Jörg Homberger

Two Evolutionary Metaheuristics For The Vehicle Routing Problem With Time Windows

AbstractThe vehicle routing problem with time windows (VRPTW) is an extension of the well-known vehicle routing problem with a central depot. The objective is to design an optimal set of routes that services all customers and satisfies the given constraints, especially the time window constraints. The objective function considered here combines the minimization of the number of vehicles (primary criterion) and the total travel distance minimization (secondary criterion). In this paper, two evolution strategies for solving the VRPTW are proposed. The evolution strategies were tested on 58 problems from the literature with sizes varying from 100 to 417 customers and 2 to 54 vehicles. The generated new best known solutions indicate that evolution strategies are effective in reducing both the number of vehicles and the total travel distance

A multi‐agent system for the decentralized resource‐constrained multi‐project scheduling problem

A restart evolution strategy (RES) for the resource-constrained project scheduling problem (RCPSP), as well as its integration in a multi-agent system (MAS) for solving the decentralized resource-constrained multi-project scheduling problem (DRCMPSP) will be presented. To evaluate the developed approach, problem instances of the RCPSP taken from the literature with up to 300 activities are used, as well as 80 generated instances of the DRCMPSP, with up to 20 projects and with up to 120 activities each. For 73 instances of the RCPSP, the RES found better solutions than the best ones found so far. In addition, the MAS is suitable for solving large multi-project instances decentrally. The results for the DRCMPSP instances show that the presented decentralized MAS is competitive with a central solution approach.

Decentralized multi-level uncapacitated lot-sizing by automated negotiation

An automated negotiation mechanism for decentralized production coordination is presented and evaluated. The coordination problem contains a set of self-interested software agents, representing the production facilities of a supply chain, searching for a mutually agreeable production plan, while taking private information into account. The negotiation mechanism is applied and evaluated using a multi-facility production coordination problem, which is a reformulation of the well-known multi-level uncapacitated lot-sizing problem (MLULSP). The basic element of the mechanism is a decentralized simulated annealing method, consisting of a transition rule carried out by a neutral mediator agent and a cooperative acceptance rule carried out by negotiating agents. We use 176 benchmark problems from relevant literature for the evaluation. Experimental results show that the proposed negotiation mechanism comes close to those results which are obtained by centralized planning. Furthermore, the developed simulated annealing method applied in a single, centralized planning task is competitive with the best known solution methods for the MLULSP. It was possible to compute new best solutions for 24 of the benchmark problems.

A Parallel Genetic Algorithm for the Multilevel Unconstrained Lot-Sizing Problem

Acoarse-grained parallel genetic algorithm (PGA) for the multilevel unconstrained lot-sizing problem (MLULSP) is described and evaluated using 176 benchmark problems from the literature, with problem sizes varying from 5 to 500 products and with simulations ranging from 12 to 52 periods. The parallelization approach consists of concurrently executing several subpopulations (demes) of a genetic algorithm with the occasional migration of individuals between them. The migration is controlled by the migration model of Cantu-Paz [Cantu-Paz, E. 2001. Migration policies, selection pressure, and parallel evolutionary algorithms. J. Heuristics7 311--334]. The genetic algorithm used is based on a new binary coding for the MLULSP. The PGA, which is the first application of a parallel metaheuristic to the MLULSP, is competitive with the best known solution methods. It was possible with the new method to calculate new best solutions for 34 of the benchmark problems. Furthermore, the migration enables a super-linear speedup. The results indicate that parallel genetic algorithms are suitable for solving large-problem instances of the MLULSP with acceptable computing times.

A Pheromone-Based Negotiation Mechanism for Lot-Sizing in Supply Chains

A new generic negotiation mechanism to coordinate decentralized planning of a group of independent and self-interested decision makers or agents, who are searching for an agreeable contract regarding multiple interdependent issues, in the case of asymmetric information is presented. The basic idea of the mechanism is that the group members carry out a joint search based on a mediated pheromone matrix. By means of the Borda maximin voting rule, the agents determine contract proposals in each round of the negotiation process which are then used for the adaptation of pheromones or the generation of new contracts, respectively. The new negotiation mechanism is applied to the problem of decentralized lot-sizing in a supply chain. The resulting solution approach for the multi-level uncapacitated lot-sizing problem (MLULSP) is evaluated on the basis of 40 benchmark problems taken from the relevant literature. The derived results come close to those results which are obtained by centralized planning. Moreover, the new mechanism is competitive with other negotiation approaches which have been presented in the literature so far.

An Ant Colony Optimization Approach for the Multi-Level Unconstrained Lot-Sizing Problem

An Ant Colony Optimization approach for the MultiLevel Unconstrained Lot-Sizing Problem (MLULSP) is described and evaluated using 176 benchmark problems from the literature, with problem sizes varying from 5 to 500 products and up to 52 periods. The approach consists of a binary encoding of production plans. The lot-sizing decisions are mapped on a routing graph to apply the metaheuristic concept of ant systems. The proposed approach is competitive with the best known solution methods. It was possible with the new method to calculate new best solutions for 11 of the benchmark problems.

Integrating Side Payments into Collaborative Planning for the Distributed Multi-level Unconstrained Lot Sizing Problem

Collaborative planning mechanisms coordinate the decisions of multiple, autonomous, and self-interested decisions makers under asymmetric information. The approach proposed in this paper extends collaborative planning for the distributed multi-level uncapacitated lot-sizing problem by integrating compensation payments. Compensation or side payments provide an incentive for individual decision makers to accept inferior local solutions that may direct the search to superior global solutions for a coalition of decision makers. The approach uses neighborhood search, voting-based solution acceptance criteria and takes into account varying side payments which are negotiated. Based on 272 benchmark instances the computational study shows that the presented approach is able to achieve substantial progress compared to earlier methods. It therefore is beneficial to incorporate side payments into negotiation processes based on collaborative search.

Decentralized Multi-Project Scheduling

This chapter is concerned with the decentralized resource-constrained multi-project scheduling problem (DRCMPSP), which is characterized in that individual involved decision makers pursue individual goals, whereas some overall coordination mechanism is needed to resolve conflicts due to the interdependencies between multiple projects. The connection between activities from these projects may result from temporal and resource-orientated constraints. In general, there may be two kinds of autonomous decision makers, on the one hand those that control individual projects, and on the other hand those that control globally available resources. After providing a more detailed description of such kinds of problems and the resulting peculiarities of decentralized decision making, a classification of respective problem types is provided, which leads to related requirements for solution procedures. Overall, there are two basic solution approaches, namely auctions and negotiations. These methods are described in connection with a review of the related literature.

A Two-Level Parallel Genetic Algorithm for the Uncapacitated Warehouse Location Problem

A new genetic algorithm (GA) for the uncapacitated warehouse location problem (UWLP) and its parallelization are described. The parallel method is based on two ideas. (1) The GA is using a new integer coding for the UWLP. (2) The parallelization takes advantage of a developed two- level strategy. The first level of parallelization consists of executing several subpopulations of the GA concurrently with the occasional migration of individuals between them. On the second level, the solution space is separated into several disjunctive parts. The developed method, which is the first application of a parallel metaheuristic to the UWLP, is evaluated using a large set of 717 benchmark problems available from the literature, whereas the other known solution methods are always applied to subsets of these instances. The results show, that the parallel method is competitive with the best known solution methods so far.

Generic negotiation mechanisms with side payments – Design, analysis and application for decentralized resource-constrained multi-project scheduling problems

Negotiation mechanisms have been proven useful for decentralized resource-constrained multi-project scheduling with self-interested parties (agents) that work together in completing a project. The current paper is concerned with such kinds of multi-agent problems, where each involved party pursues the individual goal of maximizing the discounted cash flow that is connected to its own project activities. Since the parties assess schedules and proposed changes to solutions in terms of money, it is appropriate to utilize money transfers (side payments). We design and analyze different automated negotiation procedures with side payments for resolving conflicts of interest between two agents and experimentally compare results with negotiation mechanisms without the use of money transfers. In principle, we consider two generic negotiation approaches: firstly, an agent may offer tentative payments in order to incentivize the other agent to accept changes to the project schedule within iterative improvement-based negotiation processes; secondly, agents offer or claim money for selecting the final solution from an approximate set of Pareto-optimal solutions that have been generated by a preceding search process. Taking account of self-interested agents and private preference information we discuss suitable elements of the mechanism with regard to strategic agent behavior. We provide insights regarding the effectiveness of different behavioral choices and analyze reasonable strategies of the agents from a prescriptive perspective. Overall, the proposed solution mechanism improves existing results from the literature for the considered kind of problem. Since the approach is built on general concepts, it may be also useful for other applications.