58 research outputs found
Introducing heterogeneous users and vehicles into models and algorithms for the dial-a-ride problem
AbstractDial-a-ride problems deal with the transportation of people between pickup and delivery locations. Given the fact that people are subject to transportation, constraints related to quality of service are usually present, such as time windows and maximum user ride time limits. In many real world applications, different types of users exist. In the field of patient and disabled people transportation, up to four different transportation modes can be distinguished. In this article we consider staff seats, patient seats, stretchers and wheelchair places. Furthermore, most companies involved in the transportation of the disabled or ill dispose of different types of vehicles. We introduce both aspects into state-of-the-art formulations and branch-and-cut algorithms for the standard dial-a-ride problem. Also a recent metaheuristic method is adapted to this new problem. In addition, a further service quality related issue is analyzed: vehicle waiting time with passengers aboard. Instances with up to 40 requests are solved to optimality. High quality solutions are obtained with the heuristic method
Enhancing Branch-and-Bound for Multi-Objective 0-1 Programming
In the bi-objective branch-and-bound literature, a key ingredient is
objective branching, i.e. to create smaller and disjoint sub-problems in the
objective space, obtained from the partial dominance of the lower bound set by
the upper bound set. When considering three or more objective functions,
however, applying objective branching becomes more complex, and its benefit has
so far been unclear. In this paper, we investigate several ingredients which
allow to better exploit objective branching in a multi-objective setting. We
extend the idea of probing to multiple objectives, enhance it in several ways,
and show that when coupled with objective branching, it results in significant
speed-ups in terms of CPU times. We also investigate cut generation based on
the objective branching constraints. Besides, we generalize the best-bound idea
for node selection to multiple objectives and we show that the proposed rules
outperform the, in the multi-objective literature, commonly employed
depth-first and breadth-first strategies. We also analyze problem specific
branching rules. We test the proposed ideas on available benchmark instances
for three problem classes with three and four objectives, namely the
capacitated facility location problem, the uncapacitated facility location
problem, and the knapsack problem. Our enhanced multi-objective
branch-and-bound algorithm outperforms the best existing branch-and-bound based
approach and is the first to obtain competitive and even slightly better
results than a state-of-the-art objective space search method on a subset of
the problem classes
Modeling and solving a vehicle-sharing problem
Motivated by the change in mobility patterns, we present a new modeling
approach for the vehicle-sharing problem. We aim at assigning vehicles to
user-trips so as to maximize savings compared to other modes of transport. We
base our formulations on the minimum-cost and the multi-commodity flow problem.
These formulations make the problem applicable in daily operations. In the
analysis we discuss an optimal composition of a shared fleet, restricted sets
of modes of transport, and variations of the objective function
Bi-objective facility location in the presence of uncertainty
Multiple and usually conflicting objectives subject to data uncertainty are
main features in many real-world problems. Consequently, in practice,
decision-makers need to understand the trade-off between the objectives,
considering different levels of uncertainty in order to choose a suitable
solution. In this paper, we consider a two-stage bi-objective single source
capacitated model as a base formulation for designing a last-mile network in
disaster relief where one of the objectives is subject to demand uncertainty.
We analyze scenario-based two-stage risk-neutral stochastic programming,
adaptive (two-stage) robust optimization, and a two-stage risk-averse
stochastic approach using conditional value-at-risk (CVaR). To cope with the
bi-objective nature of the problem, we embed these concepts into two criterion
space search frameworks, the -constraint method and the balanced box
method, to determine the Pareto frontier. Additionally, a matheuristic
technique is developed to obtain high-quality approximations of the Pareto
frontier for large-size instances. In an extensive computational experiment, we
evaluate and compare the performance of the applied approaches based on
real-world data from a Thies drought case, Senegal
Modeling and solving the multimodal car- and ride-sharing problem
We introduce the multimodal car- and ride-sharing problem (MMCRP), in which a
pool of cars is used to cover a set of ride requests, while uncovered requests
are assigned to other modes of transport (MOT). A car's route consists of one
or more trips. Each trip must have a specific but non-predetermined driver,
start in a depot and finish in a (possibly different) depot. Ride-sharing
between users is allowed, even when two rides do not have the same origin
and/or destination. A user has always the option of using other modes of
transport according to an individual list of preferences.
The problem can be formulated as a vehicle scheduling problem. In order to
solve the problem, an auxiliary graph is constructed in which each trip
starting and ending in a depot, and covering possible ride-shares, is modeled
as an edge in a time-space graph. We propose a two-layer decomposition
algorithm based on column generation, where the master problem ensures that
each request can only be covered at most once, and the pricing problem
generates new promising routes by solving a kind of shortest path problem in a
time-space network. Computational experiments based on realistic instances are
reported. The benchmark instances are based on demographic, spatial, and
economic data of Vienna, Austria. We solve large instances with the column
generation based approach to near optimality in reasonable time, and we further
investigate various exact and heuristic pricing schemes
An outer approximation algorithm for multi-objective mixed-integer linear and non-linear programming
In this paper, we present the first outer approximation algorithm for
multi-objective mixed-integer linear programming problems with any number of
objectives. The algorithm also works for certain classes of non-linear
programming problems. It produces the non-dominated extreme points as well as
the facets of the convex hull of these points. The algorithm relies on an
oracle which solves single-objective weighted-sum problems and we show that the
required number of oracle calls is polynomial in the number of facets of the
convex hull of the non-dominated extreme points in the case of multiobjective
mixed-integer programming (MOMILP). Thus, for MOMILP problems for which the
weighted-sum problem is solvable in polynomial time, the facets can be computed
with incremental-polynomial delay. From a practical perspective, the algorithm
starts from a valid lower bound set for the non-dominated extreme points and
iteratively improves it. Therefore it can be used in multi-objective
branch-and-bound algorithms and still provide a valid bound set at any stage,
even if interrupted before converging. Moreover, the oracle produces Pareto
optimal solutions, which makes the algorithm also attractive from the primal
side in a multi-objective branch-and-bound context. Finally, the oracle can
also be called with any relaxation of the primal problem, and the obtained
points and facets still provide a valid lower bound set. A computational study
on a set of benchmark instances from the literature and new non-linear
multi-objective instances is provided.Comment: 21 page
- …