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

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

Neural, Genetic, And Neurogenetic Approaches For Solving The 0-1 Multidimensional Knapsack Problem

The multi-dimensional knapsack problem (MDKP) is a well-studied problem in Decision Sciences. The problem’s NP-Hard nature prevents the successful application of exact procedures such as branch and bound, implicit enumeration and dynamic programming for larger problems. As a result, various approximate solution approaches, such as the relaxation approaches, heuristic and metaheuristic approaches have been developed and applied effectively to this problem. In this study, we propose a Neural approach, a Genetic Algorithms approach and a Neurogenetic approach, which is a hybrid of the Neural and the Genetic Algorithms approach. The Neural approach is essentially a problem-space based non-deterministic local-search algorithm. In the Genetic Algorithms approach we propose a new way of generating initial population. In the Neurogenetic approach, we show that the Neural and Genetic iterations, when interleaved appropriately, can complement each other and provide better solutions than either the Neural or the Genetic approach alone. Within the overall search, the Genetic approach provides diversification while the Neural provides intensification. We demonstrate the effectiveness of our proposed approaches through an empirical study performed on several sets of benchmark problems commonly used in the literature

Solving 0-1 Knapsack Problem by Greedy Degree and Expectation Efficiency

It is well known that 0-1 knapsack problem (KP01) plays an important role in both computing theory and real life application. Due to its NP-hardness, lots of impressive research work has been performed on many variants of the problem. Inspired by region partition of items, an effective hybrid algorithm based on greedy degree and expectation efficiency (GDEE) is presented in this paper. In the proposed algorithm, initially determinate items region, candidate items region and unknown items region are generated to direct the selection of items. A greedy degree model inspired by greedy strategy is devised to select some items as initially determinate region. Dynamic expectation efficiency strategy is designed and used to select some other items as candidate region, and the remaining items are regarded as unknown region. To obtain the final items to which the best profit corresponds, static expectation efficiency strategy is proposed whilst the parallel computing method is adopted to update the objective function value. Extensive numerical investigations based on a large number of instances are conducted. The proposed GDEE algorithm is evaluated against chemical reaction optimization algorithm and modified discrete shuffled frog leaping algorithm. The comparative results show that GDEE is much more effective in solving KP01 than other algorithms and that it is a promising tool for solving combinatorial optimization problems such as resource allocation and production scheduling

Improved binary artificial fish swarm algorithm for the 0–1 multidimensional knapsack problems

The 0–1 multidimensional knapsack problem (MKP) arises in many fields of optimization and is NP-hard. Several exact as well as heuristic methods exist. Recently, an artificial fish swarm algorithm has been developed in continuous global optimization. The algorithm uses a population of points in space to represent the position of fish in the school. In this paper, a binary version of the artificial fish swarm algorithm is proposed for solving the 0–1 MKP. In the proposed method, a point is represented by a binary string of 0/1 bits. Each bit of a trial point is generated by copying the corresponding bit from the current point or from some other specified point, with equal probability. Occasionally, some randomly chosen bits of a selected point are changed from 0 to 1, or 1 to 0, with an user defined probability. The infeasible solutions are made feasible by a decoding algorithm. A simple heuristic add_item is implemented to each feasible point aiming to improve the quality of that solution. A periodic reinitialization of the population greatly improves the quality of the solutions obtained by the algorithm. The proposed 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 gives a competitive performance when solving this kind of problems.Fundação para a Ciência e a Tecnologia (FCT

Heuristic-based firefly algorithm for bound constrained nonlinear binary optimization

Firefly algorithm (FA) is a metaheuristic for global optimization. In this paper,we address the practical testing of aheuristic-based FA (HBFA) for computing optimaof discrete nonlinear optimization problems,where the discrete variables are of binary type. An important issue in FA is the formulation of attractiveness of each firefly which in turn affects its movement in the search space. Dynamic updating schemes are proposed for two parameters, one from the attractiveness term and the other from the randomization term. Three simple heuristics capable of transforming real continuous variables into binary ones are analyzed. A new sigmoid ‘erf’ function is proposed. In the context of FA, three different implementations to incorporate the heuristics for binary variables into the algorithm are proposed. Based on a set of benchmark problems, a comparison is carried out with other binary dealing metaheuristics. The results demonstrate that the proposed HBFA is efficient and outperforms binary versions of differential evolution (DE) and particle swarm optimization (PSO). The HBFA also compares very favorably with angle modulated version of DE and PSO. It is shown that the variant of HBFA based on the sigmoid ‘erf’ function with ‘movements in continuous space’ is the best, both in terms of computational requirements and accuracy.Fundação para a Ciência e a Tecnologia (FCT

A Novel Discrete Global-Best Harmony Search Algorithm for Solving 0-1 Knapsack Problems

In order to better solve discrete 0-1 knapsack problems, a novel global-best harmony search algorithm with binary coding, called DGHS, is proposed. First, an initialization based on a greedy mechanism is employed to improve the initial solution quality in DGHS. Next, we present a novel improvisation process based on intuitive cognition of improvising a new harmony, in which the best harmony of harmony memory (HM) is used to guide the searching direction of evolution during the process of memory consideration, or else a harmony is randomly chosen from HM and then a discrete genetic mutation is done with some probability during the phase of pitch adjustment. Third, a two-phase repair operator is employed to repair an infeasible harmony vector and to further improve a feasible solution. Last, a new selection scheme is applied to decide whether or not a new randomly generated harmony is included into the HM. The proposed DGHS is evaluated on twenty knapsack problems with different scales and compared with other three metaheuristics from the literature. The experimental results indicate that DGHS is efficient, effective, and robust for solving difficult 0-1 knapsack problems

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