorithm (BAAA) to efficiently solve MKP. This algorithm is composed of discrete process, repair operators and elite local search. In discrete process, two logistic functions with different coefficients of curve are studied to achieve good discrete process results. Repair operators are performed to make the solution feasible and increase the efficiency. Finally, elite local search is introduced to improve the quality of solutions. To demonstrate the efficiency of our proposed algorithm, simulations and evaluations are carried out with total of 94 benchmark problems and compared with other bio-inspired state-of-the-art algorithms in the recent years including MBPSO, BPSOTVAC, CBPSOTVAC, GADS, bAFSA, and IbAFSA. The results show the superiority of BAAA to many compared existing algorithms

Solving large 0–1 multidimensional knapsack problems by a new simplified binary artificial fish swarm algorithm

The artificial fish swarm algorithm has recently been emerged in continuous global optimization. It uses points of a population in space to identify the position of fish in the school. Many real-world optimization problems are described by 0-1 multidimensional knapsack problems that are NP-hard. In the last decades several exact as well as heuristic methods have been proposed for solving these problems. In this paper, a new simpli ed binary version of the artificial fish swarm algorithm is presented, where a point/ fish is represented by a binary string of 0/1 bits. Trial points are created by using crossover and mutation in the different fi sh behavior that are randomly selected by using two user de ned probability values. In order to make the points feasible the presented algorithm uses a random heuristic drop item procedure followed by an add item procedure aiming to increase the profit throughout the adding of more items in the knapsack. A cyclic reinitialization of 50% of the population, and a simple local search that allows the progress of a small percentage of points towards optimality and after that refines the best point in the population greatly improve the quality of the solutions. The presented method is tested on a set of benchmark instances and a comparison with other methods available in literature is shown. The comparison shows that the proposed method can be an alternative method for solving these problems.The authors wish to thank three anonymous referees for their comments and valuable suggestions to improve the paper. The first author acknowledges Ciˆencia 2007 of FCT (Foundation for Science and Technology) Portugal for the fellowship grant C2007-UMINHO-ALGORITMI-04. Financial support from FEDER COMPETE (Operational Programme Thematic Factors of Competitiveness) and FCT under project FCOMP-01-0124-FEDER-022674 is also acknowledged

A Binary differential search algorithm for the 0-1 multidimensional knapsack problem

The multidimensional knapsack problem (MKP) is known to be NP-hard in operations research and it has a wide range of applications in engineering and management. In this study, we propose a binary differential search method to solve 0-1 MKPs where the stochastic search is guided by a Brownian motion-like random walk. Our proposed method comprises two main operations: discrete solution generation and feasible solution production. Discrete solutions are generated by integrating Brownian motion-like random search with an integer-rounding operation. However, the rounded discrete variables may violate the constraints. Thus, a feasible solution production strategy is used to maintain the feasibility of the rounded discrete variables. To demonstrate the efficiency of our proposed algorithm, we solved various 0-1 MKPs using our proposed algorithm as well as some existing meta-heuristic methods. The numerical results obtained demonstrated that our algorithm performs better than existing meta-heuristic methods. Furthermore, our algorithm has the capacity to solve large-scale 0-1 MKPs

Finding and Exploring Promising Search Space for the 0-1 Multidimensional Knapsack Problem

The 0-1 multidimensional knapsack problem(MKP) is a classical NP-hard combinatorial optimization problem. In this paper, we propose a novel heuristic algorithm simulating evolutionary computation and large neighbourhood search for the MKP. It maintains a set of solutions and abstracts information from the solution set to generate good partial assignments. To find high-quality solutions, integer programming is employed to explore the promising search space specified by the good partial assignments. Extensive experimentation with commonly used benchmark sets shows that our approach outperforms the state of the art heuristic algorithms, TPTEA and DQPSO, in solution quality. It finds new lower bound for 8 large and hard instance

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

Sine Cosine Algorithm for Optimization

This open access book serves as a compact source of information on sine cosine algorithm (SCA) and a foundation for developing and advancing SCA and its applications. SCA is an easy, user-friendly, and strong candidate in the field of metaheuristics algorithms. Despite being a relatively new metaheuristic algorithm, it has achieved widespread acceptance among researchers due to its easy implementation and robust optimization capabilities. Its effectiveness and advantages have been demonstrated in various applications ranging from machine learning, engineering design, and wireless sensor network to environmental modeling. The book provides a comprehensive account of the SCA, including details of the underlying ideas, the modified versions, various applications, and a working MATLAB code for the basic SCA

OptPlatform: metaheuristic optimisation framework for solving complex real-world problems

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonWe optimise daily, whether that is planning a round trip that visits the most attractions within a given holiday budget or just taking a train instead of driving a car in a rush hour. Many problems, just like these, are solved by individuals as part of our daily schedule, and they are effortless and straightforward. If we now scale that to many individuals with many different schedules, like a school timetable, we get to a point where it is just not feasible or practical to solve by hand. In such instances, optimisation methods are used to obtain an optimal solution. In this thesis, a practical approach to optimisation has been taken by developing an optimisation platform with all the necessary tools to be used by practitioners who are not necessarily familiar with the subject of optimisation. First, a high-performance metaheuristic optimisation framework (MOF) called OptPlatform is implemented, and the versatility and performance are evaluated across multiple benchmarks and real-world optimisation problems. Results show that, compared to competing MOFs, the OptPlatform outperforms in both the solution quality and computation time. Second, the most suitable hardware platform for OptPlatform is determined by an in-depth analysis of Ant Colony Optimisation scaling across CPU, GPU and enterprise Xeon Phi. Contrary to the common benchmark problems used in the literature, the supply chain problem solved could not scale on GPUs. Third, a variety of metaheuristics are implemented into OptPlatform. Including, a new metaheuristic based on Imperialist Competitive Algorithm (ICA), called ICA with Independence and Constrained Assimilation (ICAwICA) is proposed. The ICAwICA was compared against two different types of benchmark problems, and results show the versatile application of the algorithm, matching and in some cases outperforming the custom-tuned approaches. Finally, essential MOF features like automatic algorithm selection and tuning, lacking on existing frameworks, are implemented in OptPlatform. Two novel approaches are proposed and compared to existing methods. Results indicate the superiority of the implemented tuning algorithms within constrained tuning budget environment

Evolutionary Computation 2020

Intelligent optimization is based on the mechanism of computational intelligence to refine a suitable feature model, design an effective optimization algorithm, and then to obtain an optimal or satisfactory solution to a complex problem. Intelligent algorithms are key tools to ensure global optimization quality, fast optimization efficiency and robust optimization performance. Intelligent optimization algorithms have been studied by many researchers, leading to improvements in the performance of algorithms such as the evolutionary algorithm, whale optimization algorithm, differential evolution algorithm, and particle swarm optimization. Studies in this arena have also resulted in breakthroughs in solving complex problems including the green shop scheduling problem, the severe nonlinear problem in one-dimensional geodesic electromagnetic inversion, error and bug finding problem in software, the 0-1 backpack problem, traveler problem, and logistics distribution center siting problem. The editors are confident that this book can open a new avenue for further improvement and discoveries in the area of intelligent algorithms. The book is a valuable resource for researchers interested in understanding the principles and design of intelligent algorithms

New variants of variable neighbourhood search for 0-1 mixed integer programming and clustering

Many real-world optimisation problems are discrete in nature. Although recent rapid developments in computer technologies are steadily increasing the speed of computations, the size of an instance of a hard discrete optimisation problem solvable in prescribed time does not increase linearly with the computer speed. This calls for the development of new solution methodologies for solving larger instances in shorter time. Furthermore, large instances of discrete optimisation problems are normally impossible to solve to optimality within a reasonable computational time/space and can only be tackled with a heuristic approach. In this thesis the development of so called matheuristics, the heuristics which are based on the mathematical formulation of the problem, is studied and employed within the variable neighbourhood search framework. Some new variants of the variable neighbourhood searchmetaheuristic itself are suggested, which naturally emerge from exploiting the information from the mathematical programming formulation of the problem. However, those variants may also be applied to problems described by the combinatorial formulation. A unifying perspective on modern advances in local search-based metaheuristics, a so called hyper-reactive approach, is also proposed. Two NP-hard discrete optimisation problems are considered: 0-1 mixed integer programming and clustering with application to colour image quantisation. Several new heuristics for 0-1 mixed integer programming problem are developed, based on the principle of variable neighbourhood search. One set of proposed heuristics consists of improvement heuristics, which attempt to find high-quality near-optimal solutions starting from a given feasible solution. Another set consists of constructive heuristics, which attempt to find initial feasible solutions for 0-1 mixed integer programs. Finally, some variable neighbourhood search based clustering techniques are applied for solving the colour image quantisation problem. All new methods presented are compared to other algorithms recommended in literature and a comprehensive performance analysis is provided. Computational results show that the methods proposed either outperform the existing state-of-the-art methods for the problems observed, or provide comparable results. The theory and algorithms presented in this thesis indicate that hybridisation of the CPLEX MIP solver and the VNS metaheuristic can be very effective for solving large instances of the 0-1 mixed integer programming problem. More generally, the results presented in this thesis suggest that hybridisation of exact (commercial) integer programming solvers and some metaheuristic methods is of high interest and such combinations deserve further practical and theoretical investigation. Results also show that VNS can be successfully applied to solving a colour image quantisation problem.EThOS - Electronic Theses Online ServiceMathematical Institute, Serbian Academy of Sciences and ArtsGBUnited Kingdo

Crossover control in selection hyper-heuristics: case studies using MKP and HyFlex

Hyper-heuristics are a class of high-level search methodologies which operate over a search space of heuristics rather than a search space of solutions. Hyper-heuristic research has set out to develop methods which are more general than traditional search and optimisation techniques. In recent years, focus has shifted considerably towards cross-domain heuristic search. The intention is to develop methods which are able to deliver an acceptable level of performance over a variety of different problem domains, given a set of low-level heuristics to work with. This thesis presents a body of work investigating the use of selection hyper-heuristics in a number of different problem domains. Specifically the use of crossover operators, prevalent in many evolutionary algorithms, is explored within the context of single-point search hyper-heuristics. A number of traditional selection hyper-heuristics are applied to instances of a well-known NP-hard combinatorial optimisation problem, the multidimensional knapsack problem. This domain is chosen as a benchmark for the variety of existing problem instances and solution methods available. The results suggest that selection hyper-heuristics are a viable method to solve some instances of this problem domain. Following this, a framework is defined to describe the conceptual level at which crossover low-level heuristics are managed in single-point selection hyper-heuristics. HyFlex is an existing software framework which supports the design of heuristic search methods over multiple problem domains, i.e. cross-domain optimisation. A traditional heuristic selection mechanism is modified in order to improve results in the context of cross-domain optimisation. Finally the effect of crossover use in cross-domain optimisation is explored