Large-scale Combinatorial Optimization Research Articles

Optimizing Transport Logistics under Uncertainty with Simheuristics: Concepts, Review and Trends

Background: Uncertainty conditions have been increasingly considered in optimization problems arising in real-life transportation and logistics activities. Generally, the analysis of complex systems in these non-deterministic environments is approached with simulation techniques. However, simulation is not an optimization tool. Hence, it must be combined with optimization methods when our goal is to: (i) minimize operating costs while guaranteeing a given quality of service; or (ii) maximize system performance using limited resources. When solving NP-hard optimization problems, the use of metaheuristics allows us to deal with large-scale instances in reasonable computation times. By adding a simulation layer to the metaheuristics, the methodology becomes a simheuristic, which allows the optimization element to solve scenarios under uncertainty. Methods: This paper reviews the indexed documents in Elsevier Scopus database of both initial as well as recent applications of simheuristics in the logistics and transportation field. The paper also discusses open research lines in this knowledge area. Results: The simheuristics approaches to solving NP-hard and large-scale combinatorial optimization problems under uncertainty scenarios are discussed, as they frequently appear in real-life applications in logistics and transportation activities. Conclusions: The way in which the different simheuristic components interact puts a special emphasis in the different stages that can contribute to make the approach more efficient from a computational perspective. There are several lines of research that are still open in the field of simheuristics.

Solution of Multi-Crew Depots Railway Crew Scheduling Problems: The Chinese High-Speed Railway Case

This paper presents a novel mathematical formulation in crew scheduling, considering real challenges most railway companies face such as roundtrip policy for crew members joining from different crew depots and stricter working time standards under a sustainable development strategy. In China, the crew scheduling is manually compiled by railway companies respectively, and the plan quality varies from person to person. An improved genetic algorithm is proposed to solve this large-scale combinatorial optimization problem. It repairs the infeasible gene fragments to optimize the search scope of the solution space and enhance the efficiency of GA. To investigate the algorithm’s efficiency, a real case study was employed. Results show that the proposed model and algorithm lead to considerable improvement compared to the original planning: (i) Compared with the classical metaheuristic algorithms (GA, PSO, TS), the improved genetic algorithm can reduce the objective value by 4.47%; and (ii) the optimized crew scheduling plan reduces three crew units and increases the average utilization of crew unit working time by 6.20% compared with the original plan.

Implementasi Metode Tabu Search Dalam Penjadwalan Menggunakan Analisa Pieces

Nowadays, Scheduling subjects is one of the first steps for starting the teaching and learning process in educational institutions. To do so, The role of teachers and school staff is very important and not easy because it takes a long time to compile it. SMK PGRI 4 Denpasar is one of the schools located in the city of Denpasar which is located on Jalan Kebo Iwa No 8, Padangsambian Kaja, Denpasar, Bali. It is a vocational high school that has a tourism expertise and computer engineering study program. Based on current results of observations and interviews, the process of making the subject schedules that run at SMK PGRI 4 Denpasar is still being done using Microsoft Excel, this has resulted in frequent errors in managing schedules such as conflicting schedule and it takes a long time to correct it. Tabu Search is an optimization method based on local search, where the search process moves from one solution to the next by selecting the best solution which is not classified as a prohibited solution. It is a combinatorial optimization problem-solving method that is incorporated into local search methods. This method aims to streamline the process of finding the best solution of a large-scale (np-hard) combinatorial optimization problem. Tabu search method to optimize the process of making the subject schedule and combined using PIECES analysis (Performance, Information, Economic, Control, Efficiency, Services). From this analysis, several problems will be obtained, which in the end can be identified clearly and more specifically, so that we can conclude some suggestions that will help in designing a new and better system. The Tabu Search method can be used to optimize the process of making the subject schedules at SMK PGRI 4 Denpasar, so that the scheduling process will be more easier than using Microsoft Excel.

A Knowledge Transfer Based Scheduling Algorithm for Large-Scale Refinery Production

Decomposition algorithms for large-scale refinery scheduling problems commonly adopt the spatially dividing method. When the scheduling horizon further enlarges, the sizes of the resulting subproblems exponentially grow, leading to the performance degradation of the decomposition algorithms. In this article, to solve this issue about subproblem size caused by the long-time scheduling horizon, a knowledge transfer based algorithm is proposed, where the size of subproblems is constant and a novel concept of product flowrate is introduced to transfer operation knowledge from tractable small-scale short-time problems to intractable large-scale long-time problems to quickly obtain a satisfactory solution for large-scale problems. Experimental results show that the proposed algorithm can achieve better solutions within 10−44 s for large-scale refinery scheduling problems with 50−200 time slots (the existing model is with less than 30 time slots), compared to the CPLEX solver with a running time of 3600 s and the existing evolutionary algorithm with a running time of 100−500 s. The results also show that, at present, the heuristic method (the essence of the proposed algorithm) is the main tool to solve large-scale combinatorial optimization problems, and even in the CPLEX solver, the heuristic is also the most active part.

Hybrid quantum annealing via molecular dynamics

A novel quantum–classical hybrid scheme is proposed to efficiently solve large-scale combinatorial optimization problems. The key concept is to introduce a Hamiltonian dynamics of the classical flux variables associated with the quantum spins of the transverse-field Ising model. Molecular dynamics of the classical fluxes can be used as a powerful preconditioner to sort out the frozen and ambivalent spins for quantum annealers. The performance and accuracy of our smooth hybridization in comparison to the standard classical algorithms (the tabu search and the simulated annealing) are demonstrated by employing the MAX-CUT and Ising spin-glass problems.

Reconfiguration of Electric Power Distribution Systems: Comprehensive Review and Classification

Distribution systems play an important role, delivering the electric power of generation system to individual consumers. Distribution system reconfiguration (DSR) is a large-scale combinatorial optimization problem. For the last 45 years, the DSR problem has been widely studied; nowadays, DSR, combined with new challenges, is being highly investigated, as researchers aim to reach a better solution. This paper presents a complete review and classification of the most significant works to date, providing a literary framework for DSR specialists. A categorization of solution methods, case studies, and novelties of the most relevant works regarding DSR are provided. In order to establish a complete background, not only traditional approaches, but also those involving uncertainty, reliability, electricity market, power quality, distributed generation, capacitor placement, and switching time in DSR are highlighted. This framework can help researches to improve previous formulations and methods and can propose more efficient models to better exploit the existing infrastructure.

A Parallel Bioinspired Algorithm for Chinese Postman Problem Based on Molecular Computing

The Chinese postman problem is a classic resource allocation and scheduling problem, which has been widely used in practice. As a classical nondeterministic polynomial problem, finding its efficient algorithm has always been the research direction of scholars. In this paper, a new bioinspired algorithm is proposed to solve the Chinese postman problem based on molecular computation, which has the advantages of high computational efficiency, large storage capacity, and strong parallel computing ability. In the calculation, DNA chain is used to properly represent the vertex, edge, and corresponding weight, and then all possible path combinations are effectively generated through biochemical reactions. The feasible solution space is obtained by deleting the nonfeasible solution chains, and the optimal solution is solved by algorithm. Then the computational complexity and feasibility of the DNA algorithm are proved. By comparison, it is found that the computational complexity of the DNA algorithm is significantly better than that of previous algorithms. The correctness of the algorithm is verified by simulation experiments. With the maturity of biological operation technology, this algorithm has a broad application space in solving large‐scale combinatorial optimization problems.

A Formation Reconfiguration Algorithm for Multi‐UAVs Based on Distributed Cooperative Coevolutionary with an Adaptive Grouping Strategy

The Formation reconfiguration problem plays a crucial role in the implementation of complex tasks for multiple unmanned aerial vehicles, which attracted increasing attention in the past decade. Taking into consideration the control parameters and time discretization of the multi-UAVs in the 3 Dimensional (3-D) space, the formation reconfiguration problem can be formulated as a large-scale combinatorial optimization problem with complex constraints and tight couplings between variables. The problem results in the reduction in efficiency and effectiveness using classic bio-inspired algorithms. In this paper, a formation reconfiguration method based on cooperative coevolutionary algorithm is proposed along with a new decomposition strategy to improve the optimization capability and prevent premature convergence. In the proposed approach, variables of multi-UAV are divided into several sub-groups based on an adaptive grouping strategy. The proposed strategy groups the variables in order to better deal with the tight coupling among them, taking into account the variables' variance and multi-UAVs characteristics of the formation reconfiguration problem. Therefore, each subgroup can adopt the Self-adaptive differential evolution strategy with neighborhood search (SaNSDE) with the aim to optimize the UAV's control inputs using multithreaded programming. SaNSDE contributes to calculating the results in a fully distributed and paralleled manner. Optimal solution is then obtained through cooperation and coordination with all subcomponents. Simulation results based on extreme scenarios adopted by previous researches demonstrate that the proposed algorithm outperformed the existing approaches including Particle swarm optimization (PSO), Differential evolution (DE), and the cooperative coevolution algorithms with different well-known grouping strategies.

Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems

Combinatorial optimization assumes that all parameters of the optimization problem, e.g. the weights in the objective function, are fixed. Often, these weights are mere estimates and increasingly machine learning techniques are used to for their estimation. Recently, Smart Predict and Optimize (SPO) has been proposed for problems with a linear objective function over the predictions, more specifically linear programming problems. It takes the regret of the predictions on the linear problem into account, by repeatedly solving it during learning. We investigate the use of SPO to solve more realistic discrete optimization problems. The main challenge is the repeated solving of the optimization problem. To this end, we investigate ways to relax the problem as well as warm-starting the learning and the solving. Our results show that even for discrete problems it often suffices to train by solving the relaxation in the SPO loss. Furthermore, this approach outperforms the state-of-the-art approach of Wilder, Dilkina, and Tambe. We experiment with weighted knapsack problems as well as complex scheduling problems, and show for the first time that a predict-and-optimize approach can successfully be used on large-scale combinatorial optimization problems.

A pointer network based deep learning algorithm for unconstrained binary quadratic programming problem

Combinatorial optimization problems have been widely used in various fields. And many types of combinatorial optimization problems can be generalized into the model of unconstrained binary quadratic programming (UBQP). Therefore, designing an effective and efficient algorithm for UBQP problems will also contribute to solving other combinatorial optimization problems. Pointer network is an end-to-end sequential decision structure and combines with deep learning technology. With the utilization of the structural characteristics of combinatorial optimization problems and the ability to extract the rule behind the data by deep learning, pointer network has been successfully applied to solve several classical combinatorial optimization problems. In this paper, a pointer network based algorithm is designed to solve UBQP problems. The network model is trained by supervised learning (SL) and deep reinforcement learning (DRL) respectively. Trained pointer network models are evaluated by self-generated benchmark dataset and ORLIB dataset respectively. Experimental results show that pointer network model trained by SL has strong learning ability to specific distributed dataset. Pointer network model trained by DRL can learn more general distribution data characteristics. In other words, it can quickly solve problems with great generalization ability. As a result, the framework proposed in this paper for UBQP has great potential to solve large scale combinatorial optimization problems.

An alpha matting algorithm based on collaborative swarm optimization for high-resolution images

High-resolution image matting is one of the challenges in image composition and foreground extraction. It is essentially a large-scale combinatorial optimization problem for foreground/background pixel pairs. However, little attention has been paid to this issue. A multiclass collaborative optimization strategy based on RGB color clustering is proposed to reduce the dimension of this problem, addressing the issues caused by its ultrahigh dimension. This paper presents a collaborative feedback grouping strategy to solve this large-scale combinatorial optimization problem. Based on these two strategies, a competitive swarm optimization algorithm based on group collaboration (GC-CSO) is proposed. Its performance is verified experimentally by using an alpha matting dataset, showing that it can significantly reduce the dimension of the image matting problem and outperform the existent large-scale optimization algorithms with grouping strategies in the alpha matte comparison.

A Deep Learning Algorithm for the Max-Cut Problem Based on Pointer Network Structure with Supervised Learning and Reinforcement Learning Strategies

The Max-cut problem is a well-known combinatorial optimization problem, which has many real-world applications. However, the problem has been proven to be non-deterministic polynomial-hard (NP-hard), which means that exact solution algorithms are not suitable for large-scale situations, as it is too time-consuming to obtain a solution. Therefore, designing heuristic algorithms is a promising but challenging direction to effectively solve large-scale Max-cut problems. For this reason, we propose a unique method which combines a pointer network and two deep learning strategies (supervised learning and reinforcement learning) in this paper, in order to address this challenge. A pointer network is a sequence-to-sequence deep neural network, which can extract data features in a purely data-driven way to discover the hidden laws behind data. Combining the characteristics of the Max-cut problem, we designed the input and output mechanisms of the pointer network model, and we used supervised learning and reinforcement learning to train the model to evaluate the model performance. Through experiments, we illustrated that our model can be well applied to solve large-scale Max-cut problems. Our experimental results also revealed that the new method will further encourage broader exploration of deep neural network for large-scale combinatorial optimization problems.

A 2 $\times$ 30k-Spin Multi-Chip Scalable CMOS Annealing Processor Based on a Processing-in-Memory Approach for Solving Large-Scale Combinatorial Optimization Problems

The world’s first 2 $\times $ 30k-spin multi-chip CMOS annealing processor (AP)—based on the processing-in-memory approach for solving large-scale combinatorial optimization problem—was developed. To expand the bit width of coefficients and enhance the scalability of the AP, it has three key features: an expandable and high-accuracy spin operator for local communication, a highly integrated spin circuit using direct access to SRAM, and a low-latency inter-chip interface that does not affect the runtime or results of the annealing process. The AP is fabricated on the basis of 40-nm CMOS technology. It was experimentally demonstrated that the spin-flip ratio of the processor agrees well with theoretical values based on the Gibbs distribution over a wide temperature range. As a result, under two-chip operation with 2 $\times $ 30k spins, the AP achieves an annealing time of 22 $\mu \text{s}$ , which is 455 times and 2.6 $\times $ 104 times faster than those achieved by our previous CMOS-AP and a conventional CPU, respectively. Moreover, its energy efficiency is 1.75 $\times $ 105 times higher than that of a conventional CPU-based algorithm.

Distributed Submodular Minimization and Motion Planning Over Discrete State Space

We develop a framework for the distributed minimization of submodular functions. Submodular functions are a discrete analog of convex functions and are extensively used in large-scale combinatorial optimization problems. While there has been a significant interest in the distributed formulations of convex optimization problems, distributed minimization of submodular functions has received relatively little research attention. Our framework relies on an equivalent convex reformulation of a submodular minimization problem, which is efficiently computable. We then use this relaxation to exploit methods for the distributed optimization of convex functions. The proposed framework is applicable to submodular set functions as well as to a wider class of submodular functions defined over certain lattices. We also propose an approach for solving distributed motion-planning problems in discrete state space based on submodular function minimization. We establish through a challenging setup of the capture the flag game that submodular functions over lattices can be used to design artificial potential fields for multiagent systems with discrete inputs. These potential fields are designed such that their minima correspond to desired behaviors, that is, agents are attracted toward their goals and are repulsed from obstacles and from each other for collision avoidance. Finally, we demonstrate that the proposed distributed framework can be employed effectively for generating feasible trajectories in such motion coordination problems.

Binary optimization by momentum annealing.

One of the vital roles of computing is to solve large-scale combinatorial optimization problems in a short time. In recent years, methods have been proposed that map optimization problems to ones of searching for the ground state of an Ising model by using a stochastic process. Simulated annealing (SA) is a representative algorithm. However, it is inherently difficult to perform a parallel search. Here we propose an algorithm called momentum annealing (MA), which, unlike SA, updates all spins of fully connected Ising models simultaneously and can be implemented on GPUs that are widely used for scientific computing. MA running in parallel on GPUs is 250 times faster than SA running on a modern CPU at solving problems involving 100000 spin Ising models.

Optimization design of reconfiguration algorithm for high voltage power distribution network based on ant colony algorithm

Abstract Distribution network reconfiguration is a very complex and large-scale combinatorial optimization problem. In network reconfiguration, whether an effective solution can be obtained is a key issue. Aiming at the problems in network reconstruction by traditional algorithm, such as long time required, more times of power flow calculation and high network loss, a network optimization design algorithm based on improved ant colony algorithm for high voltage power distribution network is proposed. After analyzing the operating characteristics of the high voltage power distribution network, the network topology of the high voltage power distribution network is described by constructing a hierarchical variable-structure distribution network model. A mathematical model of distribution network reconstruction considering the opportunity constraint with the minimum network loss as the objective function is established. The power flow distribution is calculated by using the pre-push back-generation method combined with the hierarchical structure of the distribution network. The maximum and minimum ant colony algorithm is introduced to improve the pheromone updating method of the traditional ant colony algorithm, and the search range is expanded, so that the algorithm can jump out of the local optimization trap to realize the accurate solution of the power distribution network reconstruction model. The experimental results show that compared with the current network reconstruction algorithm, the proposed algorithm requires less time for convergence, less power flow calculation, and lower network loss.

Stabilized Benders Methods for Large-Scale Combinatorial Optimization, with Application to Data Privacy

The cell-suppression problem (CSP) is a very large mixed-integer linear problem arising in statistical disclosure control. However, CSP has the typical structure that allows application of the Benders decomposition, which is known to suffer from oscillation and slow convergence, compounded with the fact that the master problem is combinatorial. To overcome this drawback, we present a stabilized Benders decomposition whose master is restricted to a neighborhood of successful candidates by local-branching constraints, which are dynamically adjusted, and even dropped, during the iterations. Our experiments with synthetic and real-world instances with up to 24,000 binary variables, 181 million (M) continuous variables, and 367M constraints show that our approach is competitive with both the current state-of-the-art code for CSP and the Benders implementation in CPLEX 12.7. In some instances, stabilized Benders provided a very good solution in less than 1 minute, whereas the other approaches found no feasible solution in 1 hour. This paper was accepted by Yinyu Ye, optimization.

A large-scale multi-objective flights conflict avoidance approach supporting 4D trajectory operation

Recently, the long-term conflict avoidance approaches based on large-scale flights scheduling have attracted much attention due to their ability to provide solutions from a global point of view. However, current approaches which focus only on a single objective with the aim of minimizing the total delay and the number of conflicts, cannot provide controllers with variety of optional solutions, representing different tradeoffs. Furthermore, the flight track error is often overlooked in the current research. Therefore, in order to make the model more realistic, in this paper, we formulate the long-term conflict avoidance problem as a multi-objective optimization problem, which minimizes the total delay and reduces the number of conflicts simultaneously. As a complex air route network needs to accommodate thousands of flights, the problem is a large-scale combinatorial optimization problem with tightly coupled variables, which make the problem difficult to deal with. Hence, in order to further improve the search capability of the solution algorithm, a cooperative co-evolution (CC) algorithm is also introduced to divide the complex problem into several low dimensional sub-problems which are easier to solve. Moreover, a dynamic grouping strategy based on the conflict detection is proposed to improve the optimization efficiency and to avoid premature convergence. The well-known multi-objective evolutionary algorithm based on decomposition (MOEA/D) is then employed to tackle each sub-problem. Computational results using real traffic data from the Chinese air route network demonstrate that the proposed approach obtained better non-dominated solutions in a more effective manner than the existing approaches, including the multi-objective genetic algorithm (MOGA), NSGAII, and MOEA/D. The results also show that our approach provided satisfactory solutions for controllers from a practical point of view.

Nonlinear Dynamic Model-Based Multiobjective Sensor Network Design Algorithm for a Plant with an Estimator-Based Control System

A novel sensor network design (SND) algorithm is developed for maximizing process efficiency while minimizing sensor network cost for a nonlinear dynamic process with an estimator-based control system. The multiobjective optimization problem is solved following a lexicographic approach where the process efficiency is maximized first followed by minimization of the sensor network cost. The partial net present value, which combines the capital cost due to the sensor network and the operating cost due to deviation from the optimal efficiency, is proposed as an alternative objective. The unscented Kalman filter is considered as the nonlinear estimator. The large-scale combinatorial optimization problem is solved using a genetic algorithm. The developed SND algorithm is applied to an acid gas removal (AGR) unit as part of an integrated gasification combined cycle (IGCC) power plant with CO2 capture. Due to the computational expense, a reduced order nonlinear model of the AGR process is identified and parallel ...

Biased randomization of heuristics using skewed probability distributions: A survey and some applications

Randomized heuristics are widely used to solve large scale combinatorial optimization problems. Among the plethora of randomized heuristics, this paper reviews those that contain biased-randomized procedures (BRPs). A BRP is a procedure to select the next constructive ‘movement’ from a list of candidates in which their elements have different probabilities based on some criteria (e.g., ranking, priority rule, heuristic value, etc.). The main idea behind biased randomization is the introduction of a slight modification in the greedy constructive behavior that provides a certain degree of randomness while maintaining the logic behind the heuristic. BRPs can be categorized into two main groups according to how choice probabilities are computed: (i) BRPs using an empirical bias function; and (ii) BRPs using a skewed theoretical probability distribution. This paper analyzes the second group and illustrates, throughout a series of numerical experiments, how these BRPs can benefit from parallel computing in order to significantly outperform heuristics and even simple metaheuristic approaches, thus providing reasonably good solutions in ‘real time’ to different problems in the areas of transportation, logistics, and scheduling.