Complex Combinatorial Optimization Problem Research Articles

Combinatorial optimization approach for the efficient reuse of RC components

AbstractThe reuse of reinforced concrete (RC) components from deconstructed buildings offers a promising approach to reduce the environmental impact of new constructions. However, it represents a complex combinatorial optimization problem to efficiently place the available modules, which vary in geometry and load‐bearing capacity, into new structures while maximizing their utilization. This paper proposes a two‐stage optimization method to enable the reuse of arbitrary RC modules. First, an agent‐based model is employed to rapidly explore feasible geometric combinations of modules and preselect suitable placements based on a target span length. Second, metaheuristic optimization algorithms, namely Simulated Annealing and Tabu Search, are adapted to maximize the utilization of the modules' load‐bearing capacity while ensuring global structural integrity. The methods are demonstrated on a case study of assembling a three‐span continuous beam. Lacking real data of dismantled RC elements, a construction kit of 100 modules with varying cross‐sectional properties and material parameters is artificially sampled. The results show the agent‐based preselection effectively finds viable geometric combinations, while the metaheuristics converge on optimized module placements with up to 88% utilization on average. The proposed approach provides a computational framework to enable the direct reuse of structural concrete components, supporting the design of low‐carbon circular buildings.

Highly durable and energy‐efficient probabilistic bits based on h‐BN/SnS2 interface for integer factorization

AbstractAs social networks and related data processes have grown exponentially in complexity, the efficient resolution of combinatorial optimization problems has become increasingly crucial. Recent advancements in probabilistic computing approaches have demonstrated significant potential for addressing these problems more efficiently than conventional deterministic computing methods. In this study, we demonstrate a highly durable probabilistic bit (p‐bit) device utilizing two‐dimensional materials, specifically hexagonal boron nitride (h‐BN) and tin disulfide (SnS2) nanosheets. By leveraging the inherently stochastic nature of electron trapping and detrapping at the h‐BN/SnS2 interface, the device achieves durable probabilistic fluctuations over 108 cycles with minimal energy consumption. To mitigate the static power consumption, we integrated an active switch in series with a p‐bit device, replacing conventional resistors. Furthermore, employing the pulse width as the control variable for probabilistic switching significantly enhances noise immunity. We demonstrate the practical application of the proposed p‐bit device in implementing invertible Boolean logic gates and subsequent integer factorization, highlighting its potential for solving complex combinatorial optimization problems and extending its applicability to real‐world scenarios such as cryptographic systems.image

Robust Optimization for Cooperative Task Assignment of Heterogeneous Unmanned Aerial Vehicles with Time Window Constraints

The cooperative task assignment problem with time windows for heterogeneous multiple unmanned aerial vehicles is an attractive complex combinatorial optimization problem. In reality, unmanned aerial vehicles’ fuel consumption exhibits uncertainty due to environmental factors or operational maneuvers, and accurately determining the probability distributions for these uncertainties remains challenging. This paper investigates the heterogeneous multiple unmanned aerial vehicle cooperative task assignment model that incorporates time window constraints under uncertain environments. To model the time window constraints, we employ the big-M method. To address the uncertainty in fuel consumption, we apply an adjustable robust optimization approach combined with duality theory, which allows us to derive the robust equivalent form and transform the model into a deterministic mixed-integer linear programming problem. We conduct a series of numerical experiments to compare the optimization results across different objectives, including maximizing task profit, minimizing total distance, minimizing makespan, and incorporating three different time window constraints. The numerical results demonstrate that the robust optimization-based heterogeneous multiple unmanned aerial vehicle cooperative task assignment model effectively mitigates the impact of parameter uncertainty, while achieving a balanced trade-off between robustness and the optimality of task assignment objectives.

Automated design of state transition rules in ant colony optimization by genetic programming: a comprehensive investigation

The automated design of Ant Colony Optimization (ACO) algorithms has become increasingly significant, particularly in addressing complex combinatorial optimization problems. Although existing methods have achieved some success, they still face limitations, particularly the high dependency on expert knowledge, pre-solved data, and challenges in interpretability. Genetic Programming (GP), as a proven technology, has shown potential in optimizing the automated design state transition rules of ACO. However, existing research on GP-ACO is insufficient, particularly in terms of experimental validation and systematic evaluation. To address these issues, this study conducts comprehensive experiments to explore several key questions: the generality of GP-ACO on homogeneously distributed maps, the impact of different ACO variants on the learning capabilities of GP-ACO, the effect of 2-opt local search on the learning capabilities of GP-ACO, the enhancement of learning capabilities through the addition of more global information, and the interpretability of GP-ACO. The findings indicate that GP-ACO exhibits robust generality; variations among ACO variants have minimal impact on learning performance; 2-opt local search can somewhat diminish the performance of GP-ACO in the Max–Min Ant System; additional global information can significantly enhance the learning capabilities of GP-ACO; and GP-ACO has good interpretability.

Energy-aware and Carbon Footprint Optimization Model for Virtual Machine Placement in Data Centres –A Systematic Literature Review

Purpose—The rapid adoption of cloud resources and their applications has increased energy consumption and carbon footprint emissions in data centres, raising significant environmental concerns. One key strategy to address this challenge is optimizing the allocation of resources and applications, such as virtual machines (VMs), within data centre architectures. Virtual Machine Placement (VMP), which involves selecting the best physical machine (PM) to host user-requested VMs, is critical in reducing energy consumption and carbon emissions. Method–This study undertakes a systematic analysis of the requirements for energy-aware and carbon footprint (CFP) optimization in VMP within cloud data centres. A comparative approach is employed to evaluate the salient features of various VMP methods, examining their ability to meet energy efficiency and sustainability goals. VMP is identified as a complex combinatorial optimization problem that is NP-Hard, necessitating innovative strategies to achieve optimal solutions. Conclusion–Despite advancements in energy-efficient and CFP-optimized VMP methods, unresolved challenges remain, such as balancing energy savings with service quality and scalability. These challenges highlight the need for continued exploration of innovative techniques to address the complex nature of VMP problems. Recommendations–Future research should focus on hybrid optimization techniques, leveraging metaheuristic approaches to improve energy efficiency and sustainability. Moreover, developing real-world prototypes and frameworks to validate theoretical models can bridge the gap between research and practical implementation, paving the way for sustainable cloud computing solutions. Practical Implications–This review highlights effective energy-aware and CFPstrategies for VMPin CDC. Categorizing and analyzing recent developments provides practical insights for cloud service providers and data centre operators to implement efficient VMP methods. These findings enable better resource allocation, reduced operational costs, and minimized environmental impact, aligning with sustainability goals and improving the overall performance of cloud infrastructure systems. Keywords––carbon footprint, virtual machine placement,cloud data centre

Homeothermic P‐Bit Computing Hardware with Stochastic Operations Beyond Limit of Non‐Stochastic Materials

AbstractProbabilistic computing (p‐computing) is a customized approach for solving complex combinatorial optimization problems. However, issues of compatibility with well‐established complementary metal‐oxide‐semiconductor (CMOS) technology, robustness to environmental temperature variations and stochasticity need to be addressed. This study resolves these difficulties using a metal‐oxide‐semiconductor field‐effect transistor (MOSFET) with a floating body as a probabilistic‐bit (p‐bit) device. Unlike previously reported two‐terminal p‐bit structures, such as magnetic tunnel junction (MTJ) and memristor‐based devices, a MOSFET is commercialized for conventional von Neumann computing. Although MOSFET operation is sensitive to the ambient temperature, a homeothermic characteristic from 20 °C up to 110 °C is achieved with gate voltage (VG) control, taking advantage of the three‐terminal design. The conventional MOSFET operation is stable, reproducible, and, thus, non‐stochastic. However, the floating body effect in this specific MOSFET enhances stochasticity, enabling an irregular single transistor latch (STL). Invertible logic operations and a max‐cut solver are demonstrated with the proposed p‐bits, maintaining desirable performance even at 110 °C through VG control. Due to its compatibility with CMOS technology, large‐scale cointegration of a p‐bit array and supportive CMOS circuits is feasible.

Automatic optimization combined with genetic algorithm and CFD for temperature uniformity of OLED glass substrate

Automatic optimization combined with genetic algorithm and CFD for temperature uniformity of OLED glass substrate

Deep reinforcement learning for autonomous SideLink radio resource management in platoon-based C-V2X networks: An overview

Deep reinforcement learning for autonomous SideLink radio resource management in platoon-based C-V2X networks: An overview

Tabu Search Algorithm for Solving a Location-Routing-Inventory Problem

Location decisions, inventory control, and vehicle routing are interrelated decisions. Inventory control decisions, such as order lot size and order frequency, affect both inventory and transportation costs. Failure to take inventory and transportation costs into consideration when determining location decisions can lead to suboptimality since they have a large impact on inventory and transportation costs. Therefore, how to decide locations, determine vehicle routing, and control inventory optimally, or location-routing-inventory problem (LRIP), becomes an important issue to design logistics systems. The objective of this paper is to develop a heuristic method base on Tabu Search (TS) to solve a LRIP. The contribution of this paper which is the heuristic method based on TS to solve a LRIP has never been developed before. TS is a type of metaheuristic. The success of TS is due to its ability to direct the search process so as not to get trapped in the local optimum, in large part, like many other metaheuristics. TS has been widely used to solve complex combinatorial optimization problems. The result of the computational comparison show that the heuristic method can provide a relatively small average gap of 3.20% compared to the optimal method. Application of the proposed heuristic is done in DKI Jakarta.

Applying the Simulated Annealing Algorithm to the Set Orienteering Problem with Mandatory Visits

This study addresses the set orienteering problem with mandatory visits (SOPMV), a variant of the team orienteering problem (SOP). In SOPMV, certain critical sets must be visited. The study began by formulating the mathematical model for SOPMV. To tackle the challenge of obtaining a feasible route within time constraints using the original MILP approach, a two-stage mixed-integer linear programming (MILP) model is proposed. Subsequently, a simulated annealing (SA) algorithm and a dynamic programming method were employed to identify the optimal route. The proposed SA algorithm was used to solve the SOP and was compared to other algorithms, demonstrating its effectiveness. The SA was then applied to solve the SOPMV problem. The results indicate that the solutions obtained using SA are superior and more efficient compared to those derived from the original MILP and the two-stage MILP. Additionally, the results reveal that the solution quality deteriorates as the ratio of the set of mandatory visits increases or the maximum allowable travel time decreases. This study represents the first attempt to integrate mandatory visits into SOP, thereby establishing a new research direction in this area. The potential impact of this research is significant, as it introduces new possibilities for addressing complex combinatorial optimization problems.

A dictionary-based Bayesian approach to optimizing left-turn restriction locations in grid networks

A dictionary-based Bayesian approach to optimizing left-turn restriction locations in grid networks

Fit Entropy-Based Dynamic Communication Resource Slicing-Optimization Method in Smart Distribution Grids on the Medium-Low-Voltage Side.

With the rapid development of new energy and smart technology, the demand for inter-device communication in medium-low-voltage smart distribution grids has sharply increased, leading to a surge in the variety and quantity of communication services. To meet the needs of diverse and massive communication services, deploying service function chains to flexibly combine virtual resources has become crucial. This paper proposes an optimization method based on fit entropy and network utility to address the limited communication network resources in medium-low-voltage smart distribution grids. This was conducted by modeling the distribution grid as a three-domain model consisting of a service domain, a logical domain, and a physical domain and transforming it into a hierarchical bipartite hypergraph-matching problem, which is a complex combinatorial optimization problem. This paper introduces two matching optimization algorithms: "business domain-logic domain-physical domain integration" and "service domain-logic domain, logic domain-physical domain two-stage", which effectively address this problem based on fit entropy and utility. The simulation results demonstrate that these algorithms significantly improve service success rates and resource utilization, enhancing overall network utility.

Learning to Allocate Time-Bound and Dynamic Tasks to Multiple Robots Using Covariant Attention Neural Networks

Abstract In various applications of multi-robotics in disaster response, warehouse management, and manufacturing, tasks that are known a priori and tasks added during run time need to be assigned efficiently and without conflicts to robots in the team. This multi-robot task allocation (MRTA) process presents itself as a combinatorial optimization (CO) problem that is usually challenging to be solved in meaningful timescales using typical (mixed)integer (non)linear programming tools. Building on a growing body of work in using graph reinforcement learning to learn search heuristics for such complex CO problems, this paper presents a new graph neural network architecture called the covariant attention mechanism (CAM). CAM can not only generalize but also scale to larger problems than that encountered in training, and handle dynamic tasks. This architecture combines the concept of covariant compositional networks used here to embed the local structures in task graphs, with a context module that encodes the robots’ states. The encoded information is passed onto a decoder designed using multi-head attention mechanism. When applied to a class of MRTA problems with time deadlines, robot ferry range constraints, and multi-trip settings, CAM surpasses a state-of-the-art graph learning approach based on the attention mechanism, as well as a feasible random-walk baseline across various generalizability and scalability tests. Performance of CAM is also found to be at par with a high-performing non-learning baseline called BiG-MRTA, while noting up to a 70-fold improvement in decision-making efficiency over this baseline.

Enhancing the performance of coherent Ising machines in the large-noise regime with a fifth-order nonlinearity

Coherent Ising machines (CIMs), leveraging the bistable physical properties of coherent light to emulate Ising spins, exhibit great potential as hardware accelerators for tackling complex combinatorial optimization problems. Recent advances have demonstrated that the performance of CIMs can be enhanced either by incorporating large random noise or higher-order nonlinearities, yet their combined effects on CIM performance remain mainly unexplored. In this work, we develop a numerical CIM model that utilizes a tunable fifth-order polynomial nonlinear dynamic function under large noise levels, which has the potential to be implemented in all-optical platforms. We propose a normal form of a CIM model that allows for both supercritical and subcritical pitchfork bifurcation operational regimes, with fifth-order nonlinearity and tunable hyperparameters to control the Ising spin dynamics. In the benchmark studies, we simulate various sets of MaxCut problems using our fifth-order polynomial CIM model. The results show a significant performance improvement, achieving an average of 59.5% improvement in median time-to-solution (TTS) and an average of 6 times improvement in median success rate (SR) for dense Maxcut problems in the BiqMac library, compared to the commonly used third-order polynomial CIM model with low noise. The fifth-order polynomial CIM model in the large-noise regime also shows better performance trends as the problem size scales up. These findings reveal the enhancements on the computational performance of Ising machines in the large-nose regime from fifth-order nonlinearity, showing important implications for both simulation and hardware perspectives.

A Knowledge-Guided Competitive Co-Evolutionary Algorithm for Feature Selection

In real-world applications, feature selection is crucial for enhancing the performance of data science and machine learning models. Typically, feature selection is a complex combinatorial optimization problem and a multi-objective optimization problem. Its primary goals are to reduce the dimensionality of the dataset and enhance the performance of machine learning algorithms. The selection of features in high-dimensional datasets is challenging due to the intricate relationships between features, which pose significant challenges to the performance and computational efficiency of algorithms. This paper introduces a Knowledge-Guided Competitive Co-Evolutionary Algorithm (KCCEA) for feature selection, especially for high-dimensional features. In the proposed algorithm, we make improvements to the foundational dominance-based multi-objective evolutionary algorithm in two aspects. First, the use of feature correlation as knowledge to guide evolution enhances the search speed and quality of traditional multi-objective evolutionary algorithm solutions. Second, a dynamically allocated competitive–cooperative evolutionary mechanism is proposed, integrating the improved knowledge-guided evolution with traditional evolutionary algorithms, further enhancing the search efficiency and diversity of solutions. Through rigorous empirical testing on various datasets, the KCCEA demonstrates superior performance compared to basic multi-objective evolutionary algorithms, providing effective solutions to multi-objective feature selection problems while enhancing the interpretability and effectiveness of prediction models.

Agile earth observation satellite constellations scheduling for large area target imaging using heuristic search

Agile earth observation satellite constellations scheduling for large area target imaging using heuristic search

AquaNutriOpt: Optimizing nutrients for controlling harmful algal blooms in Python—A case study of Lake Okeechobee

AquaNutriOpt: Optimizing nutrients for controlling harmful algal blooms in Python—A case study of Lake Okeechobee

Fully CMOS‐Based p‐Bits with a Bistable Resistor for Probabilistic Computing

AbstractProbabilistic computing can solve complex combinatorial optimization problems more efficiently than conventional deterministic computing. A probabilistic bit (p‐bit) with an n‐p‐n bistable resistor (biristor) is demonstrated for probabilistic computing. It is fabricated on an 8‐inch wafer with complementary metal–oxide–semiconductor (CMOS) compatible technologies. Its stochastic behavior of threshold switching, which is based on the phenomenon of a single transistor latch, provides output with a Boltzmann distribution. The p‐bit is composed of a biristor, a serial resistor, and a comparator. The output probability of the biristor‐based p‐bits shows a sigmoidal relationship with the input voltage, showing typical p‐bit characteristics. Invertible Boolean logic operations with p‐bits are demonstrated, and weighted maximum Boolean satisfiability problems are solved with high energy efficiency and accuracy. The biristor‐based p‐bits with perfect CMOS compatibility show sufficient device stability, demonstrating the possibility of large‐scale integration with a p‐bit array for complex optimization solvers.

Formulation of the airport collaborative gate allocation problem and the Bee Colony Optimization solution approach

Formulation of the airport collaborative gate allocation problem and the Bee Colony Optimization solution approach

Meta-Learning-Based Deep Reinforcement Learning for Multiobjective Optimization Problems.

Deep reinforcement learning (DRL) has recently shown its success in tackling complex combinatorial optimization problems. When these problems are extended to multiobjective ones, it becomes difficult for the existing DRL approaches to flexibly and efficiently deal with multiple subproblems determined by the weight decomposition of objectives. This article proposes a concise meta-learning-based DRL approach. It first trains a meta-model by meta-learning. The meta-model is fine-tuned with a few update steps to derive submodels for the corresponding subproblems. The Pareto front is then built accordingly. Compared with other learning-based methods, our method can greatly shorten the training time of multiple submodels. Due to the rapid and excellent adaptability of the meta-model, more submodels can be derived so as to increase the quality and diversity of the found solutions. The computational experiments on multiobjective traveling salesman problems and multiobjective vehicle routing problems with time windows demonstrate the superiority of our method over most of the learning-based and iteration-based approaches.