The multi-depot open location routing problem with a heterogeneous fixed fleet

This paper introduces the multi-depot open location routing problem (MD-OLRP) with a heterogeneous fixed fleet. The problem is inspired by the collection problem of a company which collects raw materials from different suppliers coordinating several carriers. Each carrier has a heterogeneous fixed fleet. Moreover, there is a fixed cost for contracting each vehicle and a variable cost associated with the distance traveled. The empty haul return to the vehicles depot is not considered in the cost. The raw materials collected are delivered to a single delivery point. The problem is modeled as a Mixed Integer Linear Program (MILP) that minimizes the total cost, selecting the carriers to be contracted, the vehicles to be used from each contracted carrier and the collection routes. For small instances, the model can be solved to optimality. However, approximate procedures are necessary to handle larger instances. In this sense, in the present work we propose an intelligent metaheuristic which incorporates problem specific knowledge to solve it. The computational results show that the solution method is computationally efficient and provides high quality solutions. In particular, the new solution obtained for the case of study generates savings of 30.86% to the company. The main contributions of the paper are the new problem statement that was not found in the literature, its association to the real problem of a company and the intelligent metaheuristic proposed to solve it. Additional experimentation used the model proposed to solve a simpler problem obtaining new best solutions compared to those reported in the recent literatur

Hybrid metaheuristics for the profitable arc tour problem

The profitable arc tour problem is a variant in the vehicle routing problems. It is included in the family of the vehicle routing with profit problems in which a set of vehicle tours are constructed. The objective is to find a set of cycles in the vehicle tours that maximize the collection of profits minus travel costs, subject to constraints limiting the length of cycles that profit is available on arcs. To solve this variant we adopted two metaheuristics based on adaptive memory. We show that our algorithms provide good results in terms of solution quality and running times.

Danger theory based artificial immune system solving dynamic constrained single-objective optimization

In this paper, we propose an artificial immune system (AIS) based on the danger theory in immunology for solving dynamic nonlinear constrained single-objective optimization problems with time-dependent design spaces. Such proposed AIS executes orderly three modules-danger detection, immune evolution and memory update. The first module identifies whether there are changes in the optimization environment and decides the environmental level, which helps for creating the initial population in the environment and promoting the process of solution search. The second module runs a loop of optimization, in which three sub-populations each with a dynamic size seek simultaneously the location of the optimal solution along different directions through co-evolution. The last module stores and updates the memory cells which help the first module decide the environmental level. This optimization system is an on-line and adaptive one with the characteristics of simplicity, modularization and co-evolution. The numerical experiments and the results acquired by the nonparametric statistic procedures, based on 22 benchmark problems and an engineering problem, show that the proposed approach performs globally well over the compared algorithms and is of potential use for many kinds of dynamic optimization problems. © 2013 Springer-Verlag Berlin Heidelberg