Application of parallel heuristic algorithms for speeding up parallel implementations of the branch-and-bound method

The two-dimensional rectangular cutting problem with defects is discussed. The goal is to cut a small rectangular block of a given height and width from a large rectangular object containing a plurality of defects on the premise of satisfying several constraints, so that the sum of the area of the cut small rectangular blocks are maximized. The constraint is that each cutting operation must be guillotine, and the number of small rectangular blocks of each type is not limited and maintains a given direction. The problem is regarded as covering the original plate with small rectangular block, and a Quick Heuristic-Dynamic Programming (QHDP) algorithm is proposed. Firstly, a one-dimensional knapsack problem is established according to the height and width of small rectangular blocks, respectively, and an efficient discretization sets is generated respectively. Then, each value in the sets is used as a possible cutting line coordinate for sub-problem division. The algorithm calculates 14 typical examples. The experimental results show that it has obtained the optimal solution of all the examples, and the calculation time is less than one tenth of the best algorithm in the current literature. The algorithm complexity is analyzed and proved.

A universal approach for continuous or discrete nonlinear programmings with multiple variables and constraints

Parallel techniques for solving large scale travelling salesperson problems

Purpose. The purpose of the article is to develop a universal unified parallel synchronous algorithm for the implementation of tasks for calculation of maximum one- and multicommodity flows, as well as the creation of a software complex that provides the formation of surface graph models of flows and performs optimal planning of non-uniform flows in transport and other networks. Methodology. The paper investigates the possibilities of previously created and comprehensively verified heuristic parallel synchronous algorithm for calculating maximum one- and multicommodity flows in the networks, establishes its potential limitations, and determines additional advanced procedures that transform the algorithm into a universal parallel algorithm. The proposed parallel synchronous algorithm uses a width-first search strategy while simultaneously identifying possible paths of flows through the network with an estimation of their throughput. Herewith the possibility of analyzing several incremental flows across the network in one iteration was studied. Findings. The article proposes a universal unified parallel synchronous algorithm for calculating maximum flows in networks and develops a unified procedure and software package for planning of non-uniform as well as competitive flows in transport and other networks. The developed software complex implements the problems of formation of surface graph models of networks, for which the problem of optimal planning of non-uniform and competitive multicriteria flows in transport networks is solved. Originality. The article develops a new universal unified parallel synchronous algorithm and procedure for the calculation of optimal uniform, multicommodity and competitive flows in transport networks. Practical value. The practical value of the obtained results is determined by the universal capabilities and efficiency of the procedure for planning non-uniform flows in the networks based on the application of a new parallel synchronous algorithm, as well as the developed software complex, which provides the ability to solve the problems of analysis and planning of uniform and multicommodity flows in transport networks, as well as the implementation of calculation tasks of competitive models of transport and information flows formation. The software complex has a built-in editor of interactive network modeling and a toolbar, which provides both creation of new and downloading existing graphs of networks from the modeling libraries, preservation of optimum flows in the network in the form of an image and a text file, output of errors when working with the program.

In this paper, we propose a novel quantum-inspired evolutionary algorithm, called quantum-inspired Tabu search (QTS). QTS is based on the classical Tabu search and the characteristic of quantum computation such as superposition. We will present how we implement QTS to solve 0/1 knapsack problem. Furthermore, the results of experiments are also compared with other quantum-inspired evolutionary algorithm and other heuristic algorithms' experimental results. The final outcomes show that QTS performs much better than the other heuristic algorithms on 0/1 knapsack problem, without premature convergence and more efficiency.

In this paper, a hybrid flow shop scheduling problem with a new approach considering time lags and sequence-dependent setup time in realistic situations is presented. Since few works have been implemented in this field, the necessity of finding better solutions is a motivation to extend heuristic or meta-heuristic algorithms. This type of production system is found in industries such as food processing, chemical, textile, metallurgical, printed circuit board, and automobile manufacturing. A mixed integer linear programming (MILP) model is proposed to minimize the makespan. Since this problem is known as NP-Hard class, a meta-heuristic algorithm, named Genetic Algorithm (GA), and three heuristic algorithms (Johnson, SPTCH and Palmer) are proposed. Numerical experiments of different sizes are implemented to evaluate the performance of presented mathematical programming model and the designed GA in compare to heuristic algorithms and a benchmark algorithm. Computational results indicate that the designed GA can produce near optimal solutions in a short computational time for different size problems.

This paper makes an extensive description of a real fuel distribution problem. It includes the description of the elements, process, constraints and difficulties of the real problem, as well as the description of the efficient system that has been designed to solve it. This system combines a global strategy working with the whole set of orders and vehicles – global optimisation – and a local one – local optimisation – that tries to improve parts of the global solution, concretely pairs of routes. Both parts are combination of Simulated Annealing and a Route Building Heuristic. The main objective is to obtain good quality results in little time with this aim, the system has been parallelised, and, as a consequence, the same quality results can be obtained dividing the time by the number of processors. Satisfactory average results were obtained: the experts in the company ratified that solutions for problems with 170 orders are obtained in a couple of minutes, and savings greater than 10% are obtained as well. On the other hand, in problems of Solomon's benchmark, average results are very good in distance, whereas in vehicles, they are under 10% worse than the optimal one. This experimentation has been always done by limiting the number of solutions explored to 32,000.

We describe a new heuristic algorithm to solve the one-dimensional bin-packing problem. The proposed algorithm is optimal if the sum of requirements of items is less than or equal to twice the bin capacity. Our computational results show that effectiveness of the proposed algorithm in finding optimal or near-optimal solutions is superior to that of the FFD and BFD algorithms, specifically for those so called 'difficult' problems that require an optimal solution to fill most of the bins, if not all, exactly to capacity.

A hidden Markov model (HMM) is a natural and highly robust statistical method for automatic speech recognition. It has been tested and proved effective in a wide range of applications. The HMM model parameters are used to describe the utterance of the speech segment presented by the HMM. Many successful heuristic algorithms are developed to optimize the model parameters to best describe the training observation sequences. However, all these methods are exploring for only one local maximum in practice. No single method can be recovered from the local maximum and to obtain the global maximum or other more optimized local maxima. In this paper, a stochastic search method called the genetic algorithm (GA) is presented for HMM training. GA mimics natural evolution and performs searching within the defined searching space. Experimental results showed that using GA for HMM training (GA-HMM training) can obtain better solutions than using heuristic algorithms. One of the major drawbacks is that GAs require a lot of computation power for global searching before it can converge. Therefore, in order to outperform heuristic algorithms, a parallel version of GA called the parallel genetic algorithm (PGA) is introduced. Experimental results showed that using PGA in speech recognition systems provides 18% improvement in recognition rate with the same amount of computational time.

In order to solve the problem that mobile robot is trapped in local convergence and cannot achieve path optimization in ant colony algorithm path planning, an improved variable step size ant colony algorithm is proposed to achieve path optimization with less convergence iterations. According to the relevant characteristics of the application of ant colony algorithm in path planning, the pheromone allocation is optimized, the influence of local pheromone content on the algorithm is reduced, the ant colony is prevented from falling into local optimization when searching the path, and the weight factor is added to the transfer probability formula. improve the probability of the mobile robot moving towards the end point, effectively reduce the number of convergence iterations of the ant colony, and change the mobile robot’s mobile step size. So that it can move freely without collision within 360°, and the path length can be effectively shortened. The simulation results show that in a simple environment, the convergence iteration times and optimal path length of the improved variable step size ant colony algorithm are 2 and 28.042 m, respectively, and the convergence iteration times and optimal path length of the traditional ant colony algorithm are 25 and 29.213 m, respectively. In the complex environment, the convergence iteration times and optimal path length of the improved variable step size ant colony algorithm are 2 and 43.9602m respectively, and the convergence iteration times and optimal path length of the improved potential field ant colony algorithm are 16 and 45.1127m, respectively. Simulation results verify the effectiveness and superiority of the improved variable step size ant colony algorithm.

The Steiner tree problem in graphs (SPG) is one of the most studied problems in combinatorial optimization because of its theories and applications. It is one of the foundations to develop a Wireless Sensor Network (WSNs), such as multicast and topology design. SPG is an NP-Hard problem, and many heuristic and approximation algorithms have been proposed. Thus, this study proposes a Hybrid Genetic algorithm (HGA) to solve SPG. This study is the binary string representation for a set of chosen edges. To increase the diversity of the population and avoid falling into local optimization, we use a 2-longest Distance strategy, dynamic crossover rate, and chosen solutions must differ by at least 5%. The experiment results show that the HGA algorithm's running time equals 153.83% of the GA algorithm's, the deviation found by HGA, and the optimal distance only equals 65% that of GA.

Feature selection is an important part of data mining, image recognition and other fields. The efficiency and accuracy of classification algorithm can be improved by selecting the best feature subset. The classical feature selection technology has some limitations, and heuristic optimization algorithm for feature selection is an alternative method to solve these limitations and find the optimal solution. In this paper, we proposed a Multi Strategy Grey Wolf Optimizer algorithm (MSGWO) based on random guidance, local search and subgroup cooperation strategies for feature selection, which solves the problem that the traditional grey wolf optimizer algorithm (GWO) is easy to fall into local optimization with a single search strategy. Among them, the random guidance strategy can make full use of the random characteristics to enhance the global search ability of the population, and the local search strategy makes grey wolf individuals make full use of the search space around the current best solution, and the subgroup cooperation strategy is very important to balance the global search and local search of the algorithm in the iterative process. MSGWO algorithm cooperates with each other in three strategies to update the location of grey wolf individuals, and enhances the global and local search ability of grey wolf individuals. Experimental results show that MSGWO can quickly find the optimal feature combination and effectively improve the performance of the classification model.

Trajectory planning plays a crucial role in ensuring the safe navigation of ships, as it involves complex decision making influenced by various factors. This paper presents a heuristic algorithm, named the Markov decision process Heuristic Algorithm (MHA), for time-optimized avoidance of Unmanned Surface Vehicles (USVs) based on a Risk-Sensitive Markov decision process model. The proposed method utilizes the Risk-Sensitive Markov decision process model to generate a set of states within the USV collision avoidance search space. These states are determined based on the reachable locations and directions considering the time cost associated with the set of actions. By incorporating an enhanced reward function and a constraint time-dependent cost function, the USV can effectively plan practical motion paths that align with its actual time constraints. Experimental results demonstrate that the MHA algorithm enables decision makers to evaluate the trade-off between the budget and the probability of achieving the goal within the given budget. Moreover, the local stochastic optimization criterion assists the agent in selecting collision avoidance paths without significantly increasing the risk of collision.

This study assesses the worst-case demand and replication models for determining the bandwidth required by the origin server when a number of video programs in a video-on-demand system are replicated on replica servers. The bandwidth required by the video- on-demand system determines the number of viewers that could watch video programs simultaneously. If a video program is viewed in its entirety, the required bandwidth is estimated based on the number of concurrent viewers as well as the length of the video program. Unlike traditional research models that use the hit ratio to assess the replication benefits, this study uses the M/G/∞ model to examine the related phenomenon and problems in this field. We develop a selection model for replication using the product of the viewing request probability and the video length as the main factor in determining the videos selected for replication. This model theoretically outperforms traditional models that consider only the viewing request probability in the benefits of reducing the worst-case demand at origin server, and the simulation results validate the theoretical results. Due to resource constraints in the replica server, discussions and verifications on the optimization of the proposed replication model were carried out and the findings were used as the basis for the development of a heuristic algorithm. The results derived using this heuristic algorithm are almost the same as the optimized results derived from LINGO.

Unlocking massively parallel spectral proper orthogonal decompositions in the PySPOD package