Hybrid Meta-heuristics with VNS and Exact Methods: Application to Large Unconditional and Conditional Vertex p-Centre Problems

Large-scale unconditional and conditional vertex p-centre problems are solved using two meta-heuristics. One is based on a three-stage approach whereas the other relies on a guided multi-start principle. Both methods incorporate Variable Neighbourhood Search, exact method, and aggregation techniques. The methods are assessed on the TSP dataset which consist of up to 71,009 demand points with p varying from 5 to 100. To the best of our knowledge, these are the largest instances solved for unconditional and conditional vertex p-centre problems. The two proposed meta-heuristics yield competitive results for both classes of problems

Predictive police patrolling to target hotspots and cover response demand

This is an Open Access Article. It is published by Springer under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/Police forces are constantly competing to provide adequate service whilst faced with major funding cuts. The funding cuts result in limited resources hence methods of improving resource efficiency are vital to public safety. One area where improving the efficiency could drastically improve service is the planning of patrol routes for incident response officers. Current methods of patrolling lack direction and do not consider response demand. Police patrols have the potential to deter crime when directed to the right areas. Patrols also have the ability to position officers with access to high demand areas by pre-empting where response demand will arise. The algorithm developed in this work directs patrol routes in real-time by targeting high crime areas whilst maximising demand coverage. Methods used include kernel density estimation for hotspot identification and maximum coverage location problems for positioning. These methods result in more effective daily patrolling which reduces response times and accurately targets problem areas. Though applied in this instance to daily patrol operations, the methodology could help to reduce the need for disaster relief operations whilst also positioning proactively to allow quick response when disaster relief operations are required

An evaluation of three DoE-guided meta-heuristic-based solution methods for a three-echelon sustainable distribution network

This article evaluates the efficiency of three meta-heuristic optimiser (viz. MOGA-II, MOPSO and NSGA-II)-based solution methods for designing a sustainable three-echelon distribution network. The distribution network employs a bi-objective location-routing model. Due to the mathematically NP-hard nature of the model a multi-disciplinary optimisation commercial platform, modeFRONTIER®, is adopted to utilise the solution methods. The proposed Design of Experiment (DoE)-guided solution methods are of two phased that solve the NP-hard model to attain minimal total costs and total CO2 emission from transportation. Convergence of the optimisers are tested and compared. Ranking of the realistic results are examined using Pareto frontiers and the Technique for Order Preference by Similarity to Ideal Solution approach, followed by determination of the optimal transportation routes. A case of an Irish dairy processing industry’s three-echelon logistics network is considered to validate the solution methods. The results obtained through the proposed methods provide information on open/closed distribution centres (DCs), vehicle routing patterns connecting plants to DCs, open DCs to retailers and retailers to retailers, and number of trucks required in each route to transport the products. It is found that the DoE-guided NSGA-II optimiser based solution is more efficient when compared with the DoE-guided MOGA-II and MOPSO optimiser based solution methods in solving the bi-objective NP-hard three-echelon sustainable model. This efficient solution method enable managers to structure the physical distribution network on the demand side of a logistics network, minimising total cost and total CO2 emission from transportation while satisfying all operational constraints

Opuntia in México: Identifying Priority Areas for Conserving Biodiversity in a Multi-Use Landscape

BACKGROUND: México is one of the world's centers of species diversity (richness) for Opuntia cacti. Yet, in spite of their economic and ecological importance, Opuntia species remain poorly studied and protected in México. Many of the species are sparsely but widely distributed across the landscape and are subject to a variety of human uses, so devising implementable conservation plans for them presents formidable difficulties. Multi-criteria analysis can be used to design a spatially coherent conservation area network while permitting sustainable human usage. METHODS AND FINDINGS: Species distribution models were created for 60 Opuntia species using MaxEnt. Targets of representation within conservation area networks were assigned at 100% for the geographically rarest species and 10% for the most common ones. Three different conservation plans were developed to represent the species within these networks using total area, shape, and connectivity as relevant criteria. Multi-criteria analysis and a metaheuristic adaptive tabu search algorithm were used to search for optimal solutions. The plans were built on the existing protected areas of México and prioritized additional areas for management for the persistence of Opuntia species. All plans required around one-third of México's total area to be prioritized for attention for Opuntia conservation, underscoring the implausibility of Opuntia conservation through traditional land reservation. Tabu search turned out to be both computationally tractable and easily implementable for search problems of this kind. CONCLUSIONS: Opuntia conservation in México require the management of large areas of land for multiple uses. The multi-criteria analyses identified priority areas and organized them in large contiguous blocks that can be effectively managed. A high level of connectivity was established among the prioritized areas resulting in the enhancement of possible modes of plant dispersal as well as only a small number of blocks that would be recommended for conservation management

Neighbourhood Reduction in Global and Combinatorial Optimization: The Case of the p-Centre Problem

Neighbourhood reductions for a class of location problems known as the vertex (or discrete) and planar (or continuous) p-centre problems are presented. A brief review of these two forms of the p-centre problem is first provided followed by those respective reduction schemes that have shown to be promising. These reduction schemes have the power of transforming optimal or near optimal methods such as metaheuristics or relaxation-based procedures, which were considered relatively slow, into efficient and exciting ones that are now able to find optimal solutions or tight lower/upper bounds for larger instances. Research highlights of neighbourhood reduction for global and combinatorial optimisation problems in general and for related location problems in particular are also given

The incorporation of fixed cost and multilevel capacities into the discrete and continuous single source capacitated facility location problem

In this study we investigate the single source location problem with the presence of several possible capacities and the opening (fixed) cost of a facility that is depended on the capacity used and the area where the facility is located. Mathematical models of the problem for both the discrete and the continuous cases using the Rectilinear and Euclidean distances are produced. Our aim is to find the optimal number of open facilities, their corresponding locations, and their respective capacities alongside the assignment of the customers to the open facilities in order to minimise the total fixed and transportation costs. For relatively large problems, two solution methods are proposed namely an iterative matheuristic approach and VNS-based matheuristic technique. Dataset from the literature is adapted to assess our proposed methods. To assess the performance of the proposed solution methods, the exact method is first applied to small size instances where optimal solutions can be identified or lower and upper bounds can be recorded. Results obtained by the proposed solution methods are also reported for the larger instances