NP-hard Optimization Problem Research Articles

PPB-MCTS: A novel distributed-memory parallel partial-backpropagation Monte Carlo tree search algorithm

Monte-Carlo Tree Search (MCTS) is an adaptive and heuristic tree-search algorithm designed to uncover sub-optimal actions at each decision-making point. This method progressively constructs a search tree by gathering samples throughout its execution. Predominantly applied within the realm of gaming, MCTS has exhibited exceptional achievements. Additionally, it has displayed promising outcomes when employed to solve NP-hard combinatorial optimization problems. MCTS has been adapted for distributed-memory parallel platforms. The primary challenges associated with distributed-memory parallel MCTS are the substantial communication overhead and the necessity to balance the computational load among various processes. In this work, we introduce a novel distributed-memory parallel MCTS algorithm with partial backpropagations, referred to as Parallel Partial-Backpropagation MCTS (PPB-MCTS). Our design approach aims to significantly reduce the communication overhead while maintaining, or even slightly improving, the performance in the context of combinatorial optimization problems. To address the communication overhead challenge, we propose a strategy involving transmitting an additional backpropagation message. This strategy avoids attaching an information table to the communication messages exchanged by the processes, thus reducing the communication overhead. Furthermore, this approach contributes to enhancing the decision-making accuracy during the selection phase. The load balancing issue is also effectively addressed by implementing a shared transposition table among the parallel processes. Furthermore, we introduce two primary methods for managing duplicate states within distributed-memory parallel MCTS, drawing upon techniques utilized in addressing duplicate states within sequential MCTS. Duplicate states can transform the conventional search tree into a Directed Acyclic Graph (DAG). To evaluate the performance of our proposed parallel algorithm, we conduct an extensive series of experiments on solving instances of the Job-Shop Scheduling Problem (JSSP) and the Weighted Set-Cover Problem (WSCP). These problems are recognized for their complexity and classified as NP-hard combinatorial optimization problems with considerable relevance within industrial applications. The experiments are performed on a cluster of computers with many cores. The empirical results highlight the enhanced scalability of our algorithm compared to that of the existing distributed-memory parallel MCTS algorithms. As the number of processes increases, our algorithm demonstrates increased rollout efficiency while maintaining an improved load balance across processes.

An Evolutionary Multitasking Ant Colony Optimization Method Based on Population Diversity Control for Multimodal Transport Problems

Multimodal transport is a challenging, NP-hard problem in combinational optimization and has been solved using evolutionary algorithms, which excel at solving large-scale problems. However, few studies have used evolutionary algorithms, particularly swarm intelligence algorithms, to concurrently handle multiple multimodal transport instances. Ant colony optimization (ACO), which is a population intelligence technique that is adept at identifying the optimal paths in graphs, has been primarily used to address tasks separately rather than concurrently. Therefore, in this study, we introduce a multipopulation-based multitask environment where task-specific populations run in parallel, and ACO serves as the optimizer for each task. A variance-based population diversity measure is then calculated to characterize the distribution differences among individuals. If the population diversity of a specific task falls below a predetermined threshold, the valuable routing traits extracted from other tasks are transferred to the stagnant population. Our method is called population diversity-controlled multitask ACO (PDMTACO). We use multiple benchmark traveling salesman problem (TSP) instances at different scales to validate the efficacy of PDMTACO. Subsequently, we extend PDMTACO to address a series of multimodal transport problems. Our experimental results demonstrate that the use of information transferred by our method significantly reduces its logistics costs and carbon emissions in all multimodal transport tasks.

Dynamic programming with meta-reinforcement learning: a novel approach for multi-objective optimization

Multi-objective optimization (MOO) endeavors to identify optimal solutions from a finite array of possibilities. In recent years, deep reinforcement learning (RL) has exhibited promise through its well-crafted heuristics in tackling NP-hard combinatorial optimization (CO) problems. Nonetheless, current methodologies grapple with two key challenges: (1) They primarily concentrate on single-objective optimization quandaries, rendering them less adaptable to the more prevalent MOO scenarios encountered in real-world applications. (2) These approaches furnish an approximate solution by imbibing heuristics, lacking a systematic means to enhance or substantiate optimality. Given these challenges, this study introduces an overarching hybrid strategy, dynamic programming with meta-reinforcement learning (DPML), to resolve MOO predicaments. The approach melds meta-learning into an RL framework, addressing multiple subproblems inherent to MOO. Furthermore, the precision of solutions is elevated by endowing exact dynamic programming with the prowess of meta-graph neural networks. Empirical results substantiate the supremacy of our methodology over previous RL and heuristics approaches, bridging the chasm between theoretical underpinnings and real-world applicability within this domain.

Optimal solving of a binary knapsack problem on a D-Wave quantum machine and its implementation in production systems

AbstractThe efficient management of complex production systems is a challenge in today’s logistics. In the field of intelligent and sustainable logistics, the optimization of production batches, especially in the context of a rapidly changing product range, requires fast and precise computational solutions. This paper explores the potential of quantum computers for solving these problems. Traditional computational methods are often limited when it comes to optimizing complex logistics systems. In response to these challenges, the paper proposes the use of a hybrid algorithm that combines quantum technologies with classical computational methods. Such integration allows the computational power of both types of technologies to be harnessed, leading to faster and more efficient identification of optimal solutions. In this work, we consider the knapsack problem, a classic NP-hard optimization problem that is commonly used to verify the effectiveness of new algorithm construction methods. The algorithm presented is based on the Branch and Bound method and aims to ensure solution optimality in the context of the non-determinism of quantum computers. Within the algorithm, computations are performed alternately on a classical processor and a quantum processor. In addition, the lower and upper bounds of the objective function are computed in constant time using the D-Wave quantum machine.

Intelligent mission planning of sky survey based on the NSGA-III algorithm

In recent years, China has been scheduled to launch an all-sky survey telescope for celestial observation. The meticulous arrangement of observation sequences for this telescope is of paramount importance, given the myriad challenges and constraints inherent to such astronomical survey missions. These challenges encompass factors such as spatial limitations, stray light contamination, as well as constraints related to data storage and energy consumption. This undertaking presents a quintessential NP-hard optimization problem. To address this complexity and enhance in-orbit observation efficiency, this study closely adheres to practical engineering considerations. A comprehensive evaluation of diverse constraints is conducted, culminating in the establishment of an optimization model for systematic planning of sky survey missions. The primary optimization objectives encompass maximizing in-orbit observation duration, augmenting the count of observable celestial points, and minimizing maneuvering angles. To tackle this multifaceted problem, a mission planning algorithm is devised based on NSGA-III, a multi-objective optimization technique. The experimental results indicate that the sky survey planning algorithm proposed in this paper can effectively accomplish sky survey observation tasks, achieving the scientific objective of no fewer than 350 daily observation points. It holds the potential to provide algorithmic support for the sky survey telescope mission on the Chinese space station.

Restricted global optimization for QAOA

The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising variational quantum algorithm for addressing NP-hard combinatorial optimization problems. However, a significant limitation lies in optimizing its classical parameters, which is in itself an NP-hard problem. To circumvent this obstacle, initialization heuristics, enhanced problem encodings and beneficial problem scalings have been proposed. While such strategies further improve QAOA’s performance, their remaining problem is the sole utilization of local optimizers. We show that local optimization methods are inherently inadequate within the complex cost landscape of QAOA. Instead, global optimization techniques greatly improve QAOA’s performance across diverse problem instances. While global optimization generally requires high numbers of function evaluations, we demonstrate how restricted global optimizers still show better performance without requiring an exceeding amount of function evaluations.

Application of Lexisearch Algorithm to Vehicle Routing Problem with Time Windows

Vehicle Routing Problem with Time Windows (VRPTW) is an NP hard combinatorial scheduling optimization problem in which a minimum number of routes have to be determined so as to serve each of the destinations within their specified time windows. In this paper, the mail delivery of the Nigerian Postal Services (NIPOST) is modelled as a VRPTW in order to address the problem of delay in mail delivery occurring regularly in NIPOST. The Abuja Post Office is used as a case study and the Model of a related literature is applied with modifications to solve the problem. The problem is solved by applying Lexisearch algorithm using data that was obtained from Abuja Post Office and computational results on Solomon’s 100 instances were used to validate the algorithm.

Research on Genetic Algorithm Optimization with Fusion Tabu Search Strategy and Its Application in Solving Three-Dimensional Packing Problems

Symmetry is an important principle and characteristic that is prevalent in nature and artificial environments. In the three-dimensional packing problem, leveraging the inherent symmetry of goods and the symmetry of the packing space can enhance packing efficiency and utilization.The three-dimensional packing problem is an NP-hard combinatorial optimization problem in the field of modern logistics, with high computational complexity. This paper proposes an improved genetic algorithm by incorporating a fusion tabu search strategy to address this problem. The algorithm employs a three-dimensional loading mathematical model and utilizes a wall-building method under residual space constraints for stacking goods. Furthermore, adaptation of fitness variation strategy, chromosome adjustment, and tabu search algorithm are introduced to balance the algorithm’s global and local search capabilities, as well as to enhance population diversity and convergence speed. Through testing on benchmark cases such as Bischoff and Ratcliff, the improved algorithm demonstrates an average increase of over 3% in packing space utilization compared to traditional genetic algorithms and other heuristic algorithms, validating its feasibility and effectiveness. The proposed improved genetic algorithm provides new insights for solving three-dimensional packing problems and optimizing logistics loading schedules, offering promising prospects for various applications.

Decomposition-based multi-objective approach for a green hybrid flowshop rescheduling problem with consistent sublots

Rescheduling in a hybrid flowshop holds significant importance in modern industries that face uncertain events. Moreover, real-world manufacturing scenarios often utilise lot streaming to enhance market competitiveness. In light of escalating energy demands and their consequential environmental impacts, contemporary manufacturing companies are placing a heightened emphasis on energy efficiency. This study addressed a green hybrid flowshop rescheduling problem with consistent sublots (GHFRP_CS) in the context of urgent lot insertion. Initially, we establish an optimisation model aimed at minimising the makespan, total energy consumption, and system stability. To tackle this NP-hard multi-objective optimization problem, we develop a constructive heuristic generating promising solutions based on lot split, sequence, and local search rules. Further improvement is achieved through a multi-objective discrete artificial bee colony algorithm (MDABC). MDABC decomposes the problem into sub-problems, initiating solutions with the constructive heuristic and refining them through employed bee, onlooker bee, and scout bee phases. Computational experiments compare MDABC with other multi-objective evolutionary algorithms (MOEAs) on small- and large-scale problems. Results demonstrate MDABC's superiority, achieving fourfold accuracy and efficiency enhancement for small-scale instances and sixfold improvement for large-scale problems at low cost compared to other MOEAs.

EnMatch: Matchmaking for Better Player Engagement via Neural Combinatorial Optimization

Matchmaking is a core task in e-sports and online games, as it contributes to player engagement and further influences the game's lifecycle. Previous methods focus on creating fair games at all times. They divide players into different tiers based on skill levels and only select players from the same tier for each game. Though this strategy can ensure fair matchmaking, it is not always good for player engagement. In this paper, we propose a novel Engagement-oriented Matchmaking (EnMatch) framework to ensure fair games and simultaneously enhance player engagement. Two main issues need to be addressed. First, it is unclear how to measure the impact of different team compositions and confrontations on player engagement during the game considering the variety of player characteristics. Second, such a detailed consideration on every single player during matchmaking will result in an NP-hard combinatorial optimization problem with non-linear objectives. In light of these challenges, we turn to real-world data analysis to reveal engagement-related factors. The resulting insights guide the development of engagement modeling, enabling the estimation of quantified engagement before a match is completed. To handle the combinatorial optimization problem, we formulate the problem into a reinforcement learning framework, in which a neural combinatorial optimization problem is built and solved. The performance of EnMatch is finally demonstrated through the comparison with other state-of-the-art methods based on several real-world datasets and online deployments on two games.

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

Demand for imaging of large area targets by space-based assets such as constellations of Earth Observation Satellites (EOS) is on the rise for different applications. The area targets coverage cannot be achieved by a single satellite in a single observation opportunity, as the region for imaging spreads wider than the coverage swaths of imaging sensors. Hence, the imaging satellites are scheduled in a cooperative way to achieve maximum coverage of the area in a given planning time horizon. The scheduling algorithms also aim to maximize or minimize some specific objectives of interest while simultaneously complying with all resource constraints for an efficient use of precious space resources. As the current generation satellites are highly agile, there are many ways of choosing an imaging location in the target area for each single observation opportunity of a satellite. Even though the possible imaging region in continuous space is discretized into a finite number of strips for each observation, the huge combinatorial search space formed with all satellites’ imaging opportunities makes the problem intractable. Thus, the area target imaging scheduling is a complex combinatorial NP-hard optimization problem. Many exact and heuristic methods were evolved to provide a solution to this scheduling problem. Even though the exact methods solve the problem to optimality, they are limited to smaller problem instances because of the high computational complexities involved in those methods. More focus is seen in the literature on heuristic approaches as they guarantee scheduling performance with feasible solutions within an acceptable computational complexity. This paper presents our efficient heuristic approach proposed for the scheduling problem for imaging a large area target using a constellation of multiple satellites. Our approach is an extension of a widely used greedy approach in combination with insights from dynamic programming. In this paper, first we addressed the scheduling problem by describing it in detail and formulating it into a non-linear integer programming problem, considering the multi-objectives of achieving maximum coverage and minimum imaging resolution. The solution to the problem comprises two phases, namely the area decomposition phase and the scheduling phase. In the area decomposition phase, the area target is divided into strips dynamically for each observation opportunity of a satellite. Then exact observation period of each strip is computed using a simplified semi-analytical computational method. In the scheduling phase, we applied our heuristic search strategy, namely Forward and Backward Heuristic Search (FBHS) to obtain a near optimal solution within an acceptable computational time. Through the extensive simulations conducted under various scenarios, the effectiveness of the proposed method is verified in comparison with the baseline greedy approach.

Adaptive multi-strategy particle swarm optimization for solving NP-hard optimization problems

Particle Swarm Optimization algorithm (PSO) has been widely utilized for addressing optimization problems due to its straightforward implementation and efficiency in tackling various test functions and engineering optimization problems. Nevertheless, PSO encounters issues like premature convergence and a lack of diversity, particularly when confronted with complex high-dimensional optimization tasks. In this study, we propose an enhanced version of the Island Model Particle Swarm Optimization (IMPSO), where island models are integrated into the PSO algorithm based on several migration strategies. The first contribution consists in applying a new selection and replacement strategies based on tabu search technique, while the second contribution consists in proposing a dynamic migration rate relying on the Biogeography-Based Optimization technique. To assess and validate the effectiveness of the proposed method, several unconstrained benchmark functions are applied. The obtained results confirm that the approach yield better performance than the old version of IMPSO for solving NP-hard optimization problems. Compared to the performance of other well-known evolutionary algorithms, the proposed approach is more efficient and effective.

Balancing Pareto Front exploration of Non-dominated Tournament Genetic Algorithm (B-NTGA) in solving multi-objective NP-hard problems with constraints

The paper presents a new balanced selection operator applied to the proposed Balanced Non-dominated Tournament Genetic Algorithm (B-NTGA) that actively uses archive to solve multi- and many-objective NP-hard combinatorial optimization problems with constraints. The primary motivation is to make B-NTGA more efficient in exploring Pareto Front Approximation (PFa), focusing on “gaps” and reducing some PFa regions' sampling too frequently. Such a balancing mechanism allows B-NTGA to be more adaptive and focus on less explored PFa regions. The proposed B-NTGA is investigated on two benchmark multi- and many-objective optimization real-world problems, like Thief Traveling Problem and Multi-Skill Resource-Constrained Project Scheduling Problem. The results of experiments show that B-NTGA has a higher efficiency and better performance than state-of-the-art methods.

On upper bounds for the multiple knapsack assignment problem

The Multiple Knapsack Assignment Problem is a strongly NP-hard combinatorial optimisation problem, with several applications. We show that an upper bound for the problem, due to Kataoka and Yamada, can be computed in linear time. We then show that some bounds due to Martello and Monaci dominate the Kataoka-Yamada bound. Finally, we define an even stronger bound, which turns out to be particularly effective when the number of knapsacks is not a multiple of the number of item classes.

A self-supervised learning model for graph clustering optimization problems

The graph clustering optimization problems are ubiquitous in both scientific and engineering fields, for example the graph partitioning problem and facility location problem. Since most of these problems are NP-hard, it is challenging to design effective algorithms for them. Recently, deep learning has achieved promising performances in solving combinatorial optimization problems. However, existing supervised learning-based methods are limited by the absence of labeled instances, while reinforcement learning-based methods tend to be hard to train and converge slowly for large instances. In this paper, we propose a self-supervised model named GCOM to address NP-hard graph clustering optimization problems. It adopts a pre-training and fine-tuning framework. In the pre-training process, we utilize graph contrastive learning to mine the latent clustering relations and useful optimization strategies, which can be generalized to the downstream tasks. Additionally, two effective graph encodings are introduced to enhance the expressive power of our model. We evaluate our model on facility location problem (FLP) and balanced graph partitioning (BGP). Extensive experiments conducted on both synthetic and real-world datasets validate superior performance, strong generalization ability and high sample-efficiency of our model.

A Robust Controller Deployment Algorithm under Multiple Constraints for SDON

The deployment of controller for SDON (Software Defined Optical Networks) is an NP-hard multi-objective optimization problem, and it is difficult to find an optimal solution that satisfies all objectives. Therefore, to improve the performance of control plane, the model we proposed is constructed based on three constraints on the survivability, delay, and control redundancy, which has three advantages. first, the survivability is improved by not sharing the risk between the main control channel and the protection control channel, which also improves the utilization of network resources. Second, the accuracy of delay calculation is improved by using a delay optimization model, and a threshold value is set to constrain the delay. Finally, the greedy strategy idea is used to achieve the full network coverage of the control range and improve the convergence speed. Simulation results show that the algorithm improves the fault recovery probability by an average of 15% compared with the algorithm of KSP computed routing. In addition, the algorithm in this paper achieves the same survivability as the C-MPC algorithm while using an average 11.1% reduction in the number of controllers.

Secure Video Offloading in MEC-Enabled IIoT Networks: A Multicell Federated Deep Reinforcement Learning Approach

Wireless video offloading in mobile-edge-computing (MEC)-enabled Industrial Internet of Things imposes a risk of exposing users' private data to eavesdroppers. It is difficult for existing secure video offloading schemes to simultaneously guarantee security, reduce latency and energy consumption in privacy-sensitive multi-cell scenarios where users are unwilling to offload data to other cells. In this paper, a secure video offloading scheme based on multi-cell federated deep reinforcement learning (DRL) is proposed to facilitate a secure, real-time and efficient MEC network by efficient orchestration of limited resources. We formulate a collaborative optimization problem of video frame resolution and resources to minimize latency and energy consumption while maximizing the security rate subject to analytic accuracy and limited resources. To solve the formulated NP-hard problem, a multi-cell federated DRL algorithm based on the frameworks of multi-cell horizontal federated learning (FL) and hierarchical reward function-based twin delayed deep deterministic policy gradient (TD3) is proposed. First of all, hierarchical reward function-based TD3 is employed to solve the collaborative optimization NP-hard problem formulated for each single cell, where the optimal solution can be efficiently approached by the agent under the guidance of the innovatively designed hierarchical reward function. Then, multi-cell horizontal FL is applied on TD3 to obtain a model with higher model quality by averagely aggregating multiple individual TD3 models. Simulation results reveal that the proposed algorithm outperforms comparison algorithms in terms of utility, cost, latency, energy consumption and security rate.

A Hybrid Discrete Grey Wolf Optimizer with Local Search for Multi-UAV Patrolling

This paper addresses the multi- UAV patrolling problem, a NP-hard optimization problem that is focused on minimizing idleness, which is defined as the time between consecutive visits to specific locations. We propose the Discrete Grey Wolf Optimizer (D-GWO), which is specifically developed to handle the discrete aspects of UAV patrolling routes. This new algorithm is enhanced with a 2-opt local search strategy, which integrates the global search capabilities of D-GWO with the precision of local optimization to effectively refine solutions. Comparative experimental results show that our algorithm outperforms established methods such as ant colony optimization and simulated annealing in terms of reducing global worst idleness and overall exploration time. Our findings suggest that the D-GWO algorithm is particularly effective for complex multi-UAV patrolling tasks, significantly enhancing efficiency in security and disaster response missions.

The Effectiveness of Genetic Algorithm, And the CDS Method In Solving Flowshop Scheduling Problems

Flow shop scheduling problem is considered NP-hard for m machines and n jobs. For such NP-hard combinatorial optimization problems, heuristics play a major role in searching for near-optimal solutions. In this paper we used Genetic Algorithm, and the CDS method for solving flow shop scheduling problem with makespan as the criteria. The objective of this model is to obtain a sequence of jobs and the minimization of the total completion time (makespan). To test the effectiveness of the method, a dataset of case studies is used to compare the makespan values obtained for each method.

Solving NP-Hard Challenges in Logistics and Transportation under General Uncertainty Scenarios Using Fuzzy Simheuristics

In the field of logistics and transportation (L&T), this paper reviews the utilization of simheuristic algorithms to address NP-hard optimization problems under stochastic uncertainty. Then, the paper explores an extension of the simheuristics concept by introducing a fuzzy layer to tackle complex optimization problems involving both stochastic and fuzzy uncertainties. The hybrid approach combines simulation, metaheuristics, and fuzzy logic, offering a feasible methodology to solve large-scale NP-hard problems under general uncertainty scenarios. These scenarios are commonly encountered in L&T optimization challenges, such as the vehicle routing problem or the team orienteering problem, among many others. The proposed methodology allows for modeling various problem components—including travel times, service times, customers’ demands, or the duration of electric batteries—as deterministic, stochastic, or fuzzy items. A cross-problem analysis of several computational experiments is conducted to validate the effectiveness of the fuzzy simheuristic methodology. Being a flexible methodology that allows us to tackle NP-hard challenges under general uncertainty scenarios, fuzzy simheuristics can also be applied in fields other than L&T.