Design of Heuristic Algorithms for Hard Optimization

This open access book demonstrates all the steps required to design heuristic algorithms for difficult optimization. The classic problem of the travelling salesman is used as a common thread to illustrate all the techniques discussed. This problem is ideal for introducing readers to the subject because it is very intuitive and its solutions can be graphically represented. The book features a wealth of illustrations that allow the concepts to be understood at a glance. The book approaches the main metaheuristics from a new angle, deconstructing them into a few key concepts presented in separate chapters: construction, improvement, decomposition, randomization and learning methods. Each metaheuristic can then be presented in simplified form as a combination of these concepts. This approach avoids giving the impression that metaheuristics is a non-formal discipline, a kind of cloud sculpture. Moreover, it provides concrete applications of the travelling salesman problem, which illustrate in just a few lines of code how to design a new heuristic and remove all ambiguities left by a general framework. Two chapters reviewing the basics of combinatorial optimization and complexity theory make the book self-contained. As such, even readers with a very limited background in the field will be able to follow all the content

Heuristic methods for large centroid clustering problems

This article presents new heuristic methods for solving a class of hard centroid clustering problems including the p-median, the sum-of-squares clustering and the multi-source Weber problems. Centroid clustering is to partition a set of entities into a given number of subsets and to find the location of a centre for each subset in such a way that a dissimilarity measure between the entities and the centres is minimized. The first method proposed is a candidate list search that produces good solutions in a short amount of time if the number of centres in the problem is not too large. The second method is a general local optimization approach that finds very good solutions. The third method is designed for problems with a large number of centres; it decomposes the problem into subproblems that are solved independently. Numerical results show that these methods are efficient—dozens of best solutions known to problem instances of the literature have been improved—and fast, handling problem instances with more than 85,000 entities and 15,000 centres—much larger than those solved in the literature. The expected complexity of these new procedures is discussed and shown to be comparable to that of an existing method which is known to be very fast

Comparison of iterative searches for the quadratic assignment problem

This paper compares some of the most efficient heuristic methods for the quadratic assignment problem. These methods are known as strict taboo search, robust taboo search, reactive taboo search and genetic hybrids. It is shown that the efficiency of these methods strongly depends on the problem type and that no one method is better than all the others. A fast method for tuning the short term memory parameters of taboo searches is proposed and its validity is experimentally verified on long searches. A new type of quadratic assignment problem occurring in the design of grey patterns is proposed and it is shown how to adapt and improve the existing iterative searches for this specific problem. Finally, the usual way of implementing approximations of strict taboo search is discussed and better approximations are proposed

An n log n heuristic for the TSP

An n log n randomized method based on POPMUSIC metaheuristic is proposed for generating reasonably good solutions to the travelling salesman problem. The method improves a previous work which algorithmic complexity was in n1:6. The method has been tested on instances with billions of cities. Few dozens of runs are able to generate a very high proportion of the edges of the best solutions known. This characteristic is exploited in a new release of the Helsgaun’s implementation of Lin-Kernighan heuristic (LKH) that is also able to produce rapidly extremely good solutions for non Euclidean instances

Parallel taboo search techniques for the job shop scheduling problem

We apply the global optimization technique called taboo search to the job shop scheduling problem and show that our method is typically more efficient than the shifting bottleneck procedure, and also more efficient than a recently proposed simulated annealing implementation. We also identify a type of problem for which taboo search provides an optimal solution in a polynomial mean time in practice, while an implementation of the shifting bottleneck procedure seems to take an exponential amount of computation time. Included are computational results that establish new best solutions for a number of benchmark problems from the literature. Finally, we give a fast parallel algorithm that provides good solutions to very large problems in a very short computation time

Design of heuristic algorithms for hard optimization ::with python codes for the travelling salesman problem

This open access book demonstrates all the steps required to design heuristic algorithms for difficult optimization. The classic problem of the travelling salesman is used as a common thread to illustrate all the techniques discussed. This problem is ideal for introducing readers to the subject because it is very intuitive and its solutions can be graphically represented. The book features a wealth of illustrations that allow the concepts to be understood at a glance. The book approaches the main metaheuristics from a new angle, deconstructing them into a few key concepts presented in separate chapters: construction, improvement, decomposition, randomization and learning methods. Each metaheuristic can then be presented in simplified form as a combination of these concepts. This approach avoids giving the impression that metaheuristics is a non-formal discipline, a kind of cloud sculpture. Moreover, it provides concrete applications of the travelling salesman problem, which illustrate in just a few lines of code how to design a new heuristic and remove all ambiguities left by a general framework. Two chapters reviewing the basics of combinatorial optimization and complexity theory make the book self-contained. As such, even readers with a very limited background in the field will be able to follow all the content

A heuristic column generation method for the heterogeneous fleet VRP

This paper presents a heuristic column generation method for solving vehicle routing problems with a heterogeneous fleet of vehicles. The method may also solve the fleet size and composition vehicle routing problem and new best known solutions are reported for a set of classical problems. Numerical results show that the method is robust and efficient, particularly for medium and large size problem instances

Some efficient heuristic methods for the flow shop sequencing problem

In this paper the best heuristic methods known up to now are compared to solve the flow shop sequencing problem and we improve the complexity of the best one. Next, this problem is applied to taboo search, a new technique to solve combinatorial optimization problems, and computational experiments are reported. Finally a parallel taboo search algorithm is presented and experimental results show that this heuristic allows very good speed-up