A Pareto-metaheuristic for a bi-objective winner determination problem in a combinatorial reverse auction

The bi-objective winner determination problem (2WDP-SC) of a combinatorial procurement auction for transport contracts comes up to a multi-criteria set covering problem. We are given a set B of bundle bids. A bundle bid b in B consists of a bidding carrier c_b, a bid price p_b, and a set tau_b of transport contracts which is a subset of the set T of tendered transport contracts. Additionally, the transport quality q_t,c_b is given which is expected to be realized when a transport contract t is executed by a carrier c_b. The task of the auctioneer is to find a set X of winning bids (X is subset of B), such that each transport contract is part of at least one winning bid, the total procurement costs are minimized, and the total transport quality is maximized. This article presents a metaheuristic approach for the 2WDP-SC which integrates the greedy randomized adaptive search procedure, large neighborhood search, and self-adaptive parameter setting in order to find a competitive set of non-dominated solutions. The procedure outperforms existing heuristics. Computational experiments performed on a set of benchmark instances show that, for small instances, the presented procedure is the sole approach that succeeds to find all Pareto-optimal solutions. For each of the large benchmark instances, according to common multi-criteria quality indicators of the literature, it attains new best-known solution sets.Pareto optimization; multi-criteria winner determination; combinatorial auction; GRASP; LNS

Analyzing combined vehicle routing and break scheduling from a distributed decision making perspective

We analyze the problem of combined vehicle routing and break scheduling from a distributed decision making perspective. The problem of combined vehicle routing and break scheduling can be defined as the problem of finding vehicle routes to serve a set of customers such that a cost criterion is minimized and legal rules on driving and working hours are observed. In the literature, this problem is always analyzed from a central planning perspective. In practice, however, this problem is solved interactively between planners and drivers. In\ud many practical scenarios, the planner first clusters the customer requests and instructs the drivers which customers they have to visit. Subsequently, the drivers decide upon the routes to be taken and their break schedules. We apply a framework for distributed decision making to model this planning scenario and propose various ways for planners to anticipate the drivers' planning behavior. Especially in the case of antagonistic objectives, which are often encountered in practice, a distributed decision making perspective is necessary to analyze this planning process. Computational experiments demonstrate that a high degree of anticipation by the planner has a strong positive impact on the overall planning quality, especially in the case of conflicting planner's and drivers' objectives

Distributed Decision Making in Combined Vehicle Routing and Break Scheduling

The problem of combined vehicle routing and break scheduling comprises three subproblems: clustering of customer requests, routing of vehicles, and break scheduling. In practice, these subproblems are usually solved in the interaction between planners and drivers. We consider the case that the planner performs the clustering and the drivers perform the routing and break scheduling. To analyze this problem, we embed it into the framework of distributed decision making proposed by Schneeweiss (2003). We investigate two different degrees of anticipation of the drivers’ planning behaviour using computational experiments. The results indicate that in this application a more precise anticipation function results in better objective values for both the planner and the drivers

Heat Flows on Time-dependent Metric Measure Spaces

We consider time-dependent metric measure spaces evolving as a super Ricci flow in the sense of Sturm. We haracterize these by means of the (time-dependent) heat flow. We establish equivalence of super Ricci flows, gradient and transport estimates as well as a dynamic Bochner inequality. This can be seen as a dynamic analogue to the results by Ambrosio, Gigli and Savaré. For this we first define heat flows on time-dependent metric measure spaces. Due to the lack of symmetry we need to consider the heat equation and its adjoint. The solution to the heat equation gives rise to the heat flow on functions, whereas the solution to the adjoint gives rise to the adjoint heat flow on measures. Existence and uniqueness are guaranteed by the general theory of time-dependent elliptic operators. Moreover the two can be retained as gradient flows; the heat flow is the gradient flow of the Cheeger's energy and the dual heat flow is the gradient flow of the relative entropy. Both, functional and space, vary in time, so we first need to make sense of gradient flows in a dynamic setting. We define Brownian motions on time-dependent metric measure spaces. We prove that under a super Ricci flow there exists a coupling of Brownian motions with pathwise contraction of their trajectories

Bochner formulas, functional inequalities and generalized Ricci flow

As a consequence of the Bochner formula for the Bismut connection acting on gradients, we show sharp universal Poincar\'e and log-Sobolev inequalities along solutions to generalized Ricci flow. Using the two-form potential we define a twisted connection on spacetime which determines an adapted Brownian motion on the frame bundle, yielding an adapted Malliavin gradient on path space. We show a Bochner formula for this operator, leading to characterizations of generalized Ricci flow in terms of universal Poincar\'e and log-Sobolev type inequalities for the associated Malliavin gradient and Ornstein-Uhlenbeck operator

Dynamic programming algorithm for the vehicle routing problem with time windows and EC social legislation

In practice, apart from the problem of vehicle routing, schedulers also face the problem of nding feasible driver schedules complying with complex restrictions on drivers' driving and working hours. To address this complex interdependent problem of vehicle routing and break scheduling, we propose a dynamic programming approach for the vehicle routing problem with time windows including the EC social legislation on drivers' driving and working hours. Our algorithm includes all optional rules in these legislations, which are generally ignored in the literature. To include the legislation in the dynamic programming algorithm we propose a break scheduling method that does not increase the time-complexity of the algorithm. This is a remarkable eect that generally does not hold for local search methods, which have proved to be very successful in solving less restricted vehicle routing problems. Computational results show that our method finds solutions to benchmark instances with 18% less vehicles and 5% less travel distance than state of the art approaches. Furthermore, they show that including all optional rules of the legislation leads to an additional reduction of 4% in the number of vehicles and of 1.5%\ud regarding the travel distance. Therefore, the optional rules should be exploited in practice

RULES FOR THE IDENTIFICATION OF PORTFOLIO-INCOMPATIBLE REQUESTS IN DYNAMIC VEHICLE ROUTING

In this article, we propose and evaluate simple rules for selecting transport requests that do not fit into a request portfolio because their temporal or spatial requirements are incompatible with the requirements of other requests so that the compilation of profitable routes is compromised. We integrate these rules into an adaptive online vehicle operations planning system and analyze in numerical simulation experiments how their application has impacts on the flexibility, the stability and the profitability of the controlled transportation system and the integration of consecutively arriving requests