The bike routeing problem with energy constraints

As climate change becomes more crucial, transporting products in urban areas by bicycle gains popularity. More companies start using bicycles as an alternative transportation mode and face challenges to efficiently satisfy the needs of their customers and employees. While designing the bike routes for pick up and delivery, it is required to take into account the energy needed by cyclists to move. The energy consumed in a bike route has to be kept under a certain threshold for cyclists to be able to pedal during the whole work shift. This leads to a new variant of the vehicle routeing problem called the bike routeing problem which aims at tackling constraints arising for bicycle deliveries. We propose a novel Mixed Integer Linear Programming model to determine the bike routes for delivering goods in urban areas. An Evolutionary Local Search algorithm is developed to efficiently solve the problem using new split and local search procedures. Experimental results obtained on random and real instances show the accuracy and stability of the proposed algorithms, as well as the relevance of the new problem

Column generation algorithms for bi-objective combinatorial optimization problems with a min–max objective

International audienceMany practical combinatorial optimization problems can be described by integer linear programs having an exponential number of variables, and they are efficiently solved by column generation algorithms. For these problems, column generation is used to compute good dual bounds that can be incorporated in branch-and-price algorithms. Recent research has concentrated on describing lower and upper bounds of bi-objective and general multi-objective problems with sets of points (bound sets). An important issue to address when computing a bound set by column generation is how to efficiently search for columns corresponding to each point of the bound set. In this work, we propose a generalized column generation scheme to compute bound sets for bi-objective combinatorial optimization problems. We present specific implementations of the generalized scheme for the case where one objective is a min–max function by using a variant of the ε-constraint method to efficiently model these problems. The proposed strategies are applied to a bi-objective extension of the multi-vehicle covering tour problem, and their relative performances based on different criteria are compared. The results show that good bound sets can be obtained in reasonable times if columns are efficiently managed. The variant of the ε-constraint presented is also better than a standard ε-constraint method in terms of the quality of the bound sets