Matteo Salani

Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints

When vehicle routing problems with additional constraints, such as capacity or time windows, are solved via column generation and branch-and-price, it is common that the pricing subproblem requires the computation of a minimum cost constrained path on a graph with costs on the arcs and prizes on the vertices. A common solution technique for this problem is dynamic programming. In this paper we illustrate how the basic dynamic programming algorithm can be improved by bounded bi-directional search and we experimentally evaluate the effectiveness of the enhancement proposed. We consider as benchmark problems the elementary shortest path problems arising as pricing subproblems in branch-and-price algorithms for the capacitated vehicle routing problem, the vehicle routing problem with distribution and collection and the capacitated vehicle routing problem with time windows.

New dynamic programming algorithms for the resource constrained shortest path problem

The resource constrained elementary shortest path problem (RCESPP) arises as a pricing subproblem in branch-and-price algorithms for vehicle routing problems with additional constraints. We address the optimization of the RCESPP and we present and compare three methods. The frst method is a well-known exact dynamic programming algorithm improved by new ideas, such as bi-directional search with resource-based bounding. The second method consists of a branch-and-bound algorithm, where lower bounds are computed by dynamic programming with state space relaxation; we show how bounded bi-directional search can be adapted to state space relaxation and we present different branching strategies and their hybridization. The third method, called decremental state space relaxation, is a new one; exact dynamic programming and state space relaxation are two special cases of this new method. The experimental comparison of the three methods is defnitely favourable to decremental state space relaxation. Computational results are given for different kinds of resources, arising from the capacitated vehicle routing problem, the vehicle routing problem with distribution and collection and the vehicle routing problem with capacities and time windows

Decremental state space relaxation strategies and initialization heuristics for solving the Orienteering Problem with Time Windows with dynamic programming

We present an exact optimization algorithm for the Orienteering Problem with Time Windows (OPTW). The algorithm is based on bi-directional and bounded dynamic programming with decremental state space relaxation. We compare different strategies proposed in the literature to guide decremental state space relaxation: our experiments on instances derived from the literature show that there is no dominance between these strategies. We also propose a new heuristic technique to initialize the critical vertex set and we provide experimental evidence of its effectiveness.

Constraint-specific recovery network for solving airline recovery problems

In this paper, we consider the recovery of an airline schedule after an unforeseen event called disruption, making the planned schedule infeasible. We present a modeling framework that allows the consideration of operational constraints within a Column Generation (CG) scheme. We introduce the general concept of recovery network, generated for each individual unit of the problem, and show how unit-specific constraints are modeled using resources. We fully illustrate the concept by solving the Aircraft Recovery Problem (ARP) with maintenance planning, we give some insights into applying the model to the Passenger Recovery Problem (PRP) and we present computational results on real data.

An Exact Algorithm for the Integrated Planning of Berth Allocation and Quay Crane Assignment

In this paper we study the simultaneous optimization of berth allocation and quay crane assignment in seaport container terminals. We propose a model based on an exponential number of variables that is solved via column generation. An exact branch and price algorithm is implemented to produce optimal integer solutions to the problem. In particular, we present several accelerating techniques for the master and the pricing problem that can be generalized to other branch and price schemes. Computational results show that the proposed approach outperforms commercial solvers. Furthermore, the developed algorithm allows for a comparative analysis between the hierarchical and the integrated solution approach that confirms the added value of integration in terms of cost reduction and efficient use of resources. To the best of our knowledge, this is the first exact branch and price algorithm for both the berth allocation problem and the berth allocation problem with quay crane assignment.

A column generation algorithm for the vehicle routing problem with soft time windows

The Vehicle Routing Problem with Time Windows consists of computing a minimum cost set of routes for a fleet of vehicles of limited capacity visiting a given set of customers with known demand, with the additional constraint that each customer must be visited in a specified time window. We consider the case in which time window constraints are relaxed into “soft” constraints, that is penalty terms are added to the solution cost whenever a vehicle serves a customer outside of his time window. We present a branch-and-price algorithm which is the first exact optimization algorithm for this problem.

Lexicographic multi-objective optimization for the unit commitment problem and economic dispatch in a microgrid

In this paper, we present a multi-objective approach for the optimal control of dispatchable loads and bi-directional energy storages in a microgrid, commonly referred as the unit commitment problem and economic dispatch problem. We consider two different and possibly conflicting objectives: the minimization of the end user energy bill price and the maximization of the system stability as a function of the overall systems load. We propose a lexicographic ordering of the objectives so that the end users energy cost is considered as the primary objective and the systems stability is the secondary objective. In order to evaluate the performances, we provide a comprehensive micro-simulation environment used to study different demand response (DR) price profiles. The proposed multi-objective approach mitigates the network instability effects introduced by static DR programs with high price volatility. We conclude that almost flat DR price profiles with higher rates during high-peak periods should be preferred instead of high volatile profiles. With flat DR price profiles, both the end user and the utility company can benefit from smart-control algorithms adopting a lexicographic multi-objective optimization scheme.

A decentralized approach to demand side load management: The Swiss2Grid project

We present the Swiss2Grid project, a pilot and demonstration aimed at evaluating the impact of different distributed demand management policies in Smart Grids. The increasing diffusion of decentralised energy generation, especially photovoltaics, can lead to severe imbalances on the electric grid, which could require huge investments in grid infrastructures. The approach proposed by the Swiss2Grid project is to adopt a decentralised approach to load management at the local level. Single households use a local algorithm that, based only on local voltage and frequency measures, shifts the pre-emptible loads in time in order to minimise the costs for the consumer and to maximise the grid stability. In this paper we present the project set-up in Mendrisio, a city in Southern Switzerland, we describe the algorithm principles, and finally we present some preliminary results showing the impact of the Swiss2Grid algorithm on the Low Voltage grid.

An Integrated Airline Scheduling, Fleeting, and Pricing Model for a Monopolized Market

In airline schedule planning models, the demand and price information are usually taken as inputs to the model. Therefore, schedule and capacity decisions are taken separately from pricing decisions. In this article, we present an integrated scheduling, fleeting, and pricing model for a single airline where these decisions are taken simultaneously. This integration enables to explicitly model supply and demand interactions and make superior decisions. The model refers to a monopolized market. However, competing airlines are included in the model as a reference for the pricing decisions. The pricing decision is formulated through an itinerary choice model which determines the demand of the alternative itineraries in the same market according to their price, travel time, number of stops, and the departure time of the day. The demand model is estimated based on real data and is developed separately for economy and business classes. The seat allocation for these classes is optimized according to the behavior of the demand. The choice model is also used to appropriately model the spill and recapture effects. The resulting model is evaluated with different illustrations and the added value of the integrated approach is analyzed compared to a sequential approach. Results over a set of representative instances show that the integrated model is able to make superior decisions by jointly adjusting capacity and pricing.

Dynamic programming algorithms for the elementary shortest path problem with resource constraints

Abstract When vehicle routing problems with additional constraints (e.g. capacities or time windows) are solved via column generation and branch-and-price, it is common that the pricing problem requires the computation of a minimum cost constrained path on a graph with costs on the arcs and prizes on the nodes. The pricing problem is usually solved via dynamic programming in two possible ways: requiring elementary paths or allowing paths with cycles. We experimentally compare these two strategies and we evaluate the effectiveness of some algorithmic ideas to improve their performance.