Single Allocation Hub Location with Heterogeneous Economies of Scale

The economies of scale in hub location is usually modeled by a constant parameter, which captures the benefits companies obtain through consolidation. In their article “Single allocation hub location with heterogeneous economies of scale,” Rostami et al. relax this assumption and consider hub-hub connection costs as piecewise linear functions of the flow amounts. This spoils the triangular inequality property of the distance matrix, making the classical flow-based model invalid and further complicates the problem. The authors tackle the challenge by building a mixed-integer quadratically constrained program and by developing a methodology based on constructing Lagrangian function, linear dual functions, and specialized polynomial-time algorithms to generate enhanced cuts. The developed method offers a new strategy in Benders-type decomposition through relaxing a set of complicating constraints in subproblems when such relaxation is tight. The results confirm the efficacy of the solution methods in solving large-scale problem instances.

An artificial immune system algorithm for solving the uncapacitated single allocation p-Hub median problem

The present paper deals with a variant of hub location problems (HLP): the uncapacitated single allocation p-Hub median problem (USApHMP). This problem consists to jointly locate hub facilities and to allocate demand nodes to these selected facilities. The objective function is to minimize the routing of demands between any origin and destination pair of nodes. This problem is known to be NP-hard. Based on the artificial immune systems (AIS) framework, this paper develops a new approach to efficiently solve the USApHMP. The proposed approach is in the form of a clonal selection algorithm (CSA) that uses appropriate encoding schemes of solutions and maintains their feasibility. Comprehensive experiments and comparison of the proposed approach with other existing heuristics are conducted on benchmark from civil aeronautics board, Australian post, PlanetLab and Urand data sets. The results obtained allow to demonstrate the validity and the effectiveness of our approach. In terms of solution quality, the results obtained outperform the best-known solutions in the literature.

Uniform Welfare Guarantees Under Identical Subadditive Valuations

We study the problem of allocating indivisible goods among agents that have an identical subadditive valuation over the goods. The extent of fair- ness and efficiency of allocations is measured by the generalized means of the values that the alloca- tions generate among the agents. Parameterized by an exponent term p, generalized-mean welfares en- compass multiple well-studied objectives, such as social welfare, Nash social welfare, and egalitarian welfare. We establish that, under identical subadditive valu- ations and in the demand oracle model, one can efficiently find a single allocation that approximates the optimal generalized-mean welfare—to within a factor of 40—uniformly for all p ∈ (−∞,1]. Hence, by way of a constant-factor approximation algorithm, we obtain novel results for maximizing Nash social welfare and egalitarian welfare for identical subadditive valuations.

Solving the Uncapacitated Single Allocation p-Hub Location Problem with Fixed Cost using Anti-Predatory NIA

Background: Hub Location Problem (HLP) deals with the long-term strategic decision planning in various application domains with the aim of reducing overall transportation cost. It deals with identifying hubs and allocating spokes to hubs in order to route the flow of goods between origin-destination locations. Due to the complex nature of the problem, meta-heuristic algorithms are best suited to solve HLPs. The existing algorithms face the accuracy and consistency related issues for solving the HLPs. Objective: This paper attempts to solve a variant of HLP, which is known as Uncapacitated Single Allocation p-Hub Location Problem with Fixed Cost (USApHLP-FC), using Anti-Predatory Nature-Inspired Algorithm (APNIA)to improve accuracy and consistency in results. Method: APNIA is a recently proposed meta-heuristic nature-inspired algorithm, which is based on the anti-predatory behavior of frogs .For solving the HLP, APNIA is used for both identifying the hubs and allocating the spokes to hubs in order to reduce total cost of goods transportation. Results: A numerical problem with 10 locations is used for empirical study. The experimental result shows that APNIA outperforms other leading proposal in terms of total cost and gap value. The obtained results of APNIA are compared with the genetic algorithm, particle swarm optimization, artificial bee colony, firefly algorithm, teacher learning based optimization and Jaya algorithm. The comparative study indicates that at least 0.86% improvement in accuracy and at least 10% gain in consistency by APNIA for different number of generations. Conclusion: The experimental evaluation and performance comparison signify that APNIA based approach has improved accuracy and consistency in solutions than other compared algorithms. It establishes the robustness of anti-predatory NIA for solving the hub location problems.