This work addresses a challenging inventory routing problem that arises from a practical application faced by air-product companies, including Air Liquide. Given its computational complexity and industrial importance, this problem (denoted as IRP-Challenge2016) was presented as the topic of the French Operational Research and Decision Support Society/European Operational Research Society (ROADEF/EURO) Challenge 2016. The IRP-Challenge2016 seeks an optimal delivery schedule to minimize the unit distribution cost, while satisfying various hard constraints. It involves a single product, a heterogeneous fleet, heterogeneous drivers, multiperiods, a deterministic consumption forecast, and time-window constraints. We present a new mathematical formulation of the problem and introduce a matheuristic algorithm that integrates a local search-based metaheuristic with mathematical programming. Our algorithm combines mixed integer programming and linear programming as slave methods to optimize timing and delivery and embeds these procedures within a multineighborhood search metaheuristic to adjust routes. The method extends and enhances a preliminary version of our algorithm, which ranked third in the final round of the ROADEF/EURO Challenge 2016. Computational results for 20 challenge benchmark instances demonstrate the value of the proposed algorithm in terms of both effectiveness and efficiency with respect to the results reported in the competition. We additionally analyze several key components of our matheuristic to gain an insight into its operation.

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The p-center problem consists of choosing p centers from a set of candidates to minimize the maximum cost between any client and its assigned facility. In this paper, we transform the p-center problem into a series of set covering subproblems, and propose a vertex weighting-based tabu search (VWTS) algorithm to solve them. The proposed VWTS algorithm integrates distinguishing features such as a vertex weighting technique and a tabu search strategy to help the search to jump out of the local optima. Computational experiments on 138 most commonly used benchmark instances show that VWTS is highly competitive comparing to the state-of-the-art methods in spite of its simplicity. As a well-known NP-hard problem which has already been studied for over half a century, it is a challenging task to break the records on these classic datasets. Yet VWTS improves the best known results for 14 out of 54 large instances, and matches the optimal results for all remaining 84 ones. In addition, the computational time taken by VWTS is much shorter than other algorithms in the literature.

The optimal camera placement problem (OCP) aims to accomplish surveillance tasks with the minimum number of cameras, which is one of the topics in the GECCO 2020 Competition and can be modeled as the unicost set covering problem (USCP). This paper presents a weighting-based variable neighborhood search (WVNS) algorithm for solving OCP. First, it simplifies the problem instances with four reduction rules based on dominance and independence. Then, WVNS converts the simplified OCP into a series of decision unicost set covering subproblems and tackles them with a fast local search procedure featured by a swap-based neighborhood structure. WVNS employs an efficient incremental evaluation technique and further boosts the neighborhood evaluation by exploiting the dominance and independence features among neighborhood moves. Computational experiments on the 69 benchmark instances introduced in the GECCO 2020 Competition on OCP and USCP show that WVNS is extremely competitive comparing to the state-of-the-art methods. It outperforms or matches several best performing competitors on all instances in both the OCP and USCP tracks of the competition, and its advantage on 15 large-scale instances are over 10%. In addition, WVNS improves the previous best known results for 12 classical benchmark instances in the literature.

The shortest simple path problem with must-pass nodes (SSPP-MPN) aims to find a minimumcost simple path in a directed graph, where some specified nodes must be visited. We call these specified nodes as must-pass nodes. The SSPP-MPN has been proven to be NP-hard when the number of specified nodes is more than one, and it is at least as difficult as the traveling salesmen problem (TSP), a well-known NP-hard problem. In this paper, we propose a multi-stage metaheuristic algorithm based on multiple strategies such as k-opt move, candidate path search, conflicting nodes promotion, and connectivity relaxation for solving the SSPP-MPN. The main idea of the proposed algorithm is to transform the problem into classical TSP by relaxing the simple path constraint and try to repair the obtained solutions in order to meet the demands of the original problem. The computational results tested on three sets of totally 863 instances and comparisons with reference algorithms show the efficacy of the proposed algorithm in terms of both solution quality and computational efficiency.INDEX TERMS Constrained shortest path, must-pass nodes, multi-stage metaheuristic algorithm, routing problem, traveling salesman problem.