Jens Gottlieb

A study of greedy, local search, and ant colony optimization approaches for car sequencing problems

This paper describes and compares several heuristic approaches for the car sequencing problem. We first study greedy heuristics, and show that dynamic ones clearly outperform their static counterparts. We then describe local search and ant colony optimization (ACO) approaches, that both integrate greedy heuristics, and experimentally compare them on benchmark instances. ACO yields the best solution quality for smaller time limits, and it is comparable to local search for larger limits. Our best algorithms proved one instance being feasible, for which it was formerly unknown whether it is satisfiable or not.

Empirical Analysis of Locality, Heritability and Heuristic Bias in Evolutionary Algorithms: A Case Study for the Multidimensional Knapsack Problem

Our main aim is to provide guidelines and practical help for the design of appropriate representations and operators for evolutionary algorithms (EAs). For this purpose, we propose techniques to obtain a better understanding of various effects in the interplay of the representation and the operators. We study six different representations and associated variation operators in the context of a steady-state evolutionary algorithm for the multidimensional knapsack problem. Four of them are indirect decoder-based techniques, and two are direct encodings combined with different initialization, repair, and local improvement strategies. The complex decoders and the local improvement and repair strategies make it practically impossible to completely analyze such EAs in a fully theoretical way. After comparing the general performance of the chosen EA variants for the multidimensional knapsack problem on two benchmark suites, we present a hands-on approach for empirically analyzing important aspects of initialization, mutation, and crossover in an isolated fashion. Static, inexpensive measurements based on randomly created solutions are performed in order to quantify and visualize specific properties with respect to heuristic bias, locality, and heritability. These tests shed light onto the complex behavior of such EAs and point out reasons for good or bad performance. In addition, the proposed measures are also examined during actual EA runs, which gives further insight into dynamic aspects of evolutionary search and verifies the validity of the isolated static measurements. All measurements are described in a general way, allowing for an easy adaption to other representations and problems.

Vehicle routing with compartments: applications, modelling and heuristics

Despite the vast amount of literature about vehicle routing problems, only very little attention has been paid to vehicles with compartments that allow transportation of inhomogeneous products on the same vehicle, but in different compartments. We motivate a general vehicle routing problem with compartments that is essential for several industries, like the distribution of food or petrol. We introduce a formal model, an integer program formulation and a benchmark suite of 200 instances. A solver suite of heuristic components is presented, which covers a broad range of alternative approaches for construction, local search, large neighbourhood search and meta-heuristics. The empirical results for the benchmark instances identify effective algorithmic setups as well as essential components for achieving high solution quality. In a comparison on 23 specific and combinatorially less complex instances taken from literature, our algorithm showed to be competitive.

Solving Car Sequencing Problems by Local Optimization

Real-world car sequencingproblems deal with lots of constraints, which differ in their types and priorities. We evaluate three permutation-based local search algorithms that use different acceptance criteria for moves. The algorithms meet industrial requirements to obtain acceptable solutions in a rather short time. It is essential to employ move operators which can be evaluated quite fast. Further, usingdifferen t move types enlarges the neighbourhood, thereby decreasing the total number of local optima in the search space. The comparison of the acceptance criteria shows that the greedy approach is inferior to two variants of threshold acceptingthat allow escapingfrom local optima.

Direct Representation and Variation Operators for the Fixed Charge Transportation Problem

The fixed charge transportation problem (FCTP) has been tackled by evolutionary algorithms (EAs) using representations like permutations, Prufer numbers, or matrices. We present a new direct representation that restricts search to basic solutions and allows using problem-specific variation operators. This representation is compared w.r.t. locality and performance to permutations and Prufer numbers. It clearly outperforms all other EAs and even reaches the solution quality of tabu search, the most successful heuristic for the FCTP we are aware of.

On the Feasibility Problem of Penalty-Based Evolutionary Algorithms for Knapsack Problems

Constrained optimization problems can be tackled by evolutionary algorithms using penalty functions to guide the search towards feasibility. The core of such approaches is the design of adequate penalty functions. All authors, who designed penalties for knapsack problems, recognized the feasibility problem, i.e. the final population contains unfeasible solutions only. In contrast to previous work, this paper explains the origin of the feasibility problem. Using the concept of fitness segments, a computationally easy analysis of the fitness landscape is suggested. We investigate the effects of the initialization routine, and derive guidelines that ensure resolving the feasibility problem. A new penalty function is proposed that reliably leads to a final population containing feasible solutions, independently of the initialization method employed.

Adaptive Fitness Functions for the Satisfiability Problem

Adaptive fitness functions have led to very successful evolutionary algorithms for the satisfiability problem. Although comparisons are available for benchmarks, a deeper understanding of the effects of adaptation is desirable. Therefore, we compare three approaches based on adapting weights. The dynamics of these weights motivate the use of decay factors, which significantly improve the success rate for two adaptation schemes. The most successful technique can be further improved by accelerating the adaptation process concerning difficult clauses.

On the Effectivity of Evolutionary Algorithms for the Multidimensional Knapsack Problem

When designing evolutionary algorithms (EAs) for the multidimensional knapsack problem, it is important to consider that the optima lie on the boundary B of the feasible region of the search space. Previously published EAs are reviewed, focusing on how they take this into account. We present new initialization routines and compare several repair and optimization methods, which help to concentrate the search on B. Our experiments identify the best EAs directly exploring B.

Applications of racing algorithms: an industrial perspective

Stochastic local search (SLS) methods like evolutionary algorithms, ant colony optimisation or iterated local search receive an ever increasing attention for the solution of highly application relevant optimisation problems. Despite their noteworthy successes, several issues still hinder their even wider spread. One central issue is the configuration and parameterisation of SLS methods, which is known to be a time- and personal-intensive process. Recently, several attempts have been made to automate the tuning of SLS algorithms. One of the most promising directions is the usage of the racing methodology, which is a statistical method for selecting promising candidate configurations. We present results of a study on the application of this methodology to the tuning of a complex SLS method for an industrial vehicle scheduling and routing problem, and compare the performance of two racing methods.

A Comparison of Two Representations for the Fixed Charge Transportation Problem

In the past years several evolutionary algorithms have been applied to the fixed charge transportation problem (FCTP). Although suffering from a lack of locality, the Prufer number representation has recently been suggested for the FCTP, and - to our surprise - it has been reported to yield good results. Since this disagrees with the common intuition that locality is an important prerequisite of successful evolutionary search, we analyse the Prufer number representation in greater detail. The results show that the Prufer number representation is superior to random search but clearly inferior to the permutation representation with respect to solution quality, which is explained by our locality analysis.