A History of Metaheuristics

This chapter describes the history of metaheuristics in five distinct periods, starting long before the first use of the term and ending a long time in the future.

Interactive Reference Point-Based Guided Local Search for the Bi-objective Inventory Routing Problem

Eliciting preferences of a decision maker is a key factor to successfully combine search and decision making in an interactive method. Therefore, the progressively integration and simulation of the decision maker is a main concern in an application. We contribute in this direction by proposing an interactive method based on a reference point-based guided local search to the bi-objective Inventory Routing Problem. A local search metaheuristic, working on the delivery intervals, and the Clarke & Wright savings heuristic is employed for the subsequently obtained Vehicle Routing Problem. To elicit preferences, the decision maker selects a reference point to guide the search in interesting subregions. Additionally, the reference point is used as a reservation point to discard solutions outside the cone, introduced as a convergence criterion. Computational results of the reference point-based guided local search are reported and analyzed on benchmark data in order to show the applicability of the approach.

Solution Representations and Local Search for the bi-objective Inventory Routing Problem

The solution of the biobjective IRP is rather challenging, even for metaheuristics. We are still lacking a profound understanding of appropriate solution representations and effective neighborhood structures. Clearly, both the delivery volumes and the routing aspects of the alternatives need to be reflected in an encoding, and must be modified when searching by means of local search. Our work contributes to the better understanding of such solution representations. On the basis of an experimental investigation, the advantages and drawbacks of two encodings are studied and compared.

Neigborhood Selection in Variable Neighborhood Search

Variable neighborhood search (VNS) is a metaheuristic for solving optimization problems based on a simple principle: systematic changes of neighborhoods within the search, both in the descent to local minima and in the escape from the valleys which contain them. Designing these neighborhoods and applying them in a meaningful fashion is not an easy task. Moreover, an appropriate order in which they are applied must be determined. In this paper we attempt to investigate this issue. Assume that we are given an optimization problem that is intended to be solved by applying the VNS scheme, how many and which types of neighborhoods should be investigated and what could be appropriate selection criteria to apply these neighborhoods. More specifically, does it pay to "look ahead" (see, e.g., in the context of VNS and GRASP) when attempting to switch from one neighborhood to another?

On the use of reference points for the biobjective Inventory Routing Problem

The article presents a study on the biobjective inventory routing problem. Contrary to most previous research, the problem is treated as a true multi-objective optimization problem, with the goal of identifying Pareto-optimal solutions. Due to the hardness of the problem at hand, a reference point based optimization approach is presented and implemented into an optimization and decision support system, which allows for the computation of a true subset of the optimal outcomes. Experimental investigation involving local search metaheuristics are conducted on benchmark data, and numerical results are reported and analyzed.

Practical inventory routing: A problem definition and an optimization method

The global objective of this work is to provide practical optimization methods to companies involved in inventory routing problems, taking into account this new type of data. Also, companies are sometimes not able to deal with changing plans every period and would like to adopt regular structures for serving customers.