Quantum-inspired Evolutionary Algorithm Research Articles

A quantum-inspired evolutionary clustering algorithm for the lifetime problem of wireless sensor network

A quantum-inspired evolutionary clustering algorithm for the lifetime problem of wireless sensor network

Improved Quantum-Inspired Evolutionary Algorithm for Large-Size Lane Reservation

This paper studies a lane reservation problem for large sport events in big cities. Such events require organizers to deliver certain people and materials from athlete villages to geographically dispersed venues within a given travel duration. A lane reservation strategy is usually adopted in this circumstance to ensure that time-critical transportation tasks can be completed despite heavy urban traffic congestion. However, it causes negative impact on normal traffic. The problem aims to optimally select and reserve some lanes in a transportation network for the exclusive use of the tasks such that the total traffic impact is minimized. To solve the problem, we first develop an improved integer linear program. Then, its properties are analyzed and used to reduce the search space for its optimal solutions. Finally, we develop a fast and effective quantum-inspired evolutionary algorithm for large-size problems. Computational results on instances with up to 500 nodes in the network and 50 tasks show that the proposed algorithm is efficient in yielding high-quality solutions within a relatively short time.

The vehicle routing problem with multiple prioritized time windows: A case study

This paper addresses Multi-objective Vehicle Routing Problem with Multiple Prioritized Time Windows (VRPMPTW) in which the distributer proposes a set of all non-overlapping time windows with equal or different lengths and the customers prioritize these delivery time windows. VRPMPTW aims to find a set of routes of minimal total traveling cost and maximal customer satisfaction (with regard to the prioritized time windows), starting and ending at the depot, in such a way that each customer is visited by one vehicle given the capacity of the vehicle to satisfy a specific demand. This problem is inspired from a real life application. The contribution of this paper lies in its addressing the VRPMPTW from a problem definition, modeling and methodological point of view. We developed a mathematical model for this problem. This model can simply be used for a wide range of applications where the customers have multiple flexible time windows and violation of time windows may drop the satisfaction levels of customers and lead to profit loss in the long term. A Cooperative Coevolutionary Multi-objective Quantum-Genetic Algorithm (CCMQGA) is also proposed to solve this problem. A new local search is designed and used in CCMQGA to reach an appropriate pareto front. Finally, the proposed approach is employed in a real case study and the results of the proposed CCMQGA are compared with the current solution obtained from managerial experience, the results of NSGA-II and the multi-objective quantum-inspired evolutionary algorithm.

Parallel improved quantum inspired evolutionary algorithm to solve large size Quadratic Knapsack Problems

Quadratic Knapsack Problem (QKP), an extension of the canonical simple Knapsack Problem, is NP Hard in the stronger sense. No pseudo-polynomial time algorithm is known to exist which can solve QKP instances. QKP has been studied intensively due to its simple structure yet challenging difficulty and numerous applications. A few attempts have been made to solve large size instances of QKP due to its complexity. Quantum Inspired Evolutionary Algorithm (QIEA) provides a generic framework that has often been carefully tailored for a given problem to obtain an effective implementation. In this work, an improved and parallelized QIEA, dubbed IQIEA-P is presented. Several additional features make it more balanced in exploration and exploitation and thus have better applicability. Computational experiments are presented on large QKP instances of 1000 and 2000 items. The improvements are inherently parallelizable and, therefore, good speedups are obtained on a multi-core machine. No parallel algorithm is available for QKP. The solutions provided by QIEA-P are competitive with those obtained from the state of the art algorithm.

Towards the right amount of randomness in quantum-inspired evolutionary algorithms

Quantum-inspired evolutionary algorithms (QIEAs) combine the advantages of quantum-inspired bit (Q-bit), representation and operators with evolutionary algorithms for better performance. Using quantum-inspired representation the complete binary search space can be generated by collapsing a single Q-bit string repeatedly. Thus, even a population size of 1 can be taken in a QIEA implementation resulting in enormous saving in computation. Although this is correct in theory, QIEA implementations run into trouble in exploring large search spaces with this approach. The Q-bit string has to be initialized to produce each possible binary string with equal probability and then altered slowly to probabilistically favor generation of strings with better fitness values. This process is unacceptably slow when the search spaces are very large. Many ideas have been reported with EAs/QIEAs for speeding up convergence while ensuring that the algorithm does not get stuck in local optima. In this paper, the possible features are identified and systematically introduced and tested in the QIEA framework in various combinations. Some of these features increase the randomness in the search process for better exploration and the others compensate by local search for better exploitation together enabling a judicious combination tailored for particular problem being solved. This is referred to as "right-sizing the randomness" in the QIEA search. Benchmark instances of the well-known and well-studied Quadratic Knapsack Problem are used to demonstrate how effective these features are--individually and collectively. The new framework, dubbed QIEA-QKP, is shown to be much more effective than canonical QIEA. The framework can be utilized with profit on other problems and is being attempted.

Parameter estimation of nonlinear chaotic system by improved TLBO strategy

Estimation of parameters of chaotic systems is a subject of substantial and well-developed research issue in nonlinear science. From the viewpoint of optimization, parameter estimation can be formulated as a multi-modal constrained optimization problem with multiple decision variables. This investigation makes a systematic examination of the feasibility of applying a newly proposed population-based optimization method labeled here as teaching---learning-based optimization (TLBO) to identify the unknown parameters for a class of chaotic system. The preliminary test demonstrates that despite its global fast coarse search capability, teaching---learning-based optimization often risks getting prematurely stuck in local optima. To enhance its fine (local) searching performance of TLBO, Nelder---Mead simplex algorithm-based local improvement is incorporated into TLBO so as to continually search for the global optima through the reflection, expansion, contraction, and shrink operators. Working with the well-established Lorenz system, we assess the effectiveness and efficiency of the proposed improved TLBO strategy. The empirical results indicate the success of the proposed hybrid approach in which the global exploration and the local exploitation are well balanced, providing the best solutions for all instances used over other state-of-the-art metaheuristics for chaotic identification in literature, including particle swarm optimization, genetic algorithm, and quantum-inspired evolutionary algorithm.

Solving 0 - 1 knapsack problem by artificial chemical reaction optimization algorithm with a greedy strategy

This paper proposes a new artificial chemical reaction optimization algorithm with a greedy strategy to solve 0-1 knapsack problem. The artificial chemical reaction optimization (ACROA) inspiring the chemical reaction process is used to implement the local and global search. A new repair operator integrating a greedy strategy and random selection is used to repair the infeasible solutions. The experimental results have proven the superior performance of ACROA compared to genetic algorithm, and quantum-inspired evolutionary algorithm.

Hamming-distance-based adaptive quantum-inspired evolutionary algorithm for network coding resources optimization

An adaptive quantum-inspired evolutionary algorithm based on Hamming distance (HD-QEA) was presented to optimize the network coding resources in multicast networks. In the HD-QEA, the diversity among individuals was taken into consideration, and a suitable rotation angle step (RAS) was assigned to each individual according to the Hamming distance. Performance comparisons were conducted among the HD-QEA, a basic quantum-inspired evolutionary algorithm (QEA) and an individual's fitness based adaptive QEA. A solid demonstration was provided that the proposed HD-QEA is better than the other two algorithms in terms of the convergence speed and the global optimization capability when they are employed to optimize the network coding resources in multicast networks.

Quantum-Inspired Evolutionary Algorithm for difficult knapsack problems

Quantum Inspired Evolutionary Algorithms (QIEAs) are Evolutionary Algorithms which use concepts and principles of quantum computing. The 0/1 knapsack problem (KP) is a well known combinatorial optimization problem that has been typically used to validate the performance of QIEAs. However, there are some variants of KPs called difficult knapsack problems (DKPs) that are known to be more difficult to solve. QIEAs have not yet been fully explored for solving these. In this work, an improved QIEA, called QIEA-PSA is presented. A novel method to initialize the qubit individuals based on heuristic information for the KP instance and a method for size reduction for each new generation are introduced in the presented QIEA-PSA. Experiments are carried out for several types of DKPs that are much larger in size than those attempted hitherto. QIEA-PSA provides much better solutions than QIEA with much lesser computation times. Even a serial implementation of QIEA-PSA competes favorably on the same problem instances with a parallel implementation of an exact algorithm given recently in literature. A comparison is made which shows QIEA-PSA outperforms a recently applied population based search technique to solve benchmark KP instances. The ideas used for developing QIEA-PSA are general and may be utilized with advantage on other problems.

QEAM: An Approximate Algorithm Using P Systems with Active Membranes

This paper proposes an approximate optimization approach, called QEAM, which combines a P system with active membranes and a quantum-inspired evolutionary algorithm. QEAM uses the hierarchical arrangement of the compart- ments and developmental rules of a P system with active membranes, and the objects consisting of quantum-inspired bit individuals, a probabilistic observation and the evolutionary rules designed with quantum-inspired gates to specify the membrane algorithms. A large number of experiments carried out on benchmark instances of satisfiability problem show that QEAM outperforms QEPS (quantum-inspired evolu- tionary algorithm based on P systems) and its counterpart quantum-inspired evolu- tionary algorithm.

Quantum-Inspired Evolutionary Algorithm for Topology Optimization of Modular Cabled-Trusses

This article proposes an alternative optimization framework applied to topology optimization of modular lightweight cabled-truss structures. These structures are described as a system of intrinsically positioned cables and triangular bar formations jointed at their ends by hinged connections to form a rigid framework. The optimized topologies are determined through a stochastic discrete optimization procedure that uses ground structure approach, nonlinear finite element analysis, and quantum-inspired evolutionary algorithms. The optimization searches for optimal mass reduction with minimal losses in stiffness, such relation, is expressed by the stiffness-to-mass ratio parameter. Nonlinear finite element analysis is used to evaluate the static structural response. In order to decrease computation time, kinematically instable and structurally invalid individuals are filtered before evaluation. Modular design approach is taken into consideration to reduce the number of design variables and increase the productibility of cabled-trusses. Symmetric structural response is desired since in several mechanical applications forces can assume different directions during the working cycle. A modular ground structure with 300 elements is optimized, and optimal truss and cabled-truss topologies are compared. Complementary analyses comprise the investigation of the structural performance under different number of modules and slenderness ratios. The results indicate that the proposed optimization framework leads to optimized structures. In addition, it was observed that cabled trusses presented significant improvements in structural performance when compared with trusses.

Mixed continuous/binary quantum-inspired learning system with non-negative least square optimisation for automated design of regularised ensemble extreme learning machines

In this paper, a hybrid quantum-inspired evolutionary algorithm (QIEA) is proposed to automatically design regularised ensemble extreme learning machines (EELMs). Quantum evolutionary computing is a relatively recent spot-lighted concept which takes advantage from both the evolutionary and quantum computing laws. In general, QIEAs have been proven to be really powerful for optimising complex engineering tasks. The fascinating trait of observation operator in QIEA enables us to transform the quantum bits to both the binary and continuous spaces. Here, the authors present a mix continuous/binary version of QIEA, to find out whether it is suited for designing regularised EELMs. Indeed, the design process of EELM is conducted at two different levels, i.e. hyper and low levels. At the low level, some novel criteria are presented in the form of penalty functions to enable the optimiser searching for parsimonious, compact and accurate regularised extreme learning machines, as individual components of the ensemble. At the hyper-level, the non-negative least square error optimisation technique is utilised to deterministically find the most eligible components for designing the ensemble. Through extensive numerical experiments, the authors demonstrate that the proposed method is really efficient for the automated design of EELM identifiers.

An elitist quantum-inspired evolutionary algorithm for the flexible job-shop scheduling problem

The flexible job shop scheduling problem (FJSP) is vital to manufacturers especially in today’s constantly changing environment. It is a strongly NP-hard problem and therefore metaheuristics or heuristics are usually pursued to solve it. Most of the existing metaheuristics and heuristics, however, have low efficiency in convergence speed. To overcome this drawback, this paper develops an elitist quantum-inspired evolutionary algorithm. The algorithm aims to minimise the maximum completion time (makespan). It performs a global search with the quantum-inspired evolutionary algorithm and a local search with a method that is inspired by the motion mechanism of the electrons around atomic nucleuses. Three novel algorithms are proposed and their effect on the whole search is discussed. The elitist strategy is adopted to prevent the optimal solution from being destroyed during the evolutionary process. The results show that the proposed algorithm outperforms the best-known algorithms for FJSPs on most of the FJSP benchmarks.

A Quantum-Inspired Evolutionary Algorithm with Elite Group Guided

To improve the performance of quantum-inspired evolutionary algorithms (QIEAs), a new kind of QIEAs——elite group guided QIEA (EQIEA) are proposed through introducing an elite group guidance updating approach to solve knapsack problems. In EQIEA, the elite group at each iteration is composed of a certain number of individuals with better fitness values in the current population; all the individuals in the elite group cooperate together to affect quantum-inspired gates to produce off spring. Knapsack problems, a class of well-known NP-complete combinatorial optimization problems, are used to conduct experiments. The choices of parameters in EQIEA are discussed in an empirical way. Extensive experiments show that the EQIEA outperform six variants of QIEAs recently reported in the literature in terms of the quality of solutions. This paper also analyzes the convergence of EQIEA and the six variants of QIEAs. Experimental results show that EQIEA has better convergence than the six variants of QIEAs.

Solving the 0–1 Quadratic Knapsack Problem with a competitive Quantum Inspired Evolutionary Algorithm

Quadratic Knapsack Problem (QKP) extends the canonical simple Knapsack Problem where the value obtained by selecting a subset of objects is a function dependent not only on the value corresponding to individual objects selected but also on their pair-wise selection. QKP is NP Hard in stronger sense i.e. no pseudo-polynomial time algorithm is known to exist which can solve QKP instances. QKP has been studied intensively due to its simple structure yet challenging difficulty and numerous applications. Quantum Inspired Evolutionary Algorithm (QIEA) belongs to the class of Evolutionary Algorithms and exhibits behaviour of an Estimation of Distribution Algorithm (EDA). QIEA provides a generic framework that has to be carefully tailored for a given problem to obtain an effective implementation. Thus, several forms of QIEA exist in the literature. These have been successfully applied on many hard problems. A new QIEA, QIEA-PSA is proposed with improved exploration and exploitation capabilities. Computational experiments on these benchmarks show that QIEA-PSA is improved significantly both in terms of the quality of solutions and speed of convergence on several benchmark QKP instances. The ideas incorporated are general enough and can be utilized with advantage on other similar and not so similar problems.

A quantum-inspired gravitational search algorithm for binary encoded optimization problems

In this paper, a novel population based metaheuristic search algorithm by combination of gravitational search algorithm (GSA) and quantum computing (QC), called a Binary Quantum-Inspired Gravitational Search Algorithm (BQIGSA), is proposed. BQIGSA uses the principles of QC such as quantum bit, superposition and a modified rotation Q-gates strategy together with the main structure of GSA to present a robust optimization tool to solve binary encoded problems. To evaluate the effectiveness of the BQIGSA several experiments are carried out on the combinatorial 0–1 knapsack problems, Max-ones and Royal-Road functions. The results obtained are compared with those of other algorithms including Binary Gravitational Search Algorithm (BGSA), Conventional Genetic Algorithm (CGA), binary particle swarm optimization (BPSO), a modified version of BPSO (MBPSO), a new version of binary differential evolution (NBDE), a quantum-inspired particle swarm optimization (QIPSO), and three well-known quantum-inspired evolutionary algorithms (QIEAs). The comparison reveals that the BQIGSA has merit in the field of optimization.

A Novel Evolutionary Algorithm with Neighborhood Search for Project Portfolios Optimization Problem

This paper proposes a quantum-inspired evolutionary algorithm with neighborhood search (called QEANS) to solve the project portfolios optimization problem with limited multiple resources and bounded risks for each project portfolio. The decision concerns how to find an optimal or best assignment of projects to a set of project portfolios that maximizes the total profit. The studied problem is formulated by a 0-1 linear programming model, and a quantum-inspired evolutionary algorithm with neighborhood search is proposed to solve it. In specific, each problem solution is encoded by a Q-bits matrix, which is updated by quantum-rotation gate. In addition, crossover and mutation operators are integrated so as to increase the population diversity. Furthermore, an effective repairing procedure is proposed for dealing with the generated infeasible solutions. To prevent the local optimum, a specific neighborhood search procedure is also proposed. Randomly generated instances are used to test and justify the effectiveness of the proposed QEANS. The obtained results indicate that the proposed QEANS is effective.

An Experimental Study on Optimization in Permutation Spaces by Quantum-Inspired Evolutionary Algorithm Using Quantum Bit Representation

An Experimental Study on Optimization in Permutation Spaces by Quantum-Inspired Evolutionary Algorithm Using Quantum Bit Representation

Quantum-Inspired Features and Parameter Optimization of Spiking Neural Networks for a Case Study from Atmospheric

Abstract Identified cluster of atmospheric discharges, sufficiently near from transmissions line, could be an important alarm to support real time decisions. Lightning are important events that affect the electrical power system operation, which are often responsible for transmission lines outages, and can trigger a sequence of events that lead to system collapse. The Brazilian lightning network detection monitors nearly 18 million events monthly and all this data must be processed and analyzed. This paper uses a hybrid model named the Quantum binary-real evolving Spiking Neural Network (QbrSNN) for clustering problem, where the features and parameters of a spiking neural network (SNN) are optimized using the Quantum-Inspired Evolutionary Algorithm with representation Binary-Real (QIEA-BR). The proposed model is applied to atmospheric discharges data, with a significantly higher clustering accuracy than traditional techniques.

A novel hybrid column generation-metaheuristic approach for the vehicle routing problem with general soft time window

The vehicle routing problem with general soft time window involves designing a set of routes for a fleet of vehicles based at a central depot that is required to service a number of geographically dispersed customers while minimizing the total travel distance and delivery time costs. Delivery time cost function is a general piecewise linear function. In this study, we propose a mathematical model of this problem. Then an efficient hybrid column generation-metaheuristic approach is developed. In the proposed algorithm, the hybridization of column generation (CG) and the metaheuristic is performed in both integrative and collaborative modes. In the integrative phase, a quantum-inspired evolutionary algorithm is used to solve the sub-problems of column generation. In the collaborative phase, the column generation and electromagnetism algorithms are parallelized, and the information from these two algorithms is exchanged to find better solutions. Finally, the performance of the proposed approach is evaluated using a set of modified classic benchmark instances adopted from the literature.