Cooperative annealing Hopfield network for unconstrained binary quadratic programming problem

The updating rule of the original discrete Hopfield neural network (DHNN) is based on gradient descent dynamics, which always leads to the local minima problem. In this paper, by introducing the idea of the simulated annealing (SA) into the DHNN, we first propose an annealing HNN (AHNN) that permits temporary energy ascent to help the DHNN escape from local minima. Then, from a cooperative perspective, a population of the AHNN processes are simultaneously implemented and coupled by their acceptance probabilities, and thus a cooperative AHNN (CoAHNN) is proposed. The primary objective of the coupling in the CoAHNN is to create cooperative behavior via information exchange among neural networks. This objective helps in the decision of whether uphill moves will be accepted. In addition, coupling can provide information used online to guide the networks toward the global optimum. The CoAHNN is tested on 21 unconstrained binary quadratic programming problems (UBQP) with the size ranging from 3000 to 7000, and 48 maximum cut benchmark problems, a special case of the UBQP, with the size ranging from 512 to 3375. The UBQP consists in maximizing a quadratic 0–1 function. It is a well known NP-hard problem and is considered as a unified model for a variety of combinatorial optimization problems. Simulation results show that the CoAHNN is better than or competitive with other HNN based algorithms, metaheuristic algorithms and state-of-the-art algorithms.     

Competitive Hopfield Network Combined With Estimation of Distribution for Maximum Diversity Problems

This paper presents a discrete competitive Hopfield neural network (HNN) (DCHNN) based on the estimation of distribution algorithm (EDA) for the maximum diversity problem. In order to overcome the local minimum problem of DCHNN, the idea of EDA is combined with DCHNN. Once the network is trapped in local minima, the perturbation based on EDA can generate a new starting point for DCHNN for further search. It is expected that the further search is guided to a promising area by the probability model. Thus, the proposed algorithm can escape from local minima and further search better results. The proposed algorithm is tested on 120 benchmark problems with the size ranging from 100 to 5000. Simulation results show that the proposed algorithm is better than the other improved DCHNN such as multistart DCHNN and DCHNN with random flips and is better than or competitive with metaheuristic algorithms such as tabu-search-based algorithms and greedy randomized adaptive search procedure algorithms.      

A great deluge and tabu search hybrid with two-stage memory support for quadratic assignment problem

A two-stage memory architecture is maintained within the framework of great deluge algorithm for the solution of single-objective quadratic assignment problem. Search operators exploiting the accumulated experience in memory are also implemented to direct the search towards more promising regions of the solution space. The level-based acceptance criterion of the great deluge algorithm is applied for each best solution extracted in a particular iteration. The use of short- and long-term memory-based search supported by effective move operators resulted in a powerful combinatorial optimization algorithm. A successful variant of tabu search is employed as the local search method that is only applied over a few randomly selected memory elements when the second stage memory is updated. The success of the presented approach is illustrated using sets of well-known benchmark problems and evaluated in comparison to well-known combinatorial optimization algorithms. Experimental evaluations clearly demonstrate that the presented approach is a competitive and powerful alternative for solving quadratic assignment problems.     

Learnable tabu search guided by estimation of distribution for maximum diversity problems

This paper presents a learnable tabu search (TS) guided by estimation of distribution algorithm (EDA), called LTS-EDA, for maximum diversity problem. The LTS-EDA introduces knowledge model and can extract knowledge during the search process of TS, and thus it adopts dual or cooperative evolution/search structure, consisting of probabilistic model space in clustered EDA and solution space searched by TS. The clustered EDA, as a learnable constructive method, is used to create a new starting solution, and the simple TS, as an improvement method, attempts to improve the solution created by the clustered EDA in the LTS-EDA. A distinguishing feature of the LTS-EDA is the usage of the clustered EDA with effective linkage learning to guide TS. In the clustered EDA, different clusters (models) focus on different substructures, and the combination of information from different clusters (models) effectively combines substructures. The LTS-EDA is tested on 50 large size benchmark problems with the size ranging from 2,000 to 5,000. Simulation results show that the LTS-EDA is better than the advanced algorithms proposed recently.     

A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming

The conventional unconstrained binary quadratic programming (UBQP) problem is known to be a unified modeling and solution framework for many combinatorial optimization problems. This paper extends the single-objective UBQP to the multiobjective case (mUBQP) where multiple objectives are to be optimized simultaneously. We propose a hybrid metaheuristic which combines an elitist evolutionary multiobjective optimization algorithm and a state-of-the-art single-objective tabu search procedure by using an achievement scalarizing function. Finally, we define a formal model to generate mUBQP instances and validate the performance of the proposed approach in obtaining competitive results on large-size mUBQP instances with two and three objectives.     

Probabilistic GRASP-Tabu Search algorithms for the UBQP problem

This paper presents two algorithms combining GRASP and Tabu Search for solving the Unconstrained Binary Quadratic Programming (UBQP) problem. We first propose a simple GRASP-Tabu Search algorithm working with a single solution and then reinforce it by introducing a population management strategy. Both algorithms are based on a dedicated randomized greedy construction heuristic and a tabu search procedure. We show extensive computational results on two sets of 31 large random UBQP instances and one set of 54 structured instances derived from the MaxCut problem. Comparisons with state-of-the-art algorithms demonstrate the efficacy of our proposed algorithms in terms of both solution quality and computational efficiency. It is noteworthy that the reinforced GRASP-Tabu Search algorithm is able to improve the previous best known results for 19 MaxCut instances.     

Scheduling unrelated parallel machines with sequence-dependent setups

A methodology for minimizing the weighted tardiness of jobs in unrelated parallel machining scheduling with sequence-dependent setups is presented in this paper. To comply with industrial situations, the dynamic release of jobs and dynamic availability of machines are assumed. Recognizing the inherent difficulty in solving industrial-size problems efficiently, six different search algorithms based on tabu search are developed to identify the best schedule that gives the minimum weighted tardiness. To enhance both the efficiency and efficacy of the search algorithms, four different initial solution finding mechanisms, based on dispatching rules, are developed. While there is no evidence of identifying solutions of better quality by employing a specific initial solution finding mechanism, the use of a specific search algorithm led to identifying solutions of better quality or that required lower computation time, but not both. Based on the extensive statistical analysis performed, the search algorithm with short-term memory and fixed tabu list size is recommended for solving small size problems, while that with long-term memory and minimum frequency for solving medium and large size problems, combined with fixed tabu list size for the former and variable tabu list size for the latter.     

Discrete particle swarm optimization based on estimation of distribution for polygonal approximation problems

The polygonal approximation is an important topic in the area of pattern recognition, computer graphics and computer vision. This paper presents a novel discrete particle swarm optimization algorithm based on estimation of distribution (DPSO-EDA), for two types of polygonal approximation problems. Estimation of distribution algorithms sample new solutions from a probability model which characterizes the distribution of promising solutions in the search space at each generation. The DPSO-EDA incorporates the global statistical information collected from local best solution of all particles into the particle swarm optimization and therefore each particle has comprehensive learning and search ability. Further, constraint handling methods based on the split-and-merge local search is introduced to satisfy the constraints of the two types of problems. Simulation results on several benchmark problems show that the DPSO-EDA is better than previous methods such as genetic algorithm, tabu search, particle swarm optimization, and ant colony optimization.     

Improving GASAT by replacing tabu search by DLM and enhancing the best members

The satisfiability problem (SAT), as one of the six basic core NP-complete problems, has been the deserving object of many studies in the last two decades (Lardeux et al. 2005, 2006). GASAT (Lardeux et al. 2005, 2006; Hao et al. 2002) is one of the current state-of-the-art genetic algorithms for solving SATs. Besides, the discrete lagrange-multiplier (DLM) (Wu and Wah 1999a, b) is one of the current state-of-the-art local search algorithms for solving SATs. GASAT is a hybrid algorithm of the genetic and tabu search techniques. GASAT uses tabu search to avoid restarting the search once it converges. In this paper, we improve GASAT by replacing the tabu search by the DLM algorithm. We show that the performance of the new algorithm, DGASAT, is far better than the performance of GASAT in solving most of the benchmark instances. We further improve DGASAT by introducing the notion of improving one of the best members in the current population at a time. We show through experimentation that DGASAT + is far better than DGASAT in solving nearly all the benchmark instances.     

Discrete particle swarm optimization based on estimation of distribution for terminal assignment problems

Terminal assignment problem (TEAP) is to determine minimum cost links to form a network by connecting a given set of terminals to a given collection of concentrators. This paper presents a novel discrete particle swarm optimization (PSO) based on estimation of distribution (EDA), named DPSO-EDA, for TEAP. EDAs sample new solutions from a probability model which characterizes the distribution of promising solutions in the search space at each generation. The DPSO-EDA incorporates the global statistical information collected from personal best solutions of all particles into the PSO, and therefore each particle has comprehensive learning and search ability. In the DPSO-EDA, a modified constraint handling method based on Hopfield neural network (HNN) is also introduced to fit nicely into the framework of the PSO and thus utilize the merit of the PSO. The DPSO-EDA adopts the asynchronous updating scheme. Further, the DPSO-EDA is applied to a problem directly related to TEAP, the task assignment problem (TAAP), in order to show that the DPSO-EDA can be generalized to other related combinatorial optimization problems. Simulation results on several problem instances show that the DPSO-EDA is better than previous methods.     

An Enhanced Dynamic Slope Scaling Procedure with Tabu Scheme for Fixed Charge Network Flow Problems

A heuristic algorithm for solving large scale fixed charge network flow problems (FCNFP) based on the dynamic slope scaling procedure (DSSP) and tabu search strategies is presented. The proposed heuristic integrates the DSSP with short-term memory intensification and long-term memory diversification mechanisms in the tabu scheme to improve the performance of the pure DSSP. With the feature of dynamically evolving memory, the enhanced DSSP evaluates the solutions in the search history and iteratively adjusts the linear factors in the linear approximation of the FCNFP to produce promising search neighborhoods for good quality solutions. The comprehensive numerical experiments on various test problems ranging from sparse to dense network structures are reported. The overall comparison of the pure DSSP, the enhanced DSSP, and branch and bound (B&B by cutting-edge MIP optimizer in CPLEX) is shown in terms of solution quality and CPU time. The results show that the enhanced DSSP approach has a higher solution quality than the pure DSSP for larger scale problems. Research has been partially supported by NSF and CRDF grants.     

一种基于IP网络的QoS约束组播路由算法

针对时延约束最小代价组播路由问题,结合禁忌搜索算法和模拟退火算法的优点,提出了一种改进的混合遗传路由算法TSSAGMA。通过分析与仿真,证实了该算法在解决时延约束最小代价组播路由的问题上优于传统算法,能够在较小的代价下搜索到较好的解。     

Extensive experiments with hybrid genetic algorithms for the solution of the quadratic assignment problem

In this paper we perform extensive computational experiments solving quadratic assignment problems using various variants of a hybrid genetic algorithm. We introduce a new tabu search (simple tabu). We compared the modified robust tabu and the simple tabu as improvement algorithms in a hybrid genetic algorithm with other tabu searches (concentric tabu, ring moves, all moves, robust tabu) with superior results. We also tested several modifications of the hybrid genetic algorithm and all of them produced good results.     

A tabu search heuristic for the truck and trailer routing problem

Two new construction heuristics and a tabu search heuristic are presented for the truck and trailer routing problem, a variant of the vehicle routing problem. Computational results indicate that the heuristics are competitive to the existing approaches. The tabu search algorithm obtained better solutions for each of 21 benchmark problems.     

Genetic rule induction at an intermediate level

Lists of if–then rules (i.e. ordered rule sets) are among the most expressive and intelligible representations for inductive learning algorithms. Two extreme strategies searching for such a list of rules can be distinguished: (i) local strategies primarily based on a step-by-step search for the optimal list of rules, and (ii) global strategies primarily based on a one-strike search for the optimal list of rules. Both approaches have their disadvantages. In this paper we present an intermediate strategy. A sequential covering strategy is combined with a one-strike genetic search for the next most promising rule. To achieve this, a new rule-fitness function is introduced. Experimental results on benchmark problems are presented and the performance of our intermediate approach is compared with other rule learning algorithms. Finally, GeSeCo's performance is compared to a more local strategy on a set of tasks in which the information value of individual attributes is varied.     

Constructive heuristic algorithms for the open shop problem

In this paper we consider constructive heuristic algorithms for the open shop problem with minimization of the schedule length. By means of investigations of the structure of a feasible solution two types of heuristic algorithms are developed: construction of a rank-minimal schedule by solving successively weighted maximum cardinality matching problems and construction of an approximate schedule by applying insertion techniques combined with beam search. All presented algorithms are tested on benchmark problems from the literature. Our computational results demonstrate the excellent solution quality of our insertion algorithm, especially for greater job and machine numbers. For 29 of 30 benchmark problems with at least 10 jobs and 10 machines we improve the best known values obtained by tabu search.     

禁忌搜索与固定变量结合的启发式算法求解UBQP

提出了将固定变量与禁忌搜索结合的启发式算法来求解UBQP。此算法包含两个阶段：采用禁忌搜索得到一个参考解;根据该参考解固定或释放若干变量。选择固定变量还是释放变量由搜索的历史信息决定。此算法动态地在禁忌搜索与固定或释放变量这两个阶段之间交替进行,直到停机条件满足为止。用提出的算法对国际文献中公认的15个难算例进行实算测试,得到了全部测试算例的最优解。实验结果表明,该算法是求解UBQP的一个高效求解算法。     

An effective estimation of distribution algorithm for the multi-mode resource-constrained project scheduling problem

In this paper, an estimation of distribution algorithm (EDA) is proposed to solve the multi-mode resource-constrained project scheduling problem (MRCPSP). In the EDA, the individuals are encoded based on the activity-mode list (AML) and decoded by the multi-mode serial schedule generation scheme (MSSGS), and a novel probability model and an updating mechanism are proposed for well sampling the promising searching region. To further improve the searching quality, a multi-mode forward backward iteration (MFBI) and a multi-mode permutation based local search method (MPBLS) are proposed and incorporated into the EDA based search framework to enhance the exploitation ability. Based on the design-of-experiment (DOE) test, suitable parameter combinations are determined and some guidelines are provided to set the parameters. Simulation results based on a set of benchmarks and comparisons with some existing algorithms demonstrate the effectiveness of the proposed EDA.     

A block based estimation of distribution algorithm using bivariate model for scheduling problems

Recently, estimation of distribution algorithms (EDAs) have gradually attracted a lot of attention and have emerged as a prominent alternative to traditional evolutionary algorithms. In this paper, a block-based EDA using bivariate model is developed to solve combinatorial problems. Instead of generating a set of chromosomes, our approach generates a set of promising blocks using bivariate model and these blocks are reserved in an archive for future use. These blocks will be updated every other k generation. Then, two rules, i.e., AC1 and AC2, are developed to generate a new chromosome by combining the set of selected blocks and rest of genes. This block based approach is very efficient and effective when compared with the traditional EDAs. According to the experimental results, the block based EDA outperforms EDA, GA, ACO and other evolutionary approaches in solving benchmark permutation problems. The block based approach is a new concept and has a very promising result for other applications.     

Systems Analysis; Solving unconstrained binary quadratic programming problem by global equilibrium search

A new algorithm based on global equilibrium search (GES) is developed to solve an unconstrained binary quadratic programming (UBQP) problem. It is compared with the best methods of solving this problem. The GES algorithm is shown to be better both in speed and solution quality.