A Tabu Search Matheuristic for the Generalized Quadratic Assignment Problem

This work treats the so-called Generalized Quadratic Assignment Problem. Solution methods are based on heuristic and partially LP-optimizing ideas. Base constructive results stem from a simple 1-pass heuristic and a tree-based branch-and-bound type approach. Then we use a combination of Tabu Search and Linear Programming for the improving phase. Hence, the overall approach constitutes a type of mat- and metaheuristic algorithm. We evaluate the different algorithmic designs and report computational results for a number of data sets, instances from literature as well as own ones. The overall algorithmic performance gives rise to the assumption that the existing framework is promising and worth to be examined in greater detail

An Adaptive Memory-Based Approach Based on Partial Enumeration

We propose an iterative memory-based algorithm for solving a class of combinatorial optimization problems. The algorithm generates a sequence of gradually improving solutions by exploiting at each iteration the knowledge gained in previous iterations. At each iteration, the algorithm builds an enumerative tree and stores at each tree level a set of promising partial solutions that will be used to drive the tree exploration in the following iteration. We tested the effectiveness of the proposed method on an hard combinatorial optimization problem arising in the design of telecommunication networks, the Non Bifurcated Network Design Problem, and we report computational results on a set of test problems simulating real life instances

Scatter search and path relinking: Foundations and advanced designs

Abstract — Scatter Search and its generalized form Path Relinking, are evolutionary methods that have been successfully applied to hard optimization problems. Unlike genetic algorithms, they operate on a small set of solutions and employ diversification strategies of the form proposed in Tabu Search, which give precedence to strategic learning based on adaptive memory, with limited recourse to randomization. The fundamental concepts and principles were first proposed in the 1970s as an extension of formulations, dating back to the 1960s, for combining decision rules and problem constraints. (The constraint combination approaches, known as surrogate constraint methods, now independently provide an important class of relaxation strategies for global optimization.) The Scatter Search framework is flexible, allowing the development of alternative implementations with varying degrees of sophistication. Path Relinking, on the other hand, was first proposed in the context of the Tabu Search metaheuristics, but it has been also applied with a variety of other methods. This chapter’s goal is to provide a grounding in the essential ideas of Scatter Search and Path Relinking, together with pseudo-codes of simple versions of these methods, that will enable readers to create successful applications of their own