In a local search algorithm, one of its most important features is the definition of its neighborhood which is crucial to the algorithm’s performance. In this paper, we present an analysis of neighborhood combination search for solving the single-machine scheduling problem with sequence-dependent setup time with the objective of minimizing total weighted tardiness (SMSWT). First, We propose a new neighborhood structure named Block Swap (B1) which can be considered as an extension of the previously widely used Block Move (B2) neighborhood, and a fast incremental evaluation technique to enhance its evaluation efficiency. Second, based on the Block Swap and Block Move neighborhoods, we present two kinds of neighborhood structures: neighborhood union (denoted by B1⋃B2) and token-ring search (denoted by B1 → B2), both of which are combinations of B1 and B2. Third, we incorporate the neighborhood union and token-ring search into two representative metaheuristic algorithms: the Iterated Local Search Algorithm (ILSnew) and the Hybrid Evolutionary Algorithm (HEAnew) to investigate the performance of the neighborhood union and token-ring search. Extensive experiments show the competitiveness of the token-ring search combination mechanism of the two neighborhoods. Tested on the 120 public benchmark instances, our HEAnew has a highly competitive performance in solution quality and computational time compared with both the exact algorithms and recent metaheuristics. We have also tested the HEAnew algorithm with the selected neighborhood combination search to deal with the 64 public benchmark instances of the single-machine scheduling problem with sequence-dependent setup time. HEAnew is able to match the optimal or the best known results for all the 64 instances. In particular, the computational time for reaching the best well-known results for five challenging instances is reduced by at least 61.25

Clustering is the process of partitioning data into different clusters with the goal of minimizing the difference of objects within each cluster, where the commonly used evaluation function is defined as the sum of the squared distance from each point to the cluster center to which it belongs. Nevertheless, this general evaluation function is extremely vulnerable to outliers and noisy data, and it is sensitive to initial cluster centers. More seriously, this evaluation function cannot effectively represent the core of clustering results; even if the partition achieves the global optimum value according to the evaluation function, the clustering results may not be good. In this study, we propose a multi-start local search algorithm (MLS) with several techniques to tackle this problem. First, the center of each cluster is no longer its centroid, which reduces the dependence of the cluster algorithm on difference in size and shape of ideal clusters. Second, the number of adjacent points shared between clusters is defined as the new objective function. Third, two basic meta-operations, merge and split, are used to optimize the objective function and make the iterative process insensitive to the initial solution. The novelty of our approach is the selection criterion of the initial centers and the new objective function, which enables MLS to explore more promising search area. Experimental results demonstrate that MLS outperforms traditional centroid-based clustering algorithms in terms of both solution quality and computational efficiency, and it is quite competitive to other reference algorithms such as spectral, density, and geometric based clustering algorithms.

The paper studies a real-world Multi-Constraints Emergency Transportation Problem in disaster response under travel time uncertainty(MCETP), whose objective is to determine the set of flights and routes and the airplane and vehicle assignment for delivering necessary living supplies to disaster areas as quickly as possible. The MCETP can be modeled as a variant of the Vehicle Routing Problem (VRP), which considers a heterogeneous fleet with multi-depots delivering supplies to customers in order to minimize the maximal travel time of all routes where travel time of vehicles is predicted by experts because ground transportation network is destroyed and affected degree is unknown. By adding copy points and imaginary depots, the MCETP can be transformed into a variant of the Travelling Salesman Problem (TSP), for which a Mixed Integer Linear Programming (MILP) formulation is presented. With the proposed initial solution construction algorithm, vehicle assignment strategy and penalty function, the transformed problem can be solved by the extension of Lin–Kernighan–Helsgaun solver (LKH-3). Computational experiments on two sets of totally 50 instances show that the idea of transforming a challenging complex problem to a widely studied problem and using its state-of-the-art algorithm to solve the original problem is highly effective and efficient for the MCETP. Specifically, it can obtain the same solution quality as GUROBI but with much less time for small-scale instances. Furthermore, the proposed algorithm can solve large-scale instances while GUROBI fails to obtain a feasible solution in most cases in a reasonable time.

In this paper, we study the maximum diversity problem (MDP) which is equivalent to the quadratic unconstrained binary optimization (QUBO) problem with cardinality constraint. The MDP aims to select a subset of elements with given cardinality such that the sum of pairwise distances between any two elements in the selected subset is maximized. For solving this computationally challenging problem, we propose a two-phase tabu search based evolutionary algorithm (TPTS/EA), which integrates several distinguishing features to ensure the diversity and the quality of the evolution, such as a two-phase tabu search algorithm which consists of a dynamic candidate list (DCL) strategy-based traditional tabu search in the first phase and a solution-based tabu search procedure to refine the search in the second phase, and two path-relinking based recombination operators to generate new offspring solutions. Tested on three sets of totally 140 public instances in the literature, the study demonstrates the efficacy of the proposed TPTS/EA algorithm in terms of both solution quality and computational efficiency. Specifically, our proposed TPTS/EA algorithm is able to improve the previous best known results for 2 instances, while matching the previous best-known solutions for 130 instances. We also provide experimental evidences to highlight the beneficial effect of several important components in our TPTS/EA algorithm.

The classic p -center problem consists of choosing a set of p vertices in an undirected graph as facilities in order to minimize the maximum distance between each client vertex and its closest facility. The problem is equivalent to covering all vertices by no more than p circles with the smallest possible radius, which can be tackled by solving a series of the decision version of set covering subproblems with the same cardinality constraint (≤ p ) and gradually decreasing the covering radius. In this paper, we solve the p -center problem via set covering and SAT. We first transform the p -center problem into a series of set covering subproblems and simplify them by some reduction rules. Then, we present two kinds of encoding methods to convert them into CNF format and solve them with several state-of-the-art SAT solvers. Tested on three sets of totally 70 benchmark instances, our proposed approach can improve the previous best known results for 3 instances using the heuristic SAT solvers while proving the optimality for 59 instances using the exact SAT solvers. The computational results demonstrate the effectiveness of the proposed approach in terms of both solution quality and computational efficiency. In addition, the main advantage of our approach is twofold: The independence of the subproblems allows the problem to be solved in parallel; The approach to transform the original problem into SAT is flexible such that various state-of-the-art SAT solvers can be used.

With the development and application of GEO Earth observation satellites, the mission planning of GEO imaging satellites has become a new research issue. Due to the operational characteristics and advantages of GEO imaging satellites, GEO satellites are well suited for high frequency revisiting of point targets. This paper mainly studies the working characteristics of GEO imaging satellites and proposes a general GEO satellite imaging working mode. After the appropriate constraint simplification, a constraint satisfaction mathematical model is established. In order to solve the problem better, a genetic algorithm based on heuristic rules (HGA) is designed, through improving its population initialization function, crossover operator and mutation operator. Finally, the rationality and effectiveness of the algorithm are verified by experimental scenarios of different scales.