Peter Greistorfer - Academia.edu (original) (raw)

Papers by Peter Greistorfer

arXiv (Cornell University), Sep 29, 2021

For a reduction in environmental pollution and dependency on petroleum, electric vehicles (EV) pr... more For a reduction in environmental pollution and dependency on petroleum, electric vehicles (EV) present an advantageous alternative to traditionally fossil-fuel powered automobiles. Rapid growth in the number of EVs requires an urgent need to develop an adequate charging station infrastructure to stimulate and facilitate their usage. Due to restricted investments in the development of a sufficient infrastructure, locations have to be chosen deliberately. In this paper, three extensions considering different objectives and various constraints to the deterministic flow refuelling location problem (DFRLP), described 2017 by de Vries and Duijzer, are introduced. In the first extension we ask how many charging stations (CS) are necessary to cover a pre-specified number of EVs and therefore exchange the original objective function for a minimizing cost function. Secondly, our research shows that, when considering location-dependent construction costs, results heavily depend on the relations of said cost differences. Tests for different cost scenarios are carried out and policy implications are discussed. In the last extension, we consider the capacity of a CS to be limited. The DFRLP assumes an unlimited capacity, meaning it is always possible to refuel all EVs at all CSs, where they stop. In our model the capacity is put into relation to the total sum of demands generated by all EVs, passing a particular CS, which means that our model determines the placement and the sizes of all CSs simultaneously. Finally, all extensions are evaluated using benchmarks instances based on test instances from the literature.

The Obnoxious p-Median problem consists in selecting a subset of p facilities from a given set of... more The Obnoxious p-Median problem consists in selecting a subset of p facilities from a given set of possible locations, in such a way that the sum of the distances between each customer and its nearest facility is maximized. The problem is NP-hard and can be formulated as an integer linear program. It was introduced in the 1990s, and a branch and cut method coupled with a tabu search has been recently proposed. In this paper, we propose a heuristic method – based on the GRASP methodology – for finding approximate solutions to this optimization problem. In particular, we consider an advanced GRASP design in which a filtering mechanism avoids applying the local search method to low quality constructed solutions. Empirical results indicate that the proposed implementation compares favorably to previous methods. This fact is confirmed with non-parametric statistical tests.

One of the challenging aspects in metaheuristics design is an adequate definition of solution qua... more One of the challenging aspects in metaheuristics design is an adequate definition of solution quality , which has both cost and structural properties. Cost is always measured by an objective function, while structural properties are reflected by values of decision variables. From the application of successful metaheuristics, first and foremost scatter search (SCS, see [1]), it is well-known that structural properties play an import role when a set of solutions has to be evaluated during the course of the optimization. Those pooled solutions may be treated in a simultaneous way, e.g. in the so-called reference set of an SCS, or subsequently in multi(re)start approaches, which means that new search trajectories are initialized upon solutions which have been proved to incorporate a higher quality and have been recognized as being elite during the search history. Algorithms which are evaluating solutions upon their distance to each other or to the incumbent best-known solution have prov...

Computers & Operations Research, 2019

A generalization of the classical TSP is the so-called quadratic travelling salesman problem (QTS... more A generalization of the classical TSP is the so-called quadratic travelling salesman problem (QTSP), in which a cost coefficient is associated with the transition in every vertex, i.e. with every pair of edges traversed in succession. In this paper we consider two geometrically motivated special cases of the QTSP known from the literature, namely the angular-metric TSP, where transition costs correspond to turning angles in every vertex, and the angular-distance-metric TSP, where a linear combination of turning angles and Euclidean distances is considered. At first we introduce a wide range of heuristic approaches, motivated by the typical geometric structure of optimal solutions. In particular, we exploit lens-shaped neighborhoods of edges and a decomposition of the graph into layers of convex hulls, which are then merged into a tour by a greedy-type procedure or by utilizing an ILP model. Secondly, we consider an ILP model for a standard linearization of QTSP and compute fractional solutions of a relaxation. By rounding we obtain a collection of subtours, paths and isolated points, which are combined into a tour by various strategies, all of them involving auxiliary ILP models. Finally, different improvement heuristics are proposed, most notably a matheuristic which locally reoptimizes the solution for rectangular sectors of the given point set by an ILP approach. Extensive computational experiments for benchmark instances from the literature and extensions thereof illustrate the Pareto-efficient frontier of algorithms in a (running time, objective value)-space. It turns out that our new methods clearly dominate the previously published heuristics.

Central European Journal of Operations Research, 2019

In the automobile supplier industry companies frequently need to make bids, typically based on co... more In the automobile supplier industry companies frequently need to make bids, typically based on cost estimates for the production process, to obtain incoming orders. The production process is executed in several main stages, which are linked by intraplant logistics. To model different scenarios, we consider two separate organizational approaches towards cost estimation. In the first one, all the main stages are optimized via a central authority. The second approach models a decentralized decision making process, as it is currently used in practice. Moreover, we analyze different coordination mechanisms to improve the decentralized approach. To capture the uncertainty during the bid process, associated with key parameters like demand, capacity consumption and cost, we formulate a stochastic version of the model, capturing different risk preferences to compare risk-neutral and risk-averse decision making. The resulting MILPs are solved with CPLEX and results for an illustrative example based on a real data set are presented.

European Journal of Operational Research, 2016

The Obnoxious p-Median problem consists in selecting a subset of p facilities from a given set of... more The Obnoxious p-Median problem consists in selecting a subset of p facilities from a given set of possible locations, in such a way that the sum of the distances between each customer and its nearest facility is maximized. The problem is NP-hard and can be formulated as an integer linear program. It was introduced in the 1990s, and a branch and cut method coupled with a tabu search has been recently proposed. In this paper, we propose a heuristic method – based on the Greedy Randomized Adaptive Search Procedure, GRASP, methodology – for finding approximate solutions to this optimization problem. In particular, we consider an advanced GRASP design in which a filtering mechanism avoids applying the local search method to low quality constructed solutions. Empirical results indicate that the proposed implementation compares favorably to previous methods. This fact is confirmed with non-parametric statistical tests.

This paper considers a cyclic scheduling problem, which especially is applicable in the area of p... more This paper considers a cyclic scheduling problem, which especially is applicable in the area of public transport. The problem is the so-called Irreg-ular Polygon Scheduling Problem with the objective to maximize the distance between the nearest vertices of two different polygons. We give a mixed inte-ger LP-formulation of this NP-hard problem, derive some bounds and present a hybrid meta-heuristic algorithm for solving the problem. The main idea is to combine a Tabu Search with a Genetic Algorithm component. Computa-tional experience, based on comparative results obtained from CPLEX, shows the efficiency of the hybridization approach.

Bank-Archiv : Zeitschrift für das gesamte Bank- und Börsenwesen.- Wien : Linde-Verl, ISSN 0029-98... more Bank-Archiv : Zeitschrift für das gesamte Bank- und Börsenwesen.- Wien : Linde-Verl, ISSN 0029-9839, ZDB-ID 6359851. - Vol. 51.2003, 2, p. 119-128

Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, 1999

This paper considers a cyclic scheduling problem, which especially is applicable in the area of p... more This paper considers a cyclic scheduling problem, which especially is applicable in the area of public transport. The problem is the so-called Irregular Polygon Scheduling Problem with the objective to maximize the distance between the nearest vertices of two different polygons. We give a mixed integer LP-formulation of this NP-hard problem, derive some bounds and present a hybrid meta-heuristic algorithm for solving the problem. The main idea is to combine a Tabu Search with a Genetic Algorithm component. Computational experience, based on comparative results obtained from CPLEX, shows the efficiency of the hybridization approach.

Applied Optimization, 2003

ABSTRACT We investigate several versions of a tabu scatter search heuristic to solve permutation ... more ABSTRACT We investigate several versions of a tabu scatter search heuristic to solve permutation type optimization problems. The focus lies on the design of the three main components which are comprised in every pool-oriented method. These components are the input and output procedures, which are responsible for pool maintenance and determine the transfer of elite solutions, and a solution combination method which must effectively combine a set of elite solutions. We propose several methods for each of these three components and evaluate their combinations as heuristic design variants on a sample set of capacitated Chinese postman instances. Descriptive results are discussed in detail and supported by the testing of a statistical hypothesis.

Operations Research/Computer Science Interfaces Series

Recent metaheuristic developments have proved to be successful especially in cases where their fu... more Recent metaheuristic developments have proved to be successful especially in cases where their fundamental concepts are complemented with pool-oriented approaches such as scatter search. These algorithms maintain a reference set of high quality solutions which are repeatedly used during the search in order to guarantee a fruitful balance between diversification and intensification. However, maintaining such a pool is not a trivial undertaking. The main problem is to find a balance between the attempt to collect a number of high quality solutions, which often results in similar solution properties, and the need to guarantee a certain degree of diversity in the pool. In the present study we highlight the advantage of pool-oriented design while focusing on controlled input and output operations. We analyze the main pool components for metaheuristics and present a review of the literature on relevant strategies in tabu search, scatter search, and path relinking. Additionally, we provide a synthesis of the literature that highlights the critical aspects of effective pool maintenance.

Operations Research ’93, 1994

This paper is concerned with a routing-problem that arises in a variety of practical situations, ... more This paper is concerned with a routing-problem that arises in a variety of practical situations, e.g. in the case of household refuse collection and winter gritting or during the work of postmen and electricity- or gas-meter readers. This type of Vehicle-Routing-Problem (VRP) is called the Capacitated-Chinese-Postman-Problem (CCPP), a special instance of the general class of Capacitated-Arc-Routing-Problems (Bodin et. al. (1983), Golden et. al. (1983)) The model of the CCPP can be described as an arc-routing version of the well-known node-oriented standard VRP. Let H = (V, E, c, q) be a given graph with set of nodes V and set of edges E and let c: E→ R+ (d: E→z+) be a cost (demand) function assigning a positive real (integer) to each edge in H. The fleet of vehicles is homogenous, i.e. each vehicle has a capacity W and there is no restriction on the number of vehicles. Each edge demand must be satisfied by one vehicle i, which drives on route Ri. The cost of Ri, which starts and ends at the depot node, is c(Ri). Minimizing the total cost, the sum over all c(Ri), one has to determine a set of routes, called touring schedule T.

ABSTRACT this paper is to theoretically work out relevant pool strategies in the context of SCS a... more ABSTRACT this paper is to theoretically work out relevant pool strategies in the context of SCS and to evaluate them by means of computational comparisons. In Section 2 we examine the main components, the designs which may generally be used to control pool transfers and explain the concept of relatedness for the comparison of solutions. Section 3 deals with the application of population strategies and formulates ways and means of how they may be addressed to improve an existing SCS which uses a TS as a subroutine. Di#erent input-output strategies and solution combination methods (SCMs) have been additionally implemented and tested. Of primary interest are the capacitated CPP (CCPP) but also pure permutation problems to gain some insight in the generalizability of the arc routing results. Preliminary results, sketched in Section 4, indicate that, even if simple algorithmic modifications are used, the tuning of a pool process can have a very positive e#ect on the overall solution quality of a metaheuristic. This tendency becomes even clearer if more sophisticated mechanisms are introduced

Journal of Heuristics, 2007

... Experiments concerning sequential versus simultaneous maximization of objective function and ... more ... Experiments concerning sequential versus simultaneous maximization of objective function and distance Peter Greistorfer · Arne Løkketangen · Stefan Voß · David L. Woodruff ... complished by solving the single problem: (R) maxa,b f (a) + βf (b) + γd(a,b) subject to a ∈ X b ∈ X ...

Computers & Operations Research, 2008

Nature reserve site selection has become critical as the human population grows and environmental... more Nature reserve site selection has become critical as the human population grows and environmentalists seek ways to preserve species and their natural habitats. Simple tabu searches are developed and tested for two reserve site selection models-the maximal covering species problem and the maximal expected covering problem. The testbed is an Oregon terrestrial vertebrate data set composed of 426 species and 441 hexagonal sites. In addition, an extension to a linearized version of the maximal expected covering problem is proposed and tested.

Computers & Operations Research, 2006

The design of effective neighborhood search procedures is a primary issue for the performance of ... more The design of effective neighborhood search procedures is a primary issue for the performance of local search and advanced metaheuristic algorithms. Several recent studies have focused on the development of variable depth neighborhoods that generate sequences of interrelated elementary moves to create more complex compound moves. These methods are chiefly conceived to produce an adaptive search as the number of elementary moves in a compound move may vary from one iteration to another depending on the state of the search. The objective is to achieve this goal with modest computational effort. Although ejection chain methods are currently the most advanced methods in this domain, they usually require more complex implementations. The filter-and-fan (F&F) method appears as an alternative to ejection chain methods allowing for the creation of compound moves based on an effective tree search design. This paper reports the first implementation of the F&F approach to the uncapacitated facility location problem (UFLP). We examine a simple version of the F&F method in this study, and explore two search strategies under this framework. The results obtained on a set of 105 standard benchmark problems from the literature demonstrate that this simple but well-structured approach is highly effective for providing optimal and near-optimal solutions for the UFLP in a very short computation time, and indeed can be advantageously compared with the most advanced metaheuristic procedures in solving these problems.

Computers & Industrial Engineering, 2003

... Note that in Step 2 not only edges may be newly sequenced but they may also be directed to ac... more ... Note that in Step 2 not only edges may be newly sequenced but they may also be directed to achieve a cost reduction. However, as outlined, the edge assignment to routes is not affected by the GSH. It is solely the result of a low-level heuristic, namely the fifo-rule mentioned. ...

Journal of Heuristics, 2001

A cyclic scheduling problem with applications to transport efficiency is considered. Given a set ... more A cyclic scheduling problem with applications to transport efficiency is considered. Given a set of regular polygons, whose vertices represent regularly occurring events and are lying on a common circle line, the objective is to maximize the distance between the closest vertices of different polygons on the circle line. Lower and upper bounds for the optimal solution of this NP-hard

We consider a penalty function approach for the solving of the Max 3-SAT problem. The algorithm i... more We consider a penalty function approach for the solving of the Max 3-SAT problem. The algorithm introduced is a multi-start approach that makes use of elite-solution techniques derived from scatter search. More precisely, it is based on the so-called adaptive memory projection metaphor. The main focus of this paper is to demonstrate the usefulness of this projection idea in the context of the binary Max 3-SAT. We review the literature in that field, explain the metaheuristic proposed and present results on the basis of a DIMACS test set.

arXiv (Cornell University), Sep 29, 2021

Computers & Operations Research, 2019

Central European Journal of Operations Research, 2019

European Journal of Operational Research, 2016

The Obnoxious p-Median problem consists in selecting a subset of p facilities from a given set of... more The Obnoxious p-Median problem consists in selecting a subset of p facilities from a given set of possible locations, in such a way that the sum of the distances between each customer and its nearest facility is maximized. The problem is NP-hard and can be formulated as an integer linear program. It was introduced in the 1990s, and a branch and cut method coupled with a tabu search has been recently proposed. In this paper, we propose a heuristic method – based on the Greedy Randomized Adaptive Search Procedure, GRASP, methodology – for finding approximate solutions to this optimization problem. In particular, we consider an advanced GRASP design in which a filtering mechanism avoids applying the local search method to low quality constructed solutions. Empirical results indicate that the proposed implementation compares favorably to previous methods. This fact is confirmed with non-parametric statistical tests.

Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, 1999

This paper considers a cyclic scheduling problem, which especially is applicable in the area of p... more This paper considers a cyclic scheduling problem, which especially is applicable in the area of public transport. The problem is the so-called Irregular Polygon Scheduling Problem with the objective to maximize the distance between the nearest vertices of two different polygons. We give a mixed integer LP-formulation of this NP-hard problem, derive some bounds and present a hybrid meta-heuristic algorithm for solving the problem. The main idea is to combine a Tabu Search with a Genetic Algorithm component. Computational experience, based on comparative results obtained from CPLEX, shows the efficiency of the hybridization approach.

Applied Optimization, 2003

Operations Research/Computer Science Interfaces Series

Operations Research ’93, 1994

Journal of Heuristics, 2007

Computers & Operations Research, 2008

Computers & Operations Research, 2006

Computers & Industrial Engineering, 2003

Journal of Heuristics, 2001