Swap Operator Research Articles

An effective discrete artificial bee colony algorithm for flow shop scheduling problem with intermediate buffers

An effective discrete artificial bee colony(DABC) algorithm is proposed for the flow shop scheduling problem with intermediate buffers (IBFSP) in order to minimize the maximum completion time (i.e makespan). The effective combination of the insertion and swap operator is applied to producing neighborhood individual at the employed bee phase. The tournament selection is adopted to avoid falling into local optima, while, the optimized insert operator embeds in onlooker bee phase for further searching the neighborhood solution to enhance the local search ability of algorithm. The tournament selection with size 2 is again applied and a better selected solution will be performed destruction and construction of iterated greedy (IG) algorithm, and then the result replaces the worse one. Simulation results show that our algorithm has a better performance compared with the HDDE and CHS which were proposed recently. It provides the better known solutions for the makespan criterion to flow shop scheduling problem with limited buffers for the Car benchmark by Carlier and Rec benchmark by Reeves. The convergence curves show that the algorithm not only has faster convergence speed but also has better convergence value.

Entanglement and swap of quantum states in two qubits

Suppose that two distant parties Alice and Bob share an entangled state $\rho_{AB}$, and they want to exchange the subsystems of $\rho_{AB}$ by local operations and classical communication (LOCC). In general, this LOCC task (i.e. the LOCC transformation of $\rho_{AB} \to V\rho_{AB} V$ with $V$ being a swap operator) is impossible deterministically, but becomes possible probabilistically. In this paper, we study how the optimal probability is related to the amount of entanglement in the framework of positive partial transposed (PPT) operations, and numerically show a remarkable class of states whose probability is the smallest among every state in two quantum bits.

Producer-Scrounger Method to Solve Traveling Salesman Problem

Algorithms inspired from natural phenomena are seem to be efficient to solve various optimization problems. This paper investigates a new technique inspiring from the animal group living behavior to solve traveling salesman problem (TSP), the most popular combinatorial optimization problem. The proposed producer-scrounger method (PSM) models roles and interactions of three types of animal group members: producer, scrounger and dispersed. PSM considers a producer having the best tour, few dispersed members having worse tours and scroungers. In each iteration, the producer scans for better tour, scroungers explore new tours while moving toward producer's tour; and dispersed members randomly checks new tours. For producer's scanning, PSM randomly selects a city from the producer's tour and rearranges its connection with several near cities for better tours. Swap operator and swap sequence based operation is employed in PSM to update a scrounger towards the producer. The proposed PSM has been tested on a large number of benchmark TSPs and outcomes compared to genetic algorithm and ant colony optimization. Experimental results revealed that proposed PSM is a good technique to solve TSP providing the best tours in most of the TSPs.

A novel binary artificial bee colony algorithm based on genetic operators

This study proposes a novel binary version of the artificial bee colony algorithm based on genetic operators (GB-ABC) such as crossover and swap to solve binary optimization problems. Integrated to the neighbourhood searching mechanism of the basic ABC algorithm, the modification comprises four stages: (1) In neighbourhood of a (current) food source, randomly select two food sources from population and generate a solution including zeros (Zero) outside the population; (2) apply two-point crossover operator between the current, two neighbourhood, global best and Zero food sources to create children food sources; (3) apply swap operator to the children food sources to generate grandchildren food sources; and (4) select the best food source as a neighbourhood food source of the current solution among the children and grandchildren food sources. In this way, the global–local search ability of the basic ABC algorithm is improved in binary domain. The effectiveness of the proposed algorithm GB-ABC is tested on two well-known binary optimization problems: dynamic image clustering and 0–1 knapsack problems. The obtained results clearly indicate that GB-ABC is the most suitable algorithm in binary optimization when compared with the other well-known existing binary optimization algorithms. In addition, the achievement of the proposed algorithm is supported by applying it to the CEC2005 benchmark numerical problems.

Structural optimization of Pt–Pd alloy nanoparticles using an improved discrete particle swarm optimization algorithm

Pt–Pd alloy nanoparticles, as potential catalyst candidates for new-energy resources such as fuel cells and lithium ion batteries owing to their excellent reactivity and selectivity, have aroused growing attention in the past years. Since structure determines physical and chemical properties of nanoparticles, the development of a reliable method for searching the stable structures of Pt–Pd alloy nanoparticles has become of increasing importance to exploring the origination of their properties. In this article, we have employed the particle swarm optimization algorithm to investigate the stable structures of alloy nanoparticles with fixed shape and atomic proportion. An improved discrete particle swarm optimization algorithm has been proposed and the corresponding scheme has been presented. Subsequently, the swap operator and swap sequence have been applied to reduce the probability of premature convergence to the local optima. Furthermore, the parameters of the exchange probability and the ‘particle’ size have also been considered in this article. Finally, tetrahexahedral Pt–Pd alloy nanoparticles has been used to test the effectiveness of the proposed method. The calculated results verify that the improved particle swarm optimization algorithm has superior convergence and stability compared with the traditional one.

General swap-based multiple neighborhood tabu search for the maximum independent set problem

Given a graph G=(V,E), the Maximum Independent Set problem (MIS) aims to determine a subset S⊆V of maximum cardinality such that no two vertices of S are adjacent. This paper presents a general Swap-Based Tabu Search (SBTS) for solving the MIS. SBTS integrates distinguished features including a general and unified (k,1)-swap operator, four constrained neighborhoods and specific rules for neighborhood exploration. Extensive evaluations on two popular benchmarks (DIMACS and BHOSLIB) of 120 instances show that SBTS attains the best-known results for all the instances. To our knowledge, such a performance was not reported in the literature for a single heuristic. The best-known results on 11 additional instances from code theory are also attained.

Realistic variant of just-in-time flowshop scheduling: integration of L p -metric method in PSO-like algorithm

This study strives to schedule a just-in-time hybrid flowshop with sequence-dependent setup times by considering two performance measures, namely makespan and sum of the earliness and tardiness, simultaneously. The paper proposes a mixed integer programming model. However, since the simpler case with a single stage and with a single machine per stage is NP-hard, the utilization of the exact algorithms for the real-life problems is limited. Thus, this paper proposes a novel solving algorithm with a weighted Lp-metric-based framework. Since the particle swarm optimization is originally designed for continuous solution space, in this study, we modify the particle position based on our representation so that a particle position is decoded into a schedule using the largest processing time algorithm, Hadamard product, and swap operator. Furthermore, we apply a variable neighborhood search and a tabu search to improve the solution quality. This hybridization which combines the advantages of the individual components is the key innovative aspect of the approach. We investigate the performance of our algorithm in the comparison with several algorithms and show that it has a good performance.

Calculating the entanglement spectrum in quantum Monte Carlo with application toab initioHamiltonians

Several algorithms have been proposed to calculate the spatial entanglement spectrum from high order Renyi entropies. In this work we present an alternative approach for computing the entanglement spectrum with quantum Monte Carlo for both continuum and lattice Hamiltonians. This method provides direct access to the matrix elements of the spatially reduced density matrix and we determine an estimator that can be used in variational Monte Carlo as well as other Monte Carlo methods. The algorithm is based on using a generalization of the Swap operator, which can be extended to calculate a general class of density matrices that can include combinations of spin, space, particle and even momentum coordinates. We demonstrate the method by applying it to the Hydrogen and Nitrogen molecules and describe for the first time how the spatial entanglement spectrum encodes a covalent bond that includes all the many body correlations.

A discrete artificial bee colony algorithm incorporating differential evolution for the flow-shop scheduling problem with blocking

A flow-shop scheduling problem with blocking has important applications in a variety of industrial systems but is underrepresented in the research literature. In this study, a novel discrete artificial bee colony (ABC) algorithm is presented to solve the above scheduling problem with a makespan criterion by incorporating the ABC with differential evolution (DE). The proposed algorithm (DE-ABC) contains three key operators. One is related to the employed bee operator (i.e. adopting mutation and crossover operators of discrete DE to generate solutions with good quality); the second is concerned with the onlooker bee operator, which modifies the selected solutions using insert or swap operators based on the self-adaptive strategy; and the last is for the local search, that is, the insert-neighbourhood-based local search with a small probability is adopted to improve the algorithm's capability in exploitation. The performance of the proposed DE-ABC algorithm is empirically evaluated by applying it to well-known benchmark problems. The experimental results show that the proposed algorithm is superior to the compared algorithms in minimizing the makespan criterion.

Research on Information Applied Technology with Swarm Intelligence for the TSP Problem

As a swarm intelligence algorithm, particle swarm optimization (PSO) has received increasing attention and wide applications in information applied technology. This paper investigates the application of PSO algorithm to the traveling salesman problem (TSP) on applied technology. Proposing the concepts of swap operator and swap sequence, we present a discrete PSO algorithm by redefinition of the equation for the particles velocity. A computational experiment is reported. The results show that the method proposed in this paper can achieve good results.

Discrete artificial bee colony algorithm for lot-streaming flowshop with total flowtime minimization

Unlike a traditional flowshop problem where a job is assumed to be indivisible, in the lot-streaming flowshop problem, a job is allowed to overlap its operations between successive machines by splitting it into a number of smaller sub-lots and moving the completed portion of the sub-lots to downstream machine. In this way, the production is accelerated. This paper presents a discrete artificial bee colony (DABC) algorithm for a lot-streaming flowshop scheduling problem with total flowtime criterion. Unlike the basic ABC algorithm, the proposed DABC algorithm represents a solution as a discrete job permutation. An efficient initialization scheme based on the extended Nawaz-Enscore-Ham heuristic is utilized to produce an initial population with a certain level of quality and diversity. Employed and onlooker bees generate new solutions in their neighborhood, whereas scout bees generate new solutions by performing insert operator and swap operator to the best solution found so far. Moreover, a simple but effective local search is embedded in the algorithm to enhance local exploitation capability. A comparative experiment is carried out with the existing discrete particle swarm optimization, hybrid genetic algorithm, threshold accepting, simulated annealing and ant colony optimization algorithms based on a total of 160 randomly generated instances. The experimental results show that the proposed DABC algorithm is quite effective for the lot-streaming flowshop with total flowtime criterion in terms of searching quality, robustness and effectiveness. This research provides the references to the optimization research on lot-streaming flowshop.

Solving City Routing Issue with Particle Swarm Optimization

The city routing issue is the problem to find a shortest tour of minimum length on a fully connected graph. Various Natureinspired algorithms have been proposed towards this problem. This paper proposes an application of Particle Swarm Optimization for this Issue. Results are achieved with the concept of Swap Operator and Sequence of Swap.

An improved artificial bee colony algorithm for the blocking flowshop scheduling problem

This paper presents an improved artificial bee colony (IABC) algorithm for solving the blocking flowshop problem with the objective of minimizing makespan. The proposed IABC algorithm utilizes discrete job permutations to represent solutions and applies insert and swap operators to generate new solutions for the employed and onlooker bees. The differential evolution algorithm is employed to obtain solutions for the scout bees. An initialization scheme based on the problem-specific heuristics is presented to generate an initial population with a certain level of quality and diversity. A local search based on the insert neighborhood is embedded to improve the algorithm's local exploitation ability. The IABC is compared with the existing hybrid discrete differential evolution and discrete artificial bee colony algorithms based on the well-known flowshop benchmark of Taillard. The computational results and comparison demonstrate the superiority of the proposed IABC algorithm for the blocking flowshop scheduling problems with makespan criterion.

The Lot-Streaming Flow Scheduling Shops Based on a Hybrid Discrete Harmony Search Algorithm

To solve the lot-streaming flow shop scheduling problem with the objective to minimize the total weighted earliness and tardiness, a hybrid discrete harmony search (HDHS) algorithm is proposed in this paper. Firstly, an effective harmony memory initialization approach is presented,an initial solution in harmony memory is generated by means of the famous NEH heuristic. Secondly, the HDHS algorithm utilizes an effective improvisation mechanism to generate new harmonies represented by job permutations. Lastly, the insert neighborhood search and swap operator are designed and embedded in the algorithm to enhance the local exploitation.Experimental results demonstrate the effectiveness of the proposed HDHS algorithms.

Dynamic economic dispatch solution using an improved genetic algorithm with non‐stationary penalty functions

AbstractThis paper presents an improved genetic algorithm with non‐stationary penalty functions (IGA‐NSPF) to solve the dynamic economic dispatch (DED) problem of generating units while considering valve‐point effects. The cost function of the generating units exhibits the non‐convex characteristics, as the valve‐point effects are modeled and imposed as rectified sinusoid components in the cost function. An improved evolution direction operator and gene swap operator are introduced in the proposed approach to improve the convergence characteristic of the genetic algorithm (GA). The non‐stationary penalty functions (NSPF) are introduced to put more selective pressure on the GA to find a feasible solution, resulting in difficulty during solution searching. The non‐stationary penalty is a function of the number of iterations that, in the proposed method, are based on a sigmoid function as the number of iteration increases so does the penalty. To illustrate the effectiveness of the proposed method, a dispatch case consisting of 10 units and 24 time intervals has been considered. Numerical results indicate that the performance of the IGA‐NSPF presents the best results when compared with previous optimization methods in solving DED problems with the valve‐point effect. Copyright © 2010 John Wiley & Sons, Ltd.

All maximally entangled four-qubit states

We find an operational interpretation for the 4-tangle as a type of residual entanglement, somewhat similar to the interpretation of the 3-tangle. Using this remarkable interpretation, we are able to find the class of maximally entangled four-qubits states which is characterized by four real parameters. The states in the class are maximally entangled in the sense that their average bipartite entanglement with respect to all possible bipartite cuts is maximal. We show that while all the states in the class maximize the average tangle, there are only a few states in the class that maximize the average Tsillas or Renyi α-entropy of entanglement. Quite remarkably, we find that up to local unitaries, there exists two unique states, one maximizing the average α-Tsallis entropy of entanglement for all α ⩾ 2, while the other maximizing it for all 0 < α ⩽ 2 (including the von-Neumann case of α = 1). Furthermore, among the maximally entangled four qubits states, there are only three maximally entangled states that have the property that for two, out of the three bipartite cuts consisting of two-qubits verses two-qubits, the entanglement is 2 ebits and for the remaining bipartite cut the entanglement between the two groups of two qubits is 1 ebit. The unique three maximally entangled states are the three cluster states that are related by a swap operator. We also show that the cluster states are the only states (up to local unitaries) that maximize the average α-Renyi entropy of entanglement for all α ⩾ 2.

Characterizing operations preserving separability measures via linear preserver problems

We use classical results from the theory of linear preserver problems to characterize operators that send the set of pure states with Schmidt rank no greater than k back into itself, extending known results characterizing operators that send separable pure states to separable pure states. We also provide a new proof of an analogous statement in the multipartite setting. We use these results to develop a bipartite version of a classical result about the structure of maps that preserve rank-1 operators and then characterize the isometries for two families of norms that have recently been studied in quantum information theory. We see, in particular, that for k ≥ 2 the operator norms induced by states with Schmidt rank k are invariant only under local unitaries, the swap operator and the transpose map. However, in the k = 1 case there is an additional isometry: the partial transpose map.

Measuring Renyi Entanglement Entropy in Quantum Monte Carlo Simulations

We develop a quantum Monte Carlo procedure, in the valence bond basis, to measure the Renyi entanglement entropy of a many-body ground state as the expectation value of a unitary Swap operator acting on two copies of the system. An improved estimator involving the ratio of Swap operators for different subregions enables convergence of the entropy in a simulation time polynomial in the system size. We demonstrate convergence of the Renyi entropy to exact results for a Heisenberg chain. Finally, we calculate the scaling of the Renyi entropy in the two-dimensional Heisenberg model and confirm that the Néel ground state obeys the expected area law for systems up to linear size L=32.

A discrete artificial bee colony algorithm for the lot-streaming flow shop scheduling problem

In this paper, a discrete artificial bee colony (DABC) algorithm is proposed to solve the lot-streaming flow shop scheduling problem with the criterion of total weighted earliness and tardiness penalties under both the idling and no-idling cases. Unlike the original ABC algorithm, the proposed DABC algorithm represents a food source as a discrete job permutation and applies discrete operators to generate new neighboring food sources for the employed bees, onlookers and scouts. An efficient initialization scheme, which is based on the earliest due date (EDD), the smallest slack time on the last machine (LSL) and the smallest overall slack time (OSL) rules, is presented to construct the initial population with certain quality and diversity. In addition, a self adaptive strategy for generating neighboring food sources based on insert and swap operators is developed to enable the DABC algorithm to work on discrete/combinatorial spaces. Furthermore, a simple but effective local search approach is embedded in the proposed DABC algorithm to enhance the local intensification capability. Through the analysis of experimental results, the highly effective performance of the proposed DABC algorithm is shown against the best performing algorithms from the literature.

Experimental Study on Pair Swap Strategy in Quantum-Inspired Evolutionary Algorithm

Quantum-Inspired Evolutionary Algorithm (QEA), a type of stochastic algorithm for solving combinatorial optimization problems, is evolutionary computation using quantum bits and superposition states in quantum computation. Although coarse-grained parallel, QEA has many parameters that must be adjusted manually. The simpler algorithm, Quantum-inspired Evolutionary Computation with Pair Swap operator (QEAPS), the authors propose involves just one population and a simple genetic operation exchanging best solution information between two individuals chosen randomly, instead of the migration operation used in QEA, and thereby fewer parameters to be adjusted. The authors found in experiments that QEAPS finds highly qualified solutions, is more robust against constraint handling, and has a higher search performance of thanks to diversified best solution information.