Large-scale Combinatorial Problems Research Articles

Generalized Background Vector Method for Tailored Three-Dimensional Nonperiodic Woven Composite Designs

In critical aerospace applications such as Ceramic Matrix Composite structures, novel three-dimensional nonperiodic textile composite preforms hold great promise for creating advanced composite structures with strategically aligned fiber tows. However, the inherently challenging nature of determining tow locations, a large-scale combinatorial problem, presents a significant obstacle in textile architecture design. This study generalizes the previously developed Background Vector Method (BVM) to address diverse design requirements and constraints, effectively circumventing combinatorial design complexities via a game theoretic approach. This approach allows for the creation of tunable designs for woven architectures with complex geometries, such as channels and tapering features, through simple control parameter adjustments. The method demonstrates exceptional computational efficiency, making it suitable for large-scale nonperiodic textile structures. Case studies including woven sandwich and airfoil structures highlight the generalized BVM’s versatility and effectiveness in addressing complex design challenges within the aerospace sector.

A spinwave Ising machine

Time-multiplexed Coherent Ising Machines (CIMs) have demonstrated promising results in rapidly solving large-scale combinatorial problems. However, CIMs remain relatively large and power-demanding. Here, we demonstrate a spinwave-based Ising machine (SWIM) that due to the low spinwave group velocity allows for sufficient miniaturization and reduced power consumption. The SWIM is implemented using a 10-mm-long 5-μm-thick Yttrium Iron Garnet film with off-the-shelf microwave components and can support an 8-spin MAX-CUT problem and solve it in less than 4 μs consuming only 7 μJ. As the SWIM minimizes its energy, we observe that the spin states can demonstrate both uniform and domain-propagation-like switching. The developed SWIM has the potential for substantial further miniaturization with reduction of power consumption, scalability in the number of supported spins, increase of operational speed, and may become a versatile platform for commercially feasible high-performance solvers of combinatorial optimization problems.

Generalized Distribution Feeder Switching with Fuzzy Indexing for Energy Saving

The objective of this study is to analyze feeder loss minimization and load balance under given constrains. Effective methods are required for feeder switching/reconfiguration. Feeder switching is a mixed-integer large-scale combinatorial problem for optimization, not easily solvable with classical optimization techniques, especially involving a great number of switches. This paper proposes a fuzzy indexing algorithm for feeder switching, with membership functions defined for switches such as thermometers or indices. The optimal switches can be determined through fuzzy index operations. With membership functions defined, the developed method used numerical operations for indices instead of the “set” operation or the min-max operations of traditional fuzzy algorithms. The optimization problem becomes a simple numeric calculation instead of a large-scale sorting problem and is much faster than most algorithms. It greatly reduces the computation time and enhances efficiency, which is suitable for either planning or operation purposes. Many algorithms were tested with three typical examples chosen for illustration, including the “optimal” results with an exhausted search. It shows that the proposed algorithm is very effective and can balance the load to reduce the loss and costs in obtaining the solution.

Automated streamliner portfolios for constraint satisfaction problems

Constraint Programming (CP) is a powerful technique for solving large-scale combinatorial problems. Solving a problem proceeds in two distinct phases: modelling and solving. Effective modelling has a huge impact on the performance of the solving process. Even with the advance of modern automated modelling tools, search spaces involved can be so vast that problems can still be difficult to solve. To further constrain the model, a more aggressive step that can be taken is the addition of streamliner constraints, which are not guaranteed to be sound but are designed to focus effort on a highly restricted but promising portion of the search space. Previously, producing effective streamlined models was a manual, difficult and time-consuming task. This paper presents a completely automated process to the generation, search and selection of streamliner portfolios to produce a substantial reduction in search effort across a diverse range of problems. The results demonstrate a marked improvement in performance for both Chuffed, a CP solver with clause learning, and lingeling, a modern SAT solver.

Adaptive Sampling Simulated Annealing for the Synthesis of Disaggregate Mobility Data from Origin–Destination Matrices

Agent-based modelling has been suggested as a highly suitable approach for the tackling of future mobility challenges. However, the application of disaggregate models is often hindered by the high granularity of the required input. Recent research has suggested a combinatorial optimization-based framework to enable the conversion of typical origin–destination matrices (ODs) to suitable input for agent-based modelling (e.g., trip-chains, tours, or activity-schedules). Nonetheless, the combinatorial nature of the approach requires very efficient and scalable optimization processes to handle large-scale ODs. This study suggests an advanced optimization technique, coined as the adaptive sampling simulated annealing (ASSA) algorithm, able to exploit high-level calibration information (in the form of a joint distribution) for the efficient addressing of large-scale combinatorial problems. The proposed optimization algorithm was evaluated using high-level information about the departure profile, the types of activities, and the travel time of the expected output and a set of large-scale trip-purpose- and time-period-segmented OD matrices of 253,000 trips. The obtained results showcase the ability of the methodology to accurately and efficiently convert large-scale ODs into disaggregate mobility traces since the inputted ODs were converted into thousands of travel-demand equivalent, disaggregate mobility traces with an accuracy exceeding 90%. The implications are significant since the abundance of travel-demand information in ODs can be now exploited for the preparation of disaggregate mobility traces, suitable for sophisticated agent-based transport modelling.

A new three-dimensional encoding multiobjective evolutionary algorithm with application to the portfolio optimization problem

The existing evolutionary algorithm techniques have limited capabilities in solving large-scale combinatorial problems due to their large search space, making impractical the examination of big real-world instances. In this paper, we address this issue by introducing a new algorithm that incorporates a coding structure specially designed to keep the processing time invariant to the size of the examined test instance, allowing the consideration of large-scale problems for a fraction of time required by other techniques. We test the performance of the proposed algorithm to the optimal allocation of limited resources to a number of competing investment opportunities for optimizing the objectives. We believe that the proposed algorithm can be particularly useful in other contexts too, subject to adaptations relevant to specific problem requirements.

Ant colony algorithm for satellite control resource scheduling problem

With the increasing number of satellite, the satellite control resource scheduling problem (SCRSP) has been main challenge for satellite networks. SCRSP is a constrained and large scale combinatorial problem. More and more researches focus on how to allocate various measurement and control resources effectively to ensure the normal running of the satellites. However, the sparse solution space of SCRSP leads its complexity especially for traditional optimization algorithms. As the validity of ant colony optimization (ACO) has been shown in many combinatorial optimization problems, a simple ant colony optimization algorithm (SACO) to solve SCRSP is presented in this paper. Firstly, we give a general mathematical model of SCRSP. Then, a optimization model, called conflict construction graph, based on visible arc and working period is introduced to reduce workload of dispatchers. To meet the requirements of TT & C network and make the algorithm more practical, we make the parameters of SACO as constant, which include the bounds, update and initialization of pheromone. The effect of parameters on the algorithm performance is studied by experimental method based on SCRSP. Finally, the performance of SACO is compared with other novel ACO algorithms to show the feasibility and effectiveness of improvements.

Chaotic League Championship Algorithms

Classical optimization algorithms are insufficient in large-scale combinatorial problems and in nonlinear problems. Hence, heuristic optimization algorithms have been proposed. General purposed metaheuristic methods are evaluated in nine different groups: biology-based, physics-based, social-based, music-based, chemical-based, sports-based, mathematics-based, and hybrid methods which are combinations of these. Recently, a sports-based search and optimization algorithm entitled as league championship algorithm (LCA) has been proposed. LCA is a population-based, metaheuristic optimization algorithm that simulates a championship for general optimization with artificial teams and artificial league for several weeks. In this algorithm, according to the league program, a number is given to the couple of teams that will match and the result of match is determined as loser or winner. Winning or losing the game is closely related to power of teams. Teams are intended to improve the formation of the current team throughout the season to win the game in the coming weeks. Chaotic maps seem to improve the convergence speed and accuracy of optimization algorithms. Increasing global convergence speed and prevention of getting stuck on local solutions of LCA with chaos have been proposed for the first time in this study. In this paper, six different chaotic LCAs have been proposed and explained in detail. Comparative performance results have been examined in complex benchmark functions. Promising results have been obtained from the experimental results. Combining results appeared in different fields like LCA and complex dynamics can increase quality in some optimization problems and the chaos can be the wanted process.

Plant intelligence based metaheuristic optimization algorithms

Classical optimization algorithms are insufficient in large scale combinatorial problems and in nonlinear problems. Hence, metaheuristic optimization algorithms have been proposed. General purpose metaheuristic methods are evaluated in nine different groups: biology-based, physics-based, social-based, music-based, chemical-based, sport-based, mathematics-based, swarm-based, and hybrid methods which are combinations of these. Studies on plants in recent years have showed that plants exhibit intelligent behaviors. Accordingly, it is thought that plants have nervous system. In this work, all of the algorithms and applications about plant intelligence have been firstly collected and searched. Information is given about plant intelligence algorithms such as Flower Pollination Algorithm, Invasive Weed Optimization, Paddy Field Algorithm, Root Mass Optimization Algorithm, Artificial Plant Optimization Algorithm, Sapling Growing up Algorithm, Photosynthetic Algorithm, Plant Growth Optimization, Root Growth Algorithm, Strawberry Algorithm as Plant Propagation Algorithm, Runner Root Algorithm, Path Planning Algorithm, and Rooted Tree Optimization.

P-graph methodology for Bi-objective optimisation of bioenergy supply chains: Economic and safety perspectives

Widespread adoption of bioenergy for electricity generation could lead to a globally greener environment, with significant climatic and waste management benefits. Numerous methodologies have been developed to optimize the performance of bioenergy supply chains with different objective functions (e.g., profitability, carbon footprint, etc.) usually based on conventional optimization techniques. Such techniques are usually based on single-objective formulations, and are able to determine unique optimal solutions. Process graph (P-graph) is a graph-theoretic methodology which has been applied towards various network optimization problems in different domains. It offers advantages of computational efficiency for large-scale combinatorial problems, as well as the capability to identify both optimal and near-optimal solutions; the latter feature is especially good for decision-makers in practical applications. This paper presents an approach to the planning of bioenergy supply chains, taking into account both total cost minimization and supply chain risk reduction. The supply chain risk is accounted for in terms of transportation fatalities computed in an actuarial manner. An illustrative example based on Malaysian palm-based bioenergy supply chain is solved to illustrate the proposed approach.

A strategic conflict avoidance approach based on cooperative coevolutionary with the dynamic grouping strategy

Conflict avoidance plays a crucial role in guaranteeing the safety and efficiency of the air traffic management system. Recently, the strategic conflict avoidance (SCA) problem has attracted more and more attention. Taking into consideration the large-scale flight planning in a global view, SCA can be formulated as a large-scale combinatorial optimisation problem with complex constraints and tight couplings between variables, which is difficult to solve. In this paper, an SCA approach based on the cooperative coevolution algorithm combined with a new decomposition strategy is proposed to prevent the premature convergence and improve the search capability. The flights are divided into several groups using the new grouping strategy, referred to as the dynamic grouping strategy, which takes full advantage of the prior knowledge of the problem to better deal with the tight couplings among flights through maximising the chance of putting flights with conflicts in the same group, compared with existing grouping strategies. Then, a tuned genetic algorithm (GA) is applied to different groups simultaneously to resolve conflicts. Finally, the high-quality solutions are obtained through cooperation between different groups based on cooperative coevolution. Simulation results using real flight data from the China air route network and daily flight plans demonstrate that the proposed algorithm can reduce the number of conflicts and the average delay effectively, outperforming existing approaches including GAs, the memetic algorithm, and the cooperative coevolution algorithms with different well-known grouping strategies.

An efficient ensemble pruning algorithm using One-Path and Two-Trips searching approach

Ensemble pruning is substantial for the successful application of an ensemble system. A novel method for Ensemble Pruning via BackTracking algorithm (EnPBT) was proposed by us in our previous work. Backtracking algorithm can systematically search for the solutions of a problem in a depth-first and jumping manner, suitable for solving all those large-scale combinatorial problems. The validity of EnPBT algorithm has been verified in our previous work. However, the relatively slow pruning speed might be a drawback of EnPBT. Aiming at this problem, an efficient and novel ensemble pruning algorithm is proposed in this paper, i.e. One-Path and Two-Trips (OPTT) ensemble pruning algorithm. It is very fast in pruning speed, while its classification performance has no significant difference with EnPBT, as demonstrated in the experimental results of this work. In short, OPTT achieves a proper trade-off between pruning effectiveness and efficiency.

An Improved Simulated Annealing Algorithm for Real-Time Dynamic Job-Shop Scheduling

Job-shop scheduling is one of the core research aspects of Manufacturing Execution System (MES). It is significant for improving the utilization of enterprise resources, enhancing product quality, shortening delivery periods, reducing product cost, and raising enterprise competitive power in market economy. In order to solve this problem, Simulated Annealing (SA) algorithm is improved to solve large-scale combinatorial problem of job-shop scheduling. To make the SA algorithm more effective to solve job-shop scheduling problems, a solution encoding mode, scheduling scheme generation, initial temperature selection, temperature updating function, Markov chain length, end rule, and so on of the improved SA algorithm are discussed that affect the computation speed and convergence of the SA algorithm. Finally, the improved SA algorithm is validated by a job–shop scheduling problem of 10 workpieces and 10 machines.

A continuous framework for open pit mine planning

This paper proposes a new mathematical framework for the open pit mine planning problem, based on continuous functional analysis. The main challenge for engineers is to determine a sequence of nested profiles maximizing the net present value of the mining operation. The traditional models for this problem have been constructed by using binary decision variables, giving rise to large-scale combinatorial and Mixed Integer Programming problems. Instead, we use a continuous approach which allows for a refined imposition of slope constraints associated with geotechnical stability. The framework introduced here is posed in a suitable functional space, essentially the real-valued functions that are Lipschitz continuous on a given two dimensional bounded region. We derive existence results and investigate qualitative properties of the solutions.

A study on bacterial colony chemotaxis algorithm and simulation based on differential strategy

Bacterial colony chemotaxis (BCC) algorithm is one of the new heuristic algorithms based on colony intelligence. The algorithm much improves the convergence speed of bacterial colony (BC) algorithm while possessing the strong searching ability of a single bacterium. To further enhance the ability of breaking away from the local optimum on multimodal function, two improvements are presented, one is adjusting the sense limit (SL) self-adaptively and the other is introducing differential evolutionary strategy into algorithm. Large amounts of numerical experiments simulation show that the performances of the improved BCC algorithm have been enhanced in success rate, convergence precision and the ability of breaking away from the local optimum. The improved BCC algorithm applied to substation planning problem which is a multi-constraint, multi-objective, large-scale and non-linear combinatorial optimisation problem has good performance of global convergence and better convergence speed.

Item-Location Assignment Using Fuzzy Logic Guided Genetic Algorithms

In today's logistics environment, large-scale combinatorial problems will inevitably be met during industrial operations. This paper deals with a novel real-world optimization problem, called the item-location assignment problem, faced by a logistics company in Shenzhen, China. The objective of the company in this particular operation is to assign items to suitable locations such that the required sum of the total traveling time of the workers to complete all orders is minimized. A stochastic search technique called fuzzy logic guided genetic algorithms (FLGA) is proposed to solve this operational problem. In GA, a specially designed crossover operation, called a shift and uniform based multi-point (SUMP) crossover, and swap mutation are adopted. The performance of this novel crossover operation is tested and is shown to be more effective by comparing it to other crossover methods. Furthermore, the role of fuzzy logic is to dynamically adjust the crossover and mutation rates after each ten consecutive generations. In order to demonstrate the effectiveness of the FLGA and make comparisons with the FLGA through simulations, various search methods such as branch and bound, standard GA (i.e., without the guide of fuzzy logic), simulated annealing, tabu search, differential evolution, and two modified versions of differential evolution are adopted. Results show that the FLGA outperforms the other search methods in all of the three considered scenarios.

Guest Editors' Introduction: Advanced Heuristics in Transportation and Logistics

Transportation and logistics organizations often face large-scale combinatorial problems on both operational and strategic levels. By exploiting problem-specific characteristics, classical heuristic methods--such as constructive and iterative local search methods--aim at a relatively limited exploration of the search space, thereby producing acceptable-quality solutions in modest computing times. In a major departure from a classical heuristic, a metaheuristic method exploits not only the problem characteristics but also ideas based on artificial intelligence methodologies, such as different types of memory structures and learning mechanisms, as well as analogies with optimization methods found in nature. Solutions produced by metaheuristics typically are of a much higher quality than those obtained with classical heuristic approaches.This article is part of a special issue on advanced heuristics in transportation and logistics.

A novel eigenvector technique for Large Scale combinatorial problems in VLSI layout

Modern integrated circuit design involves laying out circuits which consist of millions of switching elements or transistors. Due to the sheer complexity, optimizing the connectivity between transistors is a very difficult problem. How a circuit is interconnected is the single most important factor in performance criteria such as signal delay, power dissipation, circuit size and cost. These factors dictate that interconnections-wires, be made as short as possible. The wire-minimization problem is formulated as a sequence of discrete optimization subproblems. These problems are known to be NP-hard, hence they can only be solved approximately using metaheuristics or linear programming techniques. Nevertheless, these methods are computationally expensive and the quality of solution depends to a great extent on an appropriate choice of starting configuration. A matrix reordering technique for solving very hard discrete optimization problems in Very Large Scale Integrated (VLSI) design which overcomes some of these shortcomings is proposed. In particular, the computational cost is reasonable-of the order of n 1.4 running time.

Tabu search algorithm for network synthesis

Large scale combinatorial problems such as the network expansion problem present an amazingly high number of alternative configurations with practically the same investment, but with substantially different structures (configurations obtained with different sets of circuit/transformer additions). The proposed parallel tabu search algorithm has shown to be effective in exploring this type of optimization landscape. The algorithm is a third generation tabu search procedure with several advanced features. This is the most comprehensive combinatorial optimization technique available for treating difficult problems such as the transmission expansion planning. The method includes features of a variety of other approaches such as heuristic search, simulated annealing and genetic algorithms. In all test cases studied there are new generation, load sites which can be connected to an existing main network: such connections may require more than one line, transformer addition, which makes the problem harder in the sense that more combinations have to be considered.

Municipal Solid Waste Collection: An Effective Data Structure For Solving The Sectorization Problem With Local Search Methods

This paper deals with the crucial sectorization problem regarding household waste collection. Our purpose is to construct a fixed number of sectors which should be balanced with respect to daily total time for collection tasks. First, we propose a model and point out that our taking into account the number of connected components of each sector results in a complex large-scale combinatorial problem. Second, we present a new effective data structure, called the sectorization matrix, which allows sectors and economic updates to be suitably representated. Finally, considering two approximate versions of the original model, we advance that the initial numerical experiments indicate that basic local search methods using moves relying on this data structure can improve a feasible solution initially given by the planner, within reasonable time requirements.