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A Binary Butterfly Optimization Algorithm for the Multidimensional Knapsack Problem
... Shahbandegan and Naderi [58] modified the BOA searching behaviour to deal with a binary multidimensional knapsack optimization problem. The binary BOA was proposed in six versions using three S-shaped and three V-shaped transfer functions to determine the most effective version. ...
... The BOA effectiveness and efficiency allow it to flourish when utilized for tackling different real-world applications. The algorithm tackled a wide range of problems: FS [22,31,34,57,60,60], numerical optimization [33,37,64,70,71,75], PV models [23,47], rarly search blindness [24], energy consumption [25], image segmentation [72], scheduling [26,59], multi disease prediction [73], medical data classification [27], optimal capacity of gas production [76], sentiment analysis [28], roller burnishing process parameters [52], pilot contamination in massive systems for 5G communication networks [55] , optimum shape design [46], combined cooling heating and power generation system [62], household CO2 emissions mitigation strategies [48], solving elliptic partial differential equations [66], reliability optimization problems [65], suspended sediment prediction [42], maximum power point tracking [43,68], engineering problems [29,61,63,67], green vehicle routing problem [78], high-dimensional optimization problems [74], model predictive control [50], crowd behaviour recognition [69], structural damage detection [77], anomaly-based intrusion detection [56], multidimensional knapsack problem [58], amended adaptive design [53], multilayer radar absorbing composite material [54], economic load dispatch problem [51], optimization of artificial neural networks [49], robustness evaluation of a control system [44], mechanical design optimization problems [35], node localization in wireless sensor networks [45], and global optimization [36,55]. The list of the BOA versions used to tackle optimization problems is presented in Table 2. ...
The butterfly optimization algorithm (BOA) is a recent successful metaheuristic swarm-based optimization algorithm. The BOA has attracted scholars’ attention due to its extraordinary features. Such as the few adaptive parameters to handle and the high balance between exploration and exploitation. Accordingly, the BOA has been extensively adapted for various optimization problems in different domains in a short period. Therefore, this paper reviews and summarizes the recently published studies that utilized the BOA for optimization problems. Initially, introductory information about the BOA is presented to illustrate the essential foundation and its relevant optimization concepts. In addition, the BOA inspiration and its mathematical model are provided with an illustrative example to prove its high capabilities. Subsequently, all reviewed studies are classified into three main classes based on the adaptation form, including original, modified, and hybridized. The main BOA applications are also thoroughly explained. Furthermore, the BOA advantages and drawbacks in dealing with optimization problems are analyzed. Finally, the paper is summarized in conclusion with the future directions that can be investigated further.
... Dana et al. [17] designed a hybrid BOA (HBOA) by adding Tabu Search (TS) algorithm and local search swap and flip strategies with BOA to minimize the distribution costs on green vehicle routing problem. In [18], the authors proposed six binary versions of BOA using three S-shaped and three V-shaped transfer functions and this binary BOA (BBOA) was applied to solve the 0-1 multi-dimensional knapsack problem. ...
... In Levy flights, the step sizes are too aggressive; they may generate new solutions often outside the domain or on the boundary. For that reason, 0.001 multiplier is used in Eq. (18) to reduce the step size. ...
Though the Butterfly Bptimization Algorithm (BOA) has already proved its effectiveness as a robust optimization algorithm, it has certain disadvantages. So, a new variant of BOA, namely mLBOA, is proposed here to improve its performance. The proposed algorithm employs a self-adaptive parameter setting, Lagrange interpolation formula, and a new local search strategy embedded with Levy flight search to enhance its searching ability to make a better trade-off between exploration and exploitation. Also, the fragrance generation scheme of BOA is modified, which leads for exploring the domain effectively for better searching. To evaluate the performance, it has been applied to solve the IEEE CEC 2017 benchmark suite. The results have been compared to that of six state-of-the-art algorithms and five BOA variants. Moreover, various statistical tests, such as the Friedman rank test, Wilcoxon rank test, convergence analysis, and complexity analysis, have been conducted to justify the rank, significance, and complexity of the proposed mLBOA. Finally, the mLBOA has been applied to solve three real-world engineering design problems. From all the analyses, it has been found that the proposed mLBOA is a competitive algorithm compared to other popular state-of-the-art algorithms and BOA variants.
Real-world problems are complex as they are multidimensional and multimodal in nature that encourages computer scientists to develop better and efficient problem-solving methods. Nature-inspired metaheuristics have shown better performances than that of traditional approaches. Till date, researchers have presented and experimented with various nature-inspired metaheuristic algorithms to handle various search problems. This paper introduces a new nature-inspired algorithm, namely butterfly optimization algorithm (BOA) that mimics food search and mating behavior of butterflies, to solve global optimization problems. The framework is mainly based on the foraging strategy of butterflies, which utilize their sense of smell to determine the location of nectar or mating partner. In this paper, the proposed algorithm is tested and validated on a set of 30 benchmark test functions and its performance is compared with other metaheuristic algorithms. BOA is also employed to solve three classical engineering problems (spring design, welded beam design, and gear train design). Results indicate that the proposed BOA is more efficient than other metaheuristic algorithms.
In recent years, due to their straightforward structure and efficiency, the chaos-based cryptographic algorithms have become a good candidate for image encryption. However, they still suffer from many weaknesses, such as insensitivity to the plain image, weak key streams, small key space, non-resistance to some attacks and failure to meet some security criteria. For this purpose in this paper, a novel hybrid image encryption algorithm named Hyper-chaotic Feeded GA (HFGA) is proposed to fill the gaps in two stages; initial encryption by using a hyper-chaotic system, and then outputs reinforcement by employing a customized Genetic Algorithm (GA). By applying an innovative technique, called gene-labelling, the proposed algorithm not only optimizes the preliminary encrypted images in terms of security criteria but also allows the legal receiver to easily and securely decrypt the optimized cipher image. In fact, in the first stage, besides unpredictable random sequences generated by a hyper-chaotic system, a new sensitive diffusion function is proposed which makes the algorithm resistant to differential attacks. In the second stage, the generated cipher images, which are labeled in a special way, will be used as the initial population of a GA which enhances randomness of the cipher images. The results of several experiments and statistical analysis show that the proposed image encryption scheme provides an efficient and secure way for fast image encrypting as well as providing robustness against some well-known statistical attacks.
Any complex application can be realized as a graph of dependent tasks, and scheduling these tasks onto a limited number of computational resources while satisfying their dependencies is a well-known NP-complete optimization problem. For microprocessor systems, several algorithms have been proposed that can efficiently find suboptimal schedules. A solution for dynamically reconfigurable hardware (DRHW), however, is more complicated, as the time and complexity of reconfiguration has to be scheduled as well. The reconfiguration overhead in these systems is significant, and quickly becomes a crucial factor in real-world applications. In this paper, a meta-heuristic method known as Feasibility Assured TSP-likened Scheduling (FATS) is proposed in which the scheduling problem is translated into a construction graph, similar to Travelling Sales Person (TSP) problem, such that it would be able to benefit from the advantages of Ant Colony Optimization (ACO) algorithm. Moreover, by exploiting such a construction graph, precedence constraints and system limitations are satisfied beforehand, the feasibility of solutions is assured, while avoiding the costly solution repair operations. To demonstrate the performance of the proposed method, it was tested on several synthetic and real-world benchmark task graphs and the results were compared with a selection of classic and state-of-the-art algorithms. A comprehensive set of experiments was performed to evaluate the method in terms of efficiency, execution time, scalability and reliability. In brief, the results of experiments on benchmarks showed that on average FATS outperforms HPSO-GA and BGA by 8.4 % and 12.2 % respectively in terms of the quality of the solutions, and its run-time is far less than the state-of-the-art algorithms. Also, on synthetic graphs the makespan improvements of the solutions generated by FATS and GA over the List scheduler are on average 11.2 % and 6.8 % better respectively; and from the execution-time point of view, our method is 27.37 % faster than GA. Moreover, the results confirm that the proposed method is scalable for large task graphs and its reliability is superior to other compared algorithms.
In this paper, a routing algorithm is proposed for access selection in a network to find the optimal paths among intermediate nodes with multiple interfaces. Markov Decision Process is applied in each node to find optimal policy and select proper paths to the best access point in a dynamic environment. A reward function is defined as environment feedback to optimize and adapt routing behavior of nodes based on the local information. Selection metrics in each node are interface load, link quality and destination condition. It is shown, by using the proposed algorithm, there are better management in the node which decreases interference and collision and selects links with better quality toward the best possible destination. The performance of the method is exemplified and it is shown how the throughput and average delay of the network with more interface in its nodes, improved while packet loss degrades. As an example a two-interface and a one-interface network are studied. It is shown when network load is increased, interface management will improve the throughput, in the network with two-interface nodes. Also, by considering the link quality factor in the reward function, packet dropping becomes less but average delay increases.
Multidimensional knapsack problem (MKP) is known to be a NP-hard problem, more specifically a NP-complete problem, which cannot be resolved in polynomial time up to now. MKP can be applicable in many management, industry and engineering fields, such as cargo loading, capital budgeting and resource allocation, etc. In this article, using a combinational permutation constructed by the convex combinatorial value of both the pseudo-utility ratios of MKP and the optimal solution of relaxed LP, we present a new hybrid combinatorial genetic algorithm (HCGA) to address multidimensional knapsack problems. Comparing to Chu's GA (J Heuristics 4:63-86, 1998), empirical results show that our new heuristic algorithm HCGA obtains better solutions over 270 standard test problem instances.
We study the multidimensional knapsack problem, present some theoretical and empirical results about its structure, and evaluate dierent Integer Linear Programming (ILP) based, metaheuristic, and collaborative approaches for it. We start by considering the distances between optimal solutions to the LP-relaxation and the original problem and then introduce a new core concept for the MKP, which we study extensively. The empirical analysis is then used to develop new concepts for solving the MKP using ILP-based and memetic algorithms. Dierent collaborative combinations of the presented methods are discussed and evaluated. Further computational experiments with longer run-times are also performed in order to compare the solutions of our approaches to the best known solutions of another so far leading approach for common MKP benchmark instances. The extensive computational experiments show the eectiveness of the proposed methods, which yield highly competitive results in significantly shorter run-times than previously described approaches.
Optimization algorithms have been rapidly promoted and applied in many engineering fields, such as system control, artificial intelligence, pattern recognition, computer engineering, etc.; achieving optimization in the production process has an important role in improving production efficiency and efficiency and saving resources. At the same time, the theoretical research of optimization methods also plays an important role in improving the performance of the algorithm, widening the application field of the algorithm, and improving the algorithm system. Based on the above background, the purpose of this paper is to apply the intelligent optimization algorithm based on grid technology platform to research. This article first briefly introduced the grid computing platform and optimization algorithms; then, through the two application examples of the TSP problem and the Hammerstein model recognition problem, the common intelligent optimization algorithms are introduced in detail. Introduction: Algorithm description, algorithm implementation, case analysis, algorithm evaluation and algorithm improvement. This paper also applies the GDE algorithm to solve the reactive power optimization problems of the IEEE14 node, IEEE30 node and IEEE57 node. The experimental results show that the minimum network loss of the three systems obtained by the GDE algorithm is 12.348161, 16.348152, and 23.645213, indicating that the GDE algorithm is an effective algorithm for solving the reactive power optimization problem of power systems.
With the increasing demand of users for high-speed, low-delay and high-reliability services in connected vehicles network, wireless networks with communication, caching and computing convergence become the trend of network development in the future. To improve the quality of services of vehicles network, we propose a virtualized framework for mobile vehicle services, which using a learning-based resource allocation scheme. The dynamic change processes are modeled as Markov chains without making assumptions about the optimization goal and reducing the complexity of resource allocation computing. A high performance asynchronous advantage actor–critic learning algorithm is proposed to solve the complex dynamic resource allocation problem. Base on software-defined networking and information-centric networking, the method can dynamic orchestration of computing and communication resources to enhance the performance of virtual wireless networks. Simulation results verify that the proposed scheme can converge at a fast speed and improve the network operator’s total rewards.
Feature selection is an important data preprocessing method. This paper studies a new multi-objective feature selection approach, called the Binary Differential Evolution with self-learning (MOFS-BDE). Three new operators are proposed and embedded into the MOFS-BDE to improve its performance. The novel binary mutation operator based on probability difference can guide individuals to rapidly locate potentially optimal areas, the developed One-bit Purifying Search operator (OPS) can improve the self-learning capability of the elite individuals located in the optimal areas, and the efficient non-dominated sorting operator with crowding distance can reduce the computational complexity of the selection operator in the differential evolution. Experimental results on a series of public datasets show that the effective combination of the binary mutation and OPS makes our MOFS-BDE achieve a trade-off between local exploitation and global exploration. The proposed method is competitive in comparison with some representative genetic algorithm-, particle swarm-, differential evolution-, and artificial bee colony-based feature selection algorithms.
Grey Wolf Optimizer (GWO) is a new meta-heuristic that mimics the leadership hierarchy and group hunting mechanism of grey wolves in nature. A binary version is developed to tackle the multidimensional knapsack problem which has an extensive engineering background. The proposed binary grey wolf optimizer integrates some important features including an initial elite population generator, a pseudo-utility-based quick repair operator, a new evolutionary mechanism with a differentiated position updating strategy. The proposed algorithm takes full advantage of the knowledge of the problem to be solved and highlights the distinctive feature of the optimizer in the family of evolutionary algorithm. Experimental results statistically show the effectiveness of the new optimizer and the superiority of the proposed algorithm in solving the multidimensional knapsack problem, especially the large-scale problem.
This work proposes a new Modified Multi-Verse Optimization (MMVO) algorithm for solving the 0-1 knapsack (0-1 KP) and multidimensional knapsack problems (MKP). MMVO incorporates a two-step repair strategy for handling constraints. In addition, a barrier function is employed for assigning negative values to the infeasible solutions so that their fitness cannot outperform the fitness of the feasible ones. MMVO avoids local optima by re-initializing the population every predetermined number of iterations while keeping the best solution obtained so far. For discretizing the solutions, MMVO employs a V-shaped transfer function (tanh). The research applies the proposed method to several knapsack case studies and demonstrates its application in resource allocation of Adaptive Multimedia Systems (AMS). The results show the benefits of the MMVO algorithm in solving binary test and real-world problems.
In this paper, binary variants of the Butterfly Optimization Algorithm (BOA) are proposed and used to select the optimal feature subset for classification purposes in a wrapper-mode. BOA is a recently proposed algorithm that has not been systematically applied to feature selection problems yet. BOA can efficiently explore the feature space for optimal or near-optimal feature subset minimizing a given fitness function. The two proposed binary variants of BOA are applied to select the optimal feature combination that maximizes classification accuracy while minimizing the number of selected features. In these variants, the native BOA is utilized while its continuous steps are bounded in a threshold using a suitable threshold function after squashing them. The proposed binary algorithms are compared with five state-of-the-art approaches and four latest high performing optimization algorithms. A number of assessment indicators are utilized to properly assess and compare the performance of these algorithms over 21 datasets from the UCI repository. The experimental results confirm the efficiency of the proposed approaches in improving the classification accuracy compared to other wrapper-based algorithms, which proves the ability of BOA algorithm in searching the feature space and selecting the most informative attributes for classification tasks.
This paper presents an improved fruit fly optimization algorithm (IFFOA) for solving the multidimensional knapsack problem (MKP). In IFFOA, the parallel search is employed to balance exploitation and exploration. To make full use of swarm intelligence, a modified harmony search algorithm (MHS) is proposed and applied to add cooperation among swarms in IFFOA. In MHS, novel pitch adjustment scheme and random selection rule are developed by considering specific characters of MKP and FOA. Moreover, a vertical crossover is designed to guide stagnant dimensions out of local optima and further improve the performance. Extensive numerical simulations are conducted and comparisons with other state-of-the-art algorithms verify that the proposed algorithm is an effective alternative for solving the MKP.
The Multidimensional Knapsack Problem (MKP) is known to be NP-hard in Operations Research. It has a wide range of applications in engineering and management. In this paper, we propose a binary differential search method to solve 0-1 MKPs in which the stochastic search is guided by a Brownian motion-like random walk. Our proposed method is composed of two main operations: discrete solution generating and feasible solution making. Discrete solution generating is realized through integrating a Brownian motion-like random search with an integer rounding operation. However, the rounded discrete variables may violate the constraints. To maintain the feasibility of the rounded discrete variables, a feasible solution making strategy is executed. To demonstrate the efficiency of our proposed algorithm, various 0-1 MKPs are solved by our proposed algorithm as well as by some of the existing meta-heuristic methods. The obtained numerical results indicate that our algorithm outperforms those existing meta-heuristic methods. Furthermore, it shows that our algorithm has the capability to solve large-scale 0-1 MKPs.
In this paper we propose a new hybrid heuristic approach that combines the Quantum Particle Swarm Optimization technique with a local search method to solve the Multidimensional Knapsack Problem. The approach also incorporates a heuristic repair operator that uses problem-specific knowledge instead of the penalty function technique commonly used for constrained problems. Experimental results obtained on a wide set of benchmark problems clearly demonstrate the competitiveness of the proposed method compared to the state-of-the-art heuristic methods.
Efficient decision making in vertical handoff and network selection algorithms improves users' quality of service and helps users meet service requirements, anywhere and at any time. Hence, in this paper, a user-centric network selection algorithm is proposed, utilizing the estimated reputation of the available candidate networks based on user location and combined experienced users' utility. User utility is defined based on 1) quality of service, 2) monetary cost, and 3) energy consumption metrics. In the proposed history aware-based user location algorithm, the past experience of users for available networks is considered to estimate the future utility that a user can obtain from a candidate network. The reputation factor for networks is used based on knowledge of users from each other while receiving service. Simulation results indicate that the average obtained utility by users is improved and handoff criteria, i.e. handoff number and failed and unnecessary handoffs, decrease. It can be seen that users choose networks with good past operations and this can encourage operators to provide good quality services for increasing their revenue.
In this work, a novel binary version of the grey wolf optimization (GWO) is proposed and used to select optimal feature subset for classification purposes. Grey wolf optimizer (GWO) is one of the latest bio-inspired optimization techniques, which simulate the hunting process of grey wolves in nature. The binary version introduced here is performed using two different approaches. In the first approach, individual steps toward the first three best solutions are binarized and then stochastic crossover is performed among the three basic moves to find the updated binary grey wolf position. In the second approach, sigmoidal function is used to squash the continuous updated position, then stochastically threshold these values to find the updated binary grey wolf position. The two approach for binary grey wolf optimization (bGWO) are hired in the feature selection domain for finding feature subset maximizing the classification accuracy while minimizing the number of selected features. The proposed binary versions were compared to two of the common optimizers used in this domain namely particle swarm optimizer and genetic algorithms. A set of assessment indicators are used to evaluate and compared the different methods over 18 different datasets from the UCI repository. Results prove the capability of the proposed binary version of grey wolf optimization (bGWO) to search the feature space for optimal feature combinations regardless of the initialization and the used stochastic operators.
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 simplified 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 fish behavior that are randomly selected by using two user defined 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.
This study presents an effective hybrid algorithm based on harmony search (HHS) for solving multidimensional knapsack problems (MKPs). In the proposed HHS algorithm, a novel harmony improvisation mechanism is developed with the modified memory consideration rule and the global-best pitch adjustment scheme to enhance the global exploration. A parallel updating strategy is employed to enrich the harmony memory diversity. To well balance the exploration and the exploitation, the fruit fly optimization (FFO) scheme is integrated as a local search strategy. For solving MKPs, binary strings are used to represent solutions and two repair operators are applied to guarantee the feasibility of the solutions. The HHS is calibrated based on the Taguchi method of design-of-experiment. Extensive numerical investigations based on well-known benchmark instances are conducted. The comparative evaluations indicate the HHS is much more effective than the existing HS and FFO variants in solving MKPs.
In this paper a new fuzzy evaluation method is proposed to rank several multi disjoint paths selection algorithms in network. This method combines fuzzy theory and Copeland method to evaluate rank of each proposed method base on bandwidth, availability and delay of end to end paths as determinative factors which their importance are expressed in linguistic variables. The Copeland ranking can be seen as an ordering of alternatives according to the stated principle that the more majority wins the better.
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.
Reconfigurable computing systems allow executing tasks in a true multitasking manner. Such systems share the reconfigurable device and processing unit as computing resources which leads to highly dynamic allocation situations. To manage such systems at runtime, a reconfigurable operating system is needed. The main part of this operating system is resource management unit which performs HW/SW partitioning, co-scheduling and placement of hardware tasks at run-time. In this paper, we present a heuristic for on-line integrated HW/SW partitioning and co-scheduling. We focus on on-line, non real-time and non-preemptive systems. The main characteristic of our heuristic is strong nexus between partitioning, scheduling and placement. Our heuristic prioritizes the arrived tasks according to different important parameters and partitions the sorted tasks according to their earliest finish time (EFT) on software and hardware processing units. A large variety of experiments have been conducted on the proposed algorithm using synthetic tasks. Obtained results show considerable benefits of this algorithm.
We investigate the dependence of the multi-knapsack objective function on the knapsack capacities and on the number of capacity constraints P, in the case when all N objects are assigned the same profit value and the weights are uniformly distributed over the unit interval. A rigorous upper bound to the optimal profit is obtained employing the annealed approximation and then compared with the exact value obtained through the Lagrangian relaxation method. The analysis is restricted to the regime where N goes to infinity and P remains finite.
In this paper we present a heuristic based upon genetic algorithms for the multidimensional knapsack problem. A heuristic operator which utilises problem-specific knowledge is incorporated into the standard genetic algorithm approach. Computational results show that the genetic algorithm heuristic is capable of obtaining high-quality solutions for problems of various characteristics, whilst requiring only a modest amount of computational effort. Computational results also show that the genetic algorithm heuristic gives superior quality solutions to a number of other heuristics.
Reconfigurable computing systems make us able to execute tasks in a true multitasking manner. Such systems share the reconfigurable device and processing unit as computing resources which leads to highly dynamic allocation situations. To manage such systems at runtime, a reconfigurable operating system is needed. The main part of this operating system is resource management unit which performs on-line scheduling and placement of hardware tasks at run-time. In this paper, we present a technique for on-line scheduling and placement. The main characteristics of our method are high resource reusing and reconfiguration overhead mitigation. A large variety of experiments have been conducted on the proposed algorithm using synthetic and real tasks. Obtained results show considerable benefits of this algorithm.
This paper presents a preprocessing procedure for the 0–1 multidimensional knapsack problem. First, a non-increasing sequence of upper bounds is generated by solving LP-relaxations. Then, a non-decreasing sequence of lower bounds is built using dynamic programming. The comparison of the two sequences allows either to prove that the best feasible solution obtained is optimal, or to fix a subset of variables to their optimal values. In addition, a heuristic solution is obtained. Computational experiments with a set of large-scale instances show the efficiency of our reduction scheme. Particularly, it is shown that our approach allows to reduce the CPU time of a leading commercial software.
The multiple-choice multidimensional knapsack problem (MMKP) concerns a wide variety of practical problems. It is strongly constrained and NP-hard; thus searching for an efficient heuristic approach for MMKP is of great significance. In this study, we attempt to solve MMKP by fusing ant colony optimization (ACO) with Lagrangian relaxation (LR). The algorithm used here follows the algorithmic scheme of max–min ant system for its outstanding performance in solving many other combinatorial optimization problems. The Lagrangian value of the item in MMKP, obtained from LR, is used as the heuristic factor in ACO since it performs best among the six domain-based heuristic factors we define. Furthermore, a novel infeasibility index is proposed for the development of a new repair operator, which converts possibly infeasible solutions into feasible ones. The proposed algorithm was compared with four existing algorithms by applying them to three groups of instances. Computational results demonstrate that the proposed algorithm is capable of producing competitive solutions.
In a previous work we proposed a variable fixing heuristics for the 0-1 Multidimensional knapsack problem (01MDK). This approach
uses fractional optima calculated in hyperplanes which contain the binary optimum. This algorithm obtained best lower bounds
on the OR-Library benchmarks. Although it is very attractive in terms of results, this method does not prove the optimality of the solutions
found and may fix variables to a non-optimal value. In this paper, we propose an implicit enumeration based on a reduced costs
analysis which tends to fix non-basic variables to their exact values. The combination of two specific constraint propagations
based on reduced costs and an efficient enumeration framework enable us to fix variables on the one hand and to prune significantly
the search tree on the other hand. Experimentally, our work provides two main contributions: (1) we obtain several new optimal
solutions on hard instances of the OR-Library and (2) we reduce the bounds of the number of items at the optimum on several harder instances.
Mitigating reconfiguration overhead in on-line task scheduling for reconfigurable computing systems
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On-line HW/SW partitioning and co-scheduling in reconfigurable computing systems
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- Bassiri