In each iteration new points obtained in the continuous phase are added to the discrete formulation. Thus, the two formulations become equivalent in a limiting sense. In this paper we introduce the idea of adding ’injection points’ in the discrete phase of RLS in order to escape a current local solution. Preliminary results are obtained on benchmark data sets for the multi-source Weber problem that support further investigation of the RLS framework. | Yugoslav Journal of Operations Research 27 (2017), Number 3, 291–300 DOI: USING INJECTION POINTS IN REFORMULATION LOCAL SEARCH FOR SOLVING CONTINUOUS LOCATION PROBLEMS Jack BRIMBERG Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, ON, K7K7B4, Canada Zvi DREZNER Steven G. Mihaylo College of Business and Economics, California State University, Fullerton, CA 92634, USA zdrezner@ ´ Nenad MLADENOVIC Mathematical Institiute, Serbian Academy of Sciences and Arts, Knez Mihajlova 36, 11000 Belgrade, Serbia nenad@ Said SALHI Centre for Logistics & Heuristic Optimization, Kent Business School, University of Kent, Canterbury CT2 7PE, United Kingdom Received: May 2016 / Accepted: October 2016 Abstract: Reformulation local search (RLS) has been recently proposed as a new approach for solving continuous location problems. The main idea, although not new, is to exploit the relation between the continuous model and its discrete counterpart. The RLS switches between the continuous model and a discrete relaxation in order to expand the search. In each iteration new points obtained in the continuous phase are added to the discrete formulation. Thus, the two formulations become equivalent in a limiting sense. In this paper we introduce the idea of adding ’injection points’ in the discrete phase of RLS in order to escape a current local solution. Preliminary results 292 J. Brimberg, et al. / Using Injection Points in Reformulation Local Search are obtained on benchmark data sets for the multi-source Weber problem that support further investigation of the RLS framework. Keywords: Continuous Location, Weber Oroblem, Formulation Space Search, Reformulation Descent, Variable Neighbourhood Search. MSC: 90B85, 90C26. 1. INTRODUCTION Continuous location problems generally require finding the location of a given number, say p, of new facility sites in RN , .
