Complex Combinatorial Optimization Problem Research Articles

Extremal Optimization Applied to the Minimum Order Frequency Assignment Problem

Extremal Optimization (EO) is a metaheuristic used to solve complex combinatorial optimization problems. However, the behavior of this algorithm has not been studied for various interesting problems. Such as, it is the case of the Minimum Order Frequency Assignment Problem (MO-FAP). Specifically, this problem seeks to minimize the number of frequencies assigned to a group of transceiver, without violating any of the problems constraints. In particular, the aim of this study was to use EO to solve the MO-FAP. Furthermore, it was found that EO was able to find the best reported value for most instances of the dataset used for experimentation. Additionally, it was possible to identify how the EO Tau hyperparameter reported better results for much higher values than those reported in the literature. Finally, the difficulty of defining and configuring a fitness function for each element of the solution was evidenced. Therefore, this can affect the effectiveness of the algorithm according to the particular characteristics of the dataset to be solved. Consequently, this opens an opportunity to develop improvements in the form of defining the contribution of each element of the solution to the objective function.

Deep Reinforcement Learning Approaches to Network Slice Scaling and Placement: A Survey

Network slicing in 5G and beyond networks allows the network to be customized for each application or service, by chaining together different virtualized network functions (VNFs) according to service requirements. The increased flexibility offered by network slicing comes at the cost of complexity in management and orchestration, which cannot be solved by traditional reactive human-in-the-loop solutions. This necessitates minimizing human intervention through the use of artificial intelligence (AI) techniques (zero-touch network management). In particular, the scaling and placement of the chain of VNFs which comprise a network slice is a complex combinatorial optimization problem which is difficult to solve effectively with traditional approaches. Driven by the benefits of deep reinforcement learning (DRL) in solving various combinatorial optimization problems, in this article, we survey various DRL-based approaches to slice scaling and placement, including different ways to model the problem and benefits of various DRL techniques in addressing specific aspects of the problem. Further, we highlight key challenges and open issues in the effective use of DRL for network slice scaling and placement.

Automated algorithm design using proximal policy optimisation with identified features

Automated algorithm design is attracting considerable recent research attention in solving complex combinatorial optimisation problems, due to that most metaheuristics may be particularly effective at certain problems or certain instances of the same problem but perform poorly at others. Within a general algorithm design framework, this study investigates reinforcement learning on the automated design of metaheuristic algorithms. Two groups of features, namely search-dependent and instance-dependent features, are firstly identified to represent the search space of algorithm design to support effective reinforcement learning on the new task of algorithm design. With these key features, a state-of-the-art reinforcement learning technique, namely proximal policy optimisation, is employed to automatically combine the basic algorithmic components within the general framework to develop effective metaheuristics. Patterns of the best designed algorithm, in particular the utilisation and transition of algorithmic components, are investigated. Experimental results on the capacitated vehicle routing problem with time windows benchmark dataset demonstrate the effectiveness of the identified features in assisting automated algorithm design with the proposed reinforcement learning model.

Optimal Transmission Switching for Short-Circuit Current Limitation Based on Deep Reinforcement Learning

The gradual expansion of power transmission networks leads to an increase in short-circuit current (SCC), which has an impact on the secure operation of transmission networks when the SCC exceeds the interrupting capacity of the circuit breakers. In this regard, optimal transmission switching (OTS) is proposed to reduce the short-circuit current while maximizing the loadability with respect to voltage stability. However, the OTS model is a complex combinatorial optimization problem with binary decision variables. To address this problem, this paper employs the deep Q-network (DQN)-based RL algorithm to solve the OTS problem. Case studies on the IEEE 30-bus system and 118-bus system are presented to demonstrate the effectiveness of the proposed method. The numerical results show that the DQN-based agent can select the effective branches at each step and reduce the SCC after implementing the OTS strategies.

Dynamic reconfiguration for TEG systems under heterogeneous temperature distribution via adaptive coordinated seeker

A thermoelectric generation (TEG) system has the weakness of relatively low thermoelectric conversion efficiency caused by heterogeneous temperature distribution (HgTD). Dynamic reconfiguration is an effective technique to improve its overall energy efficiency under HgTD. Nevertheless, numerous combinations of electrical switches make dynamic reconfiguration a complex combinatorial optimization problem. This paper aims to design a novel adaptive coordinated seeker (ACS) based on an optimal configuration strategy for large-scale TEG systems with series–parallel connected modules under HgTDs. To properly balance global exploration and local exploitation, ACS is based on ‘divide-and-conquer’ parallel computing, which synthetically coordinates the local searching capability of tabu search (TS) and the global searching capability of a pelican optimization algorithm (POA) during iterations. In addition, an equivalent re-optimization strategy for a reconfiguration solution obtained by meta-heuristic algorithms (MhAs) is proposed to reduce redundant switching actions caused by the randomness of MhAs. Two case studies are carried out to assess the feasibility and superiority of ACS in comparison with the artificial bee colony algorithm, ant colony optimization, genetic algorithm, particle swarm optimization, simulated annealing algorithm, TS, and POA. Simulation results indicate that ACS can realize fast and stable dynamic reconfiguration of a TEG system under HgTDs. In addition, RTLAB platform-based hardware-in-the-loop experiments are carried out to further validate the hardware implementation feasibility.

Location of Logistics Distribution Center Based on Improved Bald Eagle Algorithm

The location of a logistics distribution center is a complex combinatorial optimization problem, and it is difficult to achieve the best results by traditional mathematical methods. This paper proposes an improved bald eagle search applied to logistics distribution center location selection for the first time, one which uses the chaotic operator to initialize the population, increases the diversity of populations, and introduces a sine and cosine algorithm in the search stage. It increases the global search ability of the algorithm and the ability to jump further out of the local space. Through test function and location simulation experiments, it is proved that the improved algorithm has obvious advantages over other common algorithms in solution accuracy and convergence speed. It can effectively improve the efficiency of logistics distribution when applied to the location of logistics distribution centers. Finally, the improved bald eagle search algorithm is used to optimize the location model of logistics distribution center. The experimental results show that the improved bald eagle search algorithm has good solving ability in this problem, can be obtained to minimize the distribution cost, save the distribution cost effectively and improve the distribution efficiency. It can further optimize the logistics management system and increase the efficiency of logistics enterprises. Compared with similar algorithms, such as WOA, WCA, PSO, the results are improved.

Learning to compute the metric dimension of graphs

For distinct vertices x,y,z in graph G=(V,E), we say the pair of vertices x,y can be distinguished by vertex z, if the distance inequation dG(x,z)≠dG(y,z) is true. If any two different vertices in graph G can be distinguished by at least one vertex in the vertex subset S⊂V then we say S⊂V is a resolving set of graph G. The one with minimum number of nodes among all of the resolving sets is called a metric base of graph G, of which the cardinality is called the metric dimension of graph G. The metric dimension problem(MDP) of computing the metric dimension of graphs is a kind of complex combinatorial optimization problem. In this paper, a hybrid algorithm for solving the MDP is developed, through which the metric base of graphs can be learned, and consequently the metric dimension of graphs is estimated. It is particular that the hybrid algorithm combines graph representation learning with greedy repair policy. Extensive experiments show that the hybrid algorithm has higher computational accuracy and efficiency on random graphs. It is also further suggested that the learning process of MDP is greatly influenced by the attributes of complex networks and the designs of graph neural networks themselves.

An Improvement Heuristic Based on Variable Neighborhood Search for Dynamic Orienteering Problems with Changing Node Values and Changing Budgets

We study the Dynamic Orienteering Problem (DOP) with changing node values and changing budgets. It is a complex combinatorial optimization problem with many applications, e.g., in tour planning. To solve the DOP, an improvement heuristic based on Variable Neighborhood Search mathrm {VNS}_{mathrm {DOP}} is proposed. In addition, three methods for handling solutions that became invalid by budget changes are presented. Heuristic mathrm {VNS}_{mathrm {DOP}} is experimentally compared with two improvement heuristics based on state-of-the-art algorithms for the static Orienteering Problem. In addition, the influence of the three invalid solution handling methods on the algorithms’ optimization behavior is evaluated experimentally. For the experiments, benchmark instances as well as instances generated from existing road networks are used. As a quality measure for the algorithms, their performance over time is used. The results show that both types of dynamic changes, i.e., changes in the node values and changes in the budget, lead to higher volatility in the results for all compared algorithms. However, the latter type has a more negative effect on the performance. Out of the compared algorithms, the proposed heuristic mathrm {VNS}_{mathrm {DOP}} obtains the best results in most cases on a variety of problem instances with dynamic node values and dynamic budgets, showing that it has a high performance over time in dynamic environments and is able to deal with different levels of dynamic changes. For DOPs with changing budgets, the invalid solution handling method that repairs solutions by fixing the violation of the budget constraint as fast as possible performs best for the considered algorithms.

Introduction of modern information and communication technologies in transport flow management

The article proposes an economic mechanism for regulating the route network, the calculation of which allows you to choose a transport route, as well as calculate the number of flights based on the condition of achieving a break-even transport process for carriers of various forms of ownership. The Work deals with the solution of problems related to the choice of a route, which belong to the class of complex combinatorial optimization problems. They don't have simple analytical solutions. As the number of nodes increases, the computational complexity increases exponentially. The Work proposes an alternative method for solving routing problems based on the use of neural network models, which allow obtaining good suboptimal solutions with a significant reduction in time costs. As in the Hopfield network, a matrix of neurons is used here, but neurons interact not on the "each with each" principle, but in rows and columns.

Ant colony optimization equipped with an ensemble of heuristics through multi-criteria decision making: A case study in ensemble feature selection

Ant Colony Optimization (ACO) is a probabilistic and approximation metaheuristic algorithm to solve complex combinatorial optimization problems. ACO algorithm is inspired by the behavior of a colony of real ants and uses their pheromone trials to find optimal solutions. Since the beginning of the ACO algorithm, many researchers have tried to improve the performance and stability of the algorithm by using various methodologies. Resolving the exploitation/exploration dilemma by an efficient procedure is critical in improving the ACO. One of the critical parameters in ACO is selecting the heuristic that can affect the movements of ants. So far, the use of several heuristics in ACO has not been studied. We believe that using multiple heuristics instead of a single heuristic can improve the ACO algorithm. For this matter, we have proposed an ACO algorithm based on the ensemble of heuristics using a Multi-Criteria Decision-Making (MCDM) procedure. It means that the movement of the ants is defined based on the judgment of multiple experts (criteria). The idea is based on the hypothesis that different heuristics give us more information about the subsequent nodes, and the variety of these methods examines the different aspects to achieve better and optimal solutions in ACO. In this paper, we have applied our proposed method to the ensemble feature selection task to evaluate the performance of the proposed method. Blending several feature selection methods is regular to tackle the feature selection problem, and also efficiently combining feature selection methods is still challenging. Some well-known ensemble feature selection and primary feature selection methods have been compared with Ant-MCDM on twelve datasets to evaluate the performance of the proposed method in the feature selection task.

A Tutorial on Bandit Learning and Its Applications in 5G Mobile Edge Computing (Invited Paper)

Due to the rapid development of 5G and Internet-of-Things (IoT), various emerging applications have been catalyzed, ranging from face recognition, virtual reality to autonomous driving, demanding ubiquitous computation services beyond the capacity of mobile users (MUs). Mobile cloud computing (MCC) enables MUs to offload their tasks to the remote central cloud with substantial computation and storage, at the expense of long propagation latency. To solve the latency issue, mobile edge computing (MEC) pushes its servers to the edge of the network much closer to the MUs. It jointly considers the communication and computation to optimize network performance by satisfying quality-of-service (QoS) and quality-of-experience (QoE) requirements. However, MEC usually faces a complex combinatorial optimization problem with the complexity of exponential scale. Moreover, many important parameters might be unknown a-priori due to the dynamic nature of the offloading environment and network topology. In this paper, to deal with the above issues, we introduce bandit learning (BL), which enables each agent (MU/server) to make a sequential selection from a set of arms (servers/MUs) and then receive some numerical rewards. BL brings extra benefits to the joint consideration of offloading decision and resource allocation in MEC, including the matched mechanism, situation awareness through learning, and adaptability. We present a brief tutorial on BL of different variations, covering the mathematical formulations and corresponding solutions. Furthermore, we provide several applications of BL in MEC, including system models, problem formulations, proposed algorithms and simulation results. At last, we introduce several challenges and directions in the future research of BL in 5G MEC.

A New Fast Ant Colony Optimization Algorithm: The Saltatory Evolution Ant Colony Optimization Algorithm

Various studies have shown that the ant colony optimization (ACO) algorithm has a good performance in approximating complex combinatorial optimization problems such as traveling salesman problem (TSP) for real-world applications. However, disadvantages such as long running time and easy stagnation still restrict its further wide application in many fields. In this study, a saltatory evolution ant colony optimization (SEACO) algorithm is proposed to increase the optimization speed. Different from the past research, this study innovatively starts from the perspective of near-optimal path identification and refines the domain knowledge of near-optimal path identification by quantitative analysis model using the pheromone matrix evolution data of the traditional ACO algorithm. Based on the domain knowledge, a near-optimal path prediction model is built to predict the evolutionary trend of the path pheromone matrix so as to fundamentally save the running time. Extensive experiment results on a traveling salesman problem library (TSPLIB) database demonstrate that the solution quality of the SEACO algorithm is better than that of the ACO algorithm, and it is more suitable for large-scale data sets within the specified time window. This means it can provide a promising direction to deal with the problem about slow optimization speed and low accuracy of the ACO algorithm.

Logistics Distribution Path Optimization Using Support Vector Machine Algorithm under Different Constraints

Accelerating product flow, improving service level, lowering logistics costs, reducing the possibility of product losses in circulation, and thus optimizing the logistics distribution system are the issues that enterprise managers should consider in logistics distribution. Traditional algorithms can only solve simple problems, while intelligent algorithms can solve the most complex combinatorial optimization problems. The optimization problem of logistics vehicle scheduling path with different constraints is studied in this paper using the SVM algorithm, and the improved algorithm is simulated to verify its effectiveness. The simulation results show that the logistics distribution path optimization method based on the SVM algorithm has good global searching ability, effectively avoids the algorithm falling into local optimum, and reduces total distribution cost, proving the algorithm’s effectiveness. This scheme can optimize vehicle routes, increase distribution efficiency, and reduce logistics costs, and it can be used in a wide range of logistics distribution route optimization applications.

Multi-operator immune genetic algorithm for project scheduling with discounted cash flows

The resource constrained project scheduling problem with discounted cash flows (RCPSPDC) is one of the most challenging problems owing to its NP-hard characteristics. This complex combinatorial optimization problem is most relevant to project management, building and construction management, and production planning. Although several solution methods have been suggested to solve the RCPSPDC, no single method has been shown to be the best for a wide range of problems. In this study, a multi-operator immune genetic algorithm, called MO-IGA, is proposed which integrates a genetic algorithm (GA) and an immune algorithm (IA) to solve the RCPSPDC. Two different operators for each crossover, mutation, immunization, and local search operation are utilized dynamically in the MO-IGA framework. Variable insertion neighborhood search (VINS) and forward–backward improvement (FBI) are utilized for local search to enrich the searching behavior and exploration. The algorithm starts with the same probability for each crossover, mutation, immunization, and local search operator; however, the probability is updated dynamically depending on the success of each operator in producing the quality solution. An activity move rule (AMR) has been utilized to delay the task with negative cash flows as much as possible, which further improves the overall project’s net present value (NPV). A standard benchmark dataset, comprising 17,280 project instances ranging from 25 to 100 activities, is used to test the performance and effectiveness of the proposed MO-IGA. The proposed MO-IGA outperforms several datasets based on both a lower value of the average percentage deviation and the number of feasible schedule generations. The proposed MO-IGA is also shown to be more effective than the multi-operator GA (MO-GA) and multi-operator IA (MO-IA). Extensive numerical analysis, statistical tests, and comparisons with state-of-the-art algorithms proves the effectiveness of the proposed approach.

Optimisation of multiple travelling salesman problem using metaheuristic methods

The problem of travelling salesmen (TSP) is a well-known task in the field of combinatorial optimisation. However, the problem of the multiple travelling salesman (mTSP), which extends the former, is a more challenging and complex combinatorial optimisation problem. This problem included addressing real-world issues where more than one salesman needed to be responsible for. This paper covered the use of heuristic approaches to tackle 180 cities and six travelling salesmen to reduce the path distances. To transform an mTSP into a TSP, a K-means clustering algorithm was used. Genetic algorithm (GA) was applied to the cluster after the clustering was done and iterated to provide the best possible value for distance following convergence. Now, with the ant colony optimisation (ACO) algorithm, every cluster was once again solved to determine the optimum distance value as a TSP. Once the two heuristic methods were applied, it became evident that due to the thorough analysis and constructive design of the algorithm, the ant colony optimisation algorithm yielded better results and more efficient tour than the genetic algorithm.

Satellite Observation and Data-Transmission Scheduling using Imitation Learning based on Mixed Integer Linear Programming

The Earth observation satellites (EOSs) scheduling problem is generally considered as a complex combinatorial optimization problem due to various technical constraints. It is significant to develop efficient computational frameworks to solve this problem. In this paper, an intelligent EOSs scheduling framework is developed using imitation learning based on mixed integer linear programming (MILP). The scheduling framework is composed of two processes: pre-processing, modeling and solving process. In the pre-processing process, an analytical method to generate the available time windows of an EOS is derived after considering the effects of Earth's <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$J_{2}$</tex-math></inline-formula> perturbation on the elliptic orbit. Based on the pre-processing results, this problem is formulated as an MILP model in the modeling process. In the solving process, a smart algorithm is proposed based on imitation learning for branch-and-bound to accelerate the solving process. Compared with normal imitation learning, a data selection method works in our algorithm to avoid potential misleading for learning. Besides, an iterative view is also adopted to improve the performance of the trained strategy. In the end, several real-world EOSs scheduling scenarios are investigated to demonstrate the reliability and high-efficiency of this framework.

Applications of Flower Pollination Algorithm in Electrical Power Systems: A Review

The use of metaheuristic, nature inspired algorithms for solving complex optimization problems with non-linearity and multimodality, has become a popular tool in the field of science and engineering. Presently, there has been much development of such tools, with academics creating new nature-inspired algorithms that could potentially be more efficient and effective. One such algorithm is the Flower Pollination Algorithm (FPA) developed by Xin-She Yang in 2012. This metaheuristic algorithm is modelled after the evolutionary process of flowering plants and has been useful in many fields of science and engineering, particularly in electrical power systems. With the rapid expansion of industries and population growth, engineers are faced with the arduous task of satisfying the growing electrical demand. To improve electrical power systems and reduce running costs, FPA and its variants have been implemented to determine optimal solutions to complex combinatorial optimization problems, with little computational effort, and has proven to be more effective than other popular metaheuristic algorithms, such as Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). Owing to its balanced global and local search capabilities, and better convergence characteristics, numerous studies have been conducted to utilize FPA and its variants in real-world optimization problems. Thus, this paper aims to provide a comprehensive review of FPA and its variants to successfully determine optimal results to non-deterministic polynomial-time hard problems in electrical power systems and other fields of science. To accomplish this, an in- depth description of FPA and its parameters that influence its performance are discussed, including the various modifications and hybridizations of the algorithm. In addition, an in- depth review of applications using FPA and its variants in electrical power systems and other fields of science, is provided.

Finding optimal path of feeder routing problem in power distribution network by an efficient and new methodology

Feeder routing is one of the most important and challenging problems of distribution network planning. Optimal feeder routing is a complex combinatorial optimization problem, which needs a superior optimization technique to be effectively solved. In such problem, minimization of investment cost and power losses subject to distribution network limitations is the main issue. In this article, differential crow search algorithm (CSAdif) is proposed to effectively solve feeder routing problem. CSAdif utilizes the strength of multiple high-quality solutions to determine search direction. Over a relatively large real system (SKED 61-bus distribution network), simulation results show superior performance of the proposed approach in comparison with original CSA and different variants of particle swarm optimization (PSO). The value of objective function is obtained 43 780 $ where the portion of investment and losses costs is 28 042 and 15 738 $, respectively. Moreover, in the optimal configuration, power losses and minimum voltage value are 42.80 kW and 0.982 p.u., respectively.

A novel quantum algorithm for ant colony optimisation

Ant colony optimisation (ACO) is a commonly used meta-heuristic to solve complex combinatorial optimisation problems like the travelling salesman problem (TSP), vehicle routing problem (VRP) etc. However, classical ACO algorithms provide better optimal solutions but do not reduce computation time overhead to a significant extent. Algorithmic speed-up can be achieved by using parallelism offered by quantum computing. Existing quantum algorithms to solve ACO are either quantum-inspired classical algorithms or hybrid quantum-classical algorithms. Since all these algorithms need the intervention of classical computing, leveraging the true potential of quantum computing on real quantum hardware remains a challenge. This study's main contribution is to propose a fully quantum algorithm to solve ACO, enhancing the quantum information processing toolbox in the fault-tolerant quantum computing (FTQC) era. We have solved the single source single destination (SSSD) shortest-path problem using our proposed adaptive quantum circuit for representing the dynamic pheromone-updating strategy in real IBMQ devices. Our quantum ACO technique can be further used as a quantum ORACLE to solve complex optimisation problems in a fully quantum setup with significant speed up upon the availability of more qubits.

Network Reconfiguration Based on an Edge-Cloud-Coordinate Framework and Load Forecasting

With the development of distributed energy resources (DERs), the power flow (PF) in the distribution network (DN) is changed from unidirectional to bidirectional, resulting in complex control and coordinate measures. Network reconfiguration (NR) is a feasible solution for the power grid side to deal with the complex PF. This paper proposed an edge-cloud-coordinated reconfiguration framework with edge servers (ESs) in the prosumer side and cloud servers (CSs) in the utility grid side, where the edge computing (EC) technology is implemented in ES to support load forecasting (LF), while cloud computing (CC) is used in CS to reconstruct the DN. LF is implemented by the long–short-term memory network to acquire the load information in advance, and the social preference of prosumers has been considered. The NR is formulated as a complex combinatorial optimization problem with the goal of minimizing power losses, while satisfying the power flow and voltage requirement. The NR problems are solved by the proposed advanced harmony search algorithm, which can find the optimal global solution, while satisfying the complex constraints of the NR problem. Numerical results are conducted based on an IEEE 33-bus network, which shows the high accuracy of LF and demonstrates the effectiveness of the proposed framework in terms of reducing more than 40% power losses and satisfying the voltage requirement.