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A structure-based lead optimization procedure is an essential step to finding appropriate ligand molecules binding to a target protein structure in order to identify drug candidates. This procedure takes a known structure of a protein-ligand complex as input, and structurally similar compounds with the query ligand are designed in consideration with all possible combinations of atomic species. This task is, however, computationally hard since such combinatorial optimization problems belong to the non-deterministic nonpolynomial-time hard (NP-hard) class. In this paper, we propose the structure-based lead generation and optimization procedures by a degenerate optical parametric oscillator (DOPO) network. Results of numerical simulation demonstrate that the DOPO network efficiently identifies a set of appropriate ligand molecules according to the Boltzmann sampling law.

The study on multiple unmanned aerial vehicles (UAVs) reconnaissance task allocation problem is an important research field, which is significant for both military and civilian applications. This problem has often been considered as a multiple traveling salesman problem where the targets are considered as points. In this paper, we present a novel mathematical model that classifies heterogeneous targets as point targets, line targets and area targets to improve the fidelity of the model. It is a complex combinatorial optimization problem, for which we can hardly get an optimal solution as the scale of the problem expands. A new heuristic algorithm called grouping ant colony optimization algorithm is proposed for this new model. Compared with traditional ant colony algorithm, pheromone is divided into membership pheromone and sequence pheromone corresponding to grouping and permutation characteristics of the model, respectively. Also, negative feedback mechanism is introduced to accelerate convergence speed of the algorithm. The simulation results demonstrate that the new algorithm can consider comprehensively the performance of different UAVs and the characteristic of heterogeneous targets. It outperforms existing methods reported in the literature in terms of optimality of the result, and the advantage gets more obvious with the scale of reconnaissance task allocation problem expanding.

Probabilistic computing, a class of physics-based computing, bridges the gap between quantum computing and the classical von Neumann architecture. This approach provides more efficient means of addressing NP problems, which are challenging for classical computers. In this work, we analyze the core concept of probabilistic computing which is based on the Ising model framework—including bit fluctuations and energy trends. In addition, we extend the traditional binary (two-level) system into a multi-level probabilistic framework, i.e. number partitioning problem to multiway number partitioning problem, as a case study.

In the past few decades, metaheuristics have demonstrated their suitability in addressing complex problems over different domains. This success drives the scientific community towards the definition of new and better-performing heuristics and results in an increased interest in this research field. Nevertheless, new studies have been focused on developing new algorithms without providing consolidation of the existing knowledge. Furthermore, the absence of rigor and formalism to classify, design, and develop combinatorial optimization problems and metaheuristics represents a challenge to the field’s progress. This study discusses the main concepts and challenges in this area and proposes a formalism to classify, design, and code combinatorial optimization problems and metaheuristics. We believe these contributions may support the progress of the field and increase the maturity of metaheuristics as problem solvers analogous to other machine learning algorithms.

Nodes localization has been a critical subject in wireless sensor network (WSN) field. As far as existing localization algorithms are concerned, distance vector hop (DV-Hop) has the advantages of no extra hardware and implementation simplicity, however its localization accuracy cannot meet some specific requirements. In order to enhance the accuracy of WSN nodes localization, a DV-Hop based localization algorithm based on nodes negotiation and multi communication radii (NNMCR DV-Hop) is proposed in this paper. Firstly, the hop counts between WSN nodes is modified from an integer to a decimal by changing communication radius of anchor nodes through nodes negotiation. By refining the hop counts, the accuracy of the estimated distance from the unknown to the anchor nodes is improved. Secondly, the calculation of the average hop size of the anchor node is abstracted into a combinatorial optimization problem which is solved by using binary particle swarm optimization (BPSO) to improve the accuracy of the estimated distance which is between the anchor and the unknown node. Finally, when calculating the coordinates of unknown nodes, only the anchor nodes with smaller hop counts are selected to participate in the calculation. Simulation experiments show that compared with the original DV-Hop as well as other improved algorithms based on DV-Hop, NNMCR DV-Hop greatly improves the localization accuracy of unknown nodes without additional hardware.

The wild horse optimizer (WHO) is a novel metaheuristic algorithm, which has been successfully applied to solving continuous engineering problems. Considering the characteristics of the wild horse optimizer, a discrete version of the algorithm, named discrete wild horse optimizer (DWHO), is proposed to solve the capacitated vehicle routing problem (CVRP). By incorporating three local search strategies-swap operation, reverse operation, and insertion operation-along with the introduction of the largest-order-value (LOV) decoding technique, the precision and quality of the solutions have been enhanced. Experimental results conducted on 44 benchmark instances indicate that, in most test cases, the solving capability of discrete wild horse optimizer surpasses that of basic wild horse optimizer (BWHO), hybrid firefly algorithm, dynamic space reduction ant colony optimization (DSRACO), and discrete artificial ecosystem-based optimization (DAEO). The discrete wild horse optimizer provides a novel approach for solving the capacitated vehicle routing problem and also offers a new perspective for addressing other discrete problems.

The uncapacitated facility location problem (UFLP) is a popular combinatorial optimization problem with practical applications in different areas, from logistics to telecommunication networks. While most of the existing work in the literature focuses on minimizing total cost for the deterministic version of the problem, some degree of uncertainty (e.g., in the customers' demands or in the service costs) should be expected in real-life applications. Accordingly, this paper proposes a simheuristic algorithm for solving the stochastic UFLP (SUFLP), where optimization goals other than the minimum expected cost can be considered. The development of this simheuristic is structured in three stages: (i) first, an extremely fast savings-based heuristic is introduced; (ii) next, the heuristic is integrated into a metaheuristic framework, and the resulting algorithm is tested against the optimal values for the UFLP; and (iii) finally, the algorithm is extended by integrating it with simulation techniques, and the resulting simheuristic is employed to solve the SUFLP. Some numerical experiments contribute to illustrate the potential uses of each of these solving methods, depending on the version of the problem (deterministic or stochastic) as well as on whether or not a real-time solution is required.

Multiple object tracking (MOT), a key task in image recognition, poses a persistent challenge in balancing processing speed and tracking accuracy. This study presents a novel approach that leverages quantum annealing (QA) to expedite computation speed, while improving tracking accuracy through the ensemble processing of object tracking methods. A method to improve the matching integration process is also proposed. By utilizing the sequential nature of MOT, this study further augments the tracking method via reverse annealing. Experimental validation confirms the maintenance of high accuracy with an annealing time of a mere 3 s per tracking process. Notably, the time-to-solution achieved reductions of over 99% compared to conventional QA implementations. The proposed method holds significant potential for real-time MOT applications, including traffic flow measurement for urban traffic light control, collision prediction for autonomous robots and vehicles, and management of products mass-produced in factories.

As a typical meta-heuristic algorithm, ant colony optimization (ACO) has achieved good results in solving discrete combinatorial optimization problems. However, it suffers from poor solutions and the drawback of easily being trapped in local optima. This paper presents a new type of ACO called “dynamic space reduction ant colony optimization” (DSRACO) to solve the capacitated vehicle routing problem, which is a typical nondeterministic polynomial-hard optimization problem. In DSRACO, ACO is integrated with a unique dynamic space reduction method, an elite enhanced mechanism, and large-scale neighborhood search methods to improve the quality of the solution. The performance of DSRACO is evaluated using 73 well-known benchmark instances in comparison with ACO and three other cutting-edge algorithms. The experimental results show that DSRACO can solve CVRP with a satisfactory result.

DNA computing is an emerging computational model that has garnered significant attention due to its distinctive advantages at the molecular biological level. Since it was introduced by Adelman in 1994, this field has made remarkable progress in solving NP -complete problems, enhancing information security, encrypting images, controlling diseases, and advancing nanotechnology. A key challenge in DNA computing is the design of DNA coding, which aims to minimize nonspecific hybridization and enhance computational reliability. The DNA coding design is a classical combinatorial optimization problem focused on generating high-quality DNA sequences that meet specific constraints, including distance, thermodynamics, secondary structure, and sequence requirements. This paper comprehensively examines the advances in DNA coding design, highlighting mathematical models, counting theory, and commonly used DNA coding methods. These methods include the template method, multi-objective evolutionary methods, and implicit enumeration techniques.