Surrogate models are widely employed to address optimization problems with high computational complexity. However, interpretable surrogate models for Combinatorial Optimization Problems (COPs) remain underexplored. In this paper, a novel surrogate model, termed the Controllable Multimodal Landscape (CML), is proposed for the k-order Traveling Salesman Problem (k-order TSP). The proposed method is inspired by the observation that a Traveling Salesman Problem (TSP) with cities arranged on a convex hull exhibits a unimodal landscape. For the k-order TSP, multiple local optima (or high-quality solutions) are collected, and convex hull TSPs are constructed based on them to generate multiple unimodal landscapes sharing the same search space. These unimodal landscapes are then combined to form a multimodal landscape that approximates the original landscape of the k-order TSP. Particle Swarm Optimization (PSO) is used to optimize the parameters of the CML. Experimental results demonstrate that the proposed CML surrogate model achieves higher accuracy than Random Forest (RF) in most test cases involving k-order TSP instances.

To guarantee the low-congestion performance and quality of service (QoS) requirements of multi-services in Mega Low Earth Orbit Constellation Networks (MLEOCN), this paper focuses on the comprehensive communication link model in MLEOCN, commencing from users to access satellites, relayed by relay satellites, and finally delivered to the gateway by feeder satellites. Aiming at the problems of high congestion and low throughput in traditional path planning algorithms, we innovatively propose a multi-objective optimization service-correlated path optimization algorithm based on stochastic hill climbing strategy (MSCPO-SHCS). The algorithm initially achieves the joint optimization of three metrics through regular mapping and judicious weighting. Subsequently, it assesses the interplane hop via geometric parameter theory analysis (GPTA), then decouples the large-scale mixed integer optimization problem into the integer optimization problem superimposed linear programming problem, and ultimately employs the stochastic hill climbing strategy (SHCS) for path intelligent optimization. Based on the path Gaussianity assumption, we theoretically prove and numerically verify the convergence of the proposed algorithm. The simulation results indicate that the proposed algorithm boosts the throughput and load balancing coefficient compared with the greedy strategy, service-uncorrelated, minimum hop count, and resource allocation optimization. Additionally, it decreases the hop count compared with the maximum throughput and maximum balancing coefficient and maintains the optimal overall performance.

The hardness of the Unconstrained Binary Quadratic Program (UBQP) problem is due its rugged landscape. Various algorithms have been proposed for UBQP, including the Landscape Smoothing Iterated Local Search (LSILS). Different from other UBQP algorithms, LSILS tries to smooth the rugged landscape by building a convex combination of the original UBQP and a toy UBQP. In this paper, our study further investigates the impact of smoothing rugged landscapes using different toy UBQP problems, including a toy UBQP with matrix$\hat{\boldsymbol{Q}}^{1}$(construct by “$+/-1$‘), a toy UBQP with matrix$\hat{\boldsymbol{Q}}^{2}$(construct by “$+/-\mathrm{i}$’) and a toy UBQP with matrix$\hat{\boldsymbol{Q}}^{3}$(construct randomly). We first assess the landscape flatness of the three toy UBQPs. Subsequently, we test the efficiency of LSILS with different toy UBQPs. Results reveal that the toy UBQP with$\hat{\boldsymbol{Q}}^{1}$(construct by “$+/-1$”) exhibits the flattest landscape among the three, while the toy UBQP with$\hat{Q}^{3}$(construct randomly) presents the most non-flat landscape. Notably, LSILS using the toy UBQP with$\hat{\boldsymbol{Q}}^{2}$(construct by “$+/\cdot \mathbf{i})$emerges as the most effective, while$\hat{\boldsymbol{Q}}^{3}$(construct randomly) has the poorest result. These findings contribute to a detailed understanding of landscape smoothing techniques in optimizing UBQP.

Pareto local search (PLS) is a natural extension of local search for multiobjective combinatorial optimization problems (MCOPs). In our previous work, we improved the anytime performance of PLS using parallel computing techniques and proposed a parallel PLS based on decomposition (PPLS/D). In PPLS/D, the solution space is searched by multiple independent parallel processes simultaneously. This article further improves PPLS/D by introducing two new cooperative process techniques, namely, a cooperative search mechanism and a cooperative subregion-adjusting strategy. In the cooperative search mechanism, the parallel processes share high-quality solutions with each other during the search according to a distributed topology. In the proposed subregion-adjusting strategy, a master process collects useful information from all processes during the search to approximate the Pareto front (PF) and redivide the subregions evenly. In the experimental studies, three well-known NP-hard MCOPs with up to six objectives were selected as test problems. The experimental results on the Tianhe-2 supercomputer verified the effectiveness of the proposed techniques.

As an extension of local search for multiobjective case, the basic version of Pareto Local Search (PLS) suffers from a poor anytime behavior. Researches have been carried out to overcome this drawback from different aspects. In this paper, we focus on the mechanism of neighborhood exploration in bi-objective Travelling Salesman Problems (bTSPs). Inspired by existing fast local search strategies for single objective TSP, we propose two speed-up strategies to help PLS quickly find promising neighboring solutions in bTSPs. In the experimental studies, we investigate the sensitivity of parameters and test the performance of several PLS variants with different combinations of the two strategies. The experimental results verify the effectiveness of the two strategies and their combination.

This article proposes a novel landscape smoothing method for the symmetric traveling salesman problem (TSP). We first define the homotopic convex (HC) transformation of a TSP as a convex combination of a well-constructed simple TSP and the original TSP. The simple TSP, called the convex-hull TSP, is constructed by transforming a known local or global optimum. We observe that controlled by the coefficient of the convex combination, with local or global optimum: 1) the landscape of the HC transformed TSP is smoothed in terms that its number of local optima is reduced compared to the original TSP and 2) the fitness distance correlation of the HC transformed TSP is increased. Furthermore, we observe that the smoothing effect of the HC transformation depends highly on the quality of the used optimum. A high-quality optimum leads to a better smoothing effect than a low-quality optimum. We then propose an iterative algorithmic framework in which the proposed HC transformation is combined within a heuristic TSP solver. It works as an escaping scheme from local optima aiming to improve the global searchability of the combined heuristic. Case studies using the 3-Opt and the Lin-Kernighan local search as the heuristic solver show that the resultant algorithms significantly outperform their counterparts and two other smoothing-based TSP heuristic solvers on most of the test instances with up to 20 000 cities.

Pareto local search (PLS) is a basic building block in many metaheuristics for a multiobjective combinatorial optimization problem. In this paper, an enhanced PLS variant called parallel PLS based on decomposition (PPLS/D) is proposed. PPLS/D improves the efficiency of PLS using the techniques of parallel computation and problem decomposition. It decomposes the original search space into L subregions and executes L parallel processes searching in these subregions simultaneously. Inside each subregion, the PPLS/D process is guided by a unique scalar objective function. PPLS/D differs from the well-known two phase PLS in that it uses the scalar objective function to guide every move of the PLS procedure in a fine-grained manner. In the experimental studies, PPLS/D is compared against the basic PLS and a recently proposed PLS variant on the multiobjective unconstrained binary quadratic programming problems and the multiobjective traveling salesman problems with, at most, four objectives. The experimental results show that regardless of whether the initial solutions are randomly generated or generated by heuristic methods, PPLS/D always performs significantly better than the other two PLS variants.

Pareto Local Search (PLS) is a simple, yet effective optimization approach dedicated to multi-objective combinatorial optimization. It can however suffer from a high computational cost, especially when the size of the Pareto optimal set is relatively large. Recently, incorporating decomposition in PLS had revealed a high potential, not only in providing high-quality approximation sets, but also in speeding-up the search process. Using the bi-objective Unconstrained Binary Quadratic Programming (bUBQP) problem as an illustrative benchmark, we demonstrate some shortcomings in the resulting decomposition-guided Parallel Pareto Local Search (PPLS), and we propose to revisit the PPLS design accordingly. For instances with a priori unknown Pareto front shape, we show that a simple pre-processing technique to estimate the scale of the Pareto front can help PPLS to better balance the workload. Furthermore, we propose a simple technique to deal with the critically-important scalability issue raised by PPLS when deployed over a large number of computing nodes. Our investigations show that the revisited version of PPLS provides a consistent performance, suggesting that decomposition-guided PPLS can be further generalized in order to improve both parallel efficiency and approximation quality.

Although several sequential heuristics have been proposed for dealing with the Unconstrained Binary Quadratic Programming (UBQP), very little effort has been made for designing parallel algorithms for the UBQP. This paper propose a novel decentralized parallel search algorithm, called Parallel Elite Biased Tabu Search (PEBTS). It is based on D2TS, a state-of-the-art sequential UBQP metaheuristic. The key strategies in the PEBTS algorithm include: (i) a lazy distributed cooperation procedure to maintain diversity among different search processes and (ii) finely tuned bit-flip operators which can help the search escape local optima efficiently. Our experiments on the Tianhe-2 supercomputer with up to 24 computing cores show the accuracy of the efficiency of PEBTS compared with a straightforward parallel algorithm running multiple independent and non-cooperating D2TS processes.

Almost every computer user has encountered an un-responsive system failure or system hang, which leaves the user no choice but to power off the computer. In this paper, the causes of such failures are analyzed in detail and one empirical hypothesis for detecting system hang is proposed. This hypothesis exploits a small set of system performance metrics provided by the OS itself, thereby avoiding modifying the OS kernel and introducing additional cost (e.g., hardware modules). Under this hypothesis, we propose SHFH, a self-healing framework to handle system hang, which can be deployed on OS dynamically. One unique feature of SHFH is that its "light-heavy" detection strategy is designed to make intelligent tradeoffs between the performance overhead and the false positive rate induced by system hang detection. Another feature is that its diagnosis-based recovery strategy offers a better granularity to recover from system hang. Our experimental results show that SHFH can cover 95.34% of system hang scenarios, with a false positive rate of 0.58% and 0.6% performance overhead, validating the effectiveness of our empirical hypothesis.