Solution Construction Procedure Research Articles

An Iterative Sample Scenario Approach for the Dynamic Dispatch Waves Problem

A challenge in same-day delivery operations is that delivery requests are typically not known beforehand, but are instead revealed dynamically during the day. This uncertainty introduces a trade-off between dispatching vehicles to serve requests as soon as they are revealed to ensure timely delivery and delaying the dispatching decision to consolidate routing decisions with future, currently unknown requests. In this paper, we study the dynamic dispatch waves problem, a same-day delivery problem in which vehicles are dispatched at fixed decision moments. At each decision moment, the system operator must decide which of the known requests to dispatch and how to route these dispatched requests. The operator’s goal is to minimize the total routing cost while ensuring that all requests are served on time. We propose iterative conditional dispatch (ICD), an iterative solution construction procedure based on a sample scenario approach. ICD iteratively solves sample scenarios to classify requests to be dispatched, postponed, or undecided. The set of undecided requests shrinks in each iteration until a final dispatching decision is made in the last iteration. We develop two variants of ICD: one variant based on thresholds, and another variant based on similarity. A significant strength of ICD is that it is conceptually simple and easy to implement. This simplicity does not harm performance: through rigorous numerical experiments, we show that both variants efficiently navigate the large state and action spaces of the dynamic dispatch waves problem and quickly converge to a high-quality solution. Finally, we demonstrate that the threshold-based ICD variant achieves excellent results on instances from the EURO Meets NeurIPS 2022 Vehicle Routing Competition, nearly matching the performance of the winning machine learning–based strategy. History: This paper has been accepted for the Transportation Science Special Issue on DIMACS Implementation Challenge: Vehicle Routing Problems. Funding: This work was supported by TKI Dinalog, Topsector Logistics, and the Dutch Ministry of Economic Affairs and Climate Policy. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0111 .

A sharp-interface mesoscopic model for dendritic growth

The grain envelope model (GEM) describes the growth of envelopes of dendritic crystal grains during solidification. Numerically the growing envelopes are usually tracked using an interface capturing method employing a phase field equation on a fixed grid. Such an approach describes the envelope as a diffuse interface, which can lead to numerical artefacts that are possibly detrimental. In this work, we present a sharp-interface formulation of the GEM that eliminates such artefacts and can thus track the envelope with high accuracy. The new formulation uses an adaptive meshless discretization method to solve the diffusion in the liquid around the grains. We use the ability of the meshless method to operate on scattered nodes to accurately describe the interface, i.e., the envelope. The proposed algorithm combines parametric surface reconstruction, meshless discretization of parametric surfaces, global solution construction procedure and partial differential operator approximation using monomials as basis functions. The approach is demonstrated on a two-dimensional h-adaptive solution of diffusive growth of dendrites and assessed by comparison to a conventional diffuse-interface fixed-grid GEM.

An enhanced GRASP approach for the index tracking problem

AbstractIndex tracking models build portfolios of limited size that replicate the performance of a market index. As the size of the index grows, it becomes impractical to find an optimal solution. As far as we know, this work proposes the first greedy randomized adaptive search procedure (GRASP) approach for index tracking. GRASP has proven to be efficient in combinatorial optimization problems and offers a solution construction procedure different from the standard index tracking optimization approaches, bringing a new perspective to the field. Results showed that the proposed GRASP approach found solutions with almost the same quality as those found by CPLEX solver in a smaller time, and the proposed local search component was competitive depending on the problem parametrization. The results found have practical implications concerning the achievement of good solutions by GRASP approaches in a smaller time when compared with hybrid genetic algorithms, and new perspectives for building GRASP heuristics for portfolio optimization problems.

Differential-algebraic boundary-value problems with the variable rank of leading-coefficient matrix

Conditions for the solvability of the linear boundary-value problem for systems of differential-algebraic equations with the variable rank of the leading-coefficient matrix and the corresponding solution construction procedure have been found.

Differential-algebraic boundary-value problems with the variable rank of leading-coefficient matrix

Conditions for the solvability of the linear boundary-value problem for systems of differential-algebraic equations with the variable rank of the leading-coefficient matrix and the corresponding solution construction procedure have been found.

A covering traveling salesman problem with profit in the last mile delivery

This paper introduces and formulates a covering traveling salesman problem with profit arose in the last mile delivery. In this problem, a set of vertices including a central depot, customers and parcel lockers (PL) are given, and the goal is to construct a Hamiltonian cycle within a pre-defined cost over a subset of customers and/or PLs to collect maximum profits, each unvisited customer is covered by a PL in the cycle or outsourced. To solve the problem, a two-phase heuristic combined with a feasible solution construction procedure and an improvement procedure is proposed. The algorithm is evaluated on two sets of instances, and the computational results indicated its efficiency.

Genetic Programming Hyper-Heuristics with Vehicle Collaboration for Uncertain Capacitated Arc Routing Problems

Due to its direct relevance to post-disaster operations, meter reading and civil refuse collection, the Uncertain Capacitated Arc Routing Problem (UCARP) is an important optimisation problem. Stochastic models are critical to study as they more accurately represent the real world than their deterministic counterparts. Although there have been extensive studies in solving routing problems under uncertainty, very few have considered UCARP, and none consider collaboration between vehicles to handle the negative effects of uncertainty. This article proposes a novel Solution Construction Procedure (SCP) that generates solutions to UCARP within a collaborative, multi-vehicle framework. It consists of two types of collaborative activities: one when a vehicle unexpectedly expends capacity (route failure), and the other during the refill process. Then, we propose a Genetic Programming Hyper-Heuristic (GPHH) algorithm to evolve the routing policy used within the collaborative framework. The experimental studies show that the new heuristic with vehicle collaboration and GP-evolved routing policy significantly outperforms the compared state-of-the-art algorithms on commonly studied test problems. This is shown to be especially true on instances with larger numbers of tasks and vehicles. This clearly shows the advantage of vehicle collaboration in handling the uncertain environment, and the effectiveness of the newly proposed algorithm.

Robust secrecy beamforming for full-duplex two-way relay networks under imperfect channel state information

Consider a two-way amplify-and-forward (AF) relay network where two legitimate nodes communicate through a relay in the presence of an eavesdropper. Assuming full duplexity at the legitimate nodes and the relay, a robust artificial noise (AN)-aided AF scheme is proposed to maximize the worst-case sum secrecy rate under imperfect channel state information (CSI) of the eavesdropper. This robust sum secrecy rate maximization (SSRM) problem is formulated as a max-min semi-infinite problem and is tackled by the semidefinite relaxation (SDR) method. In particular, we first convert the max-min semi-infinite problem into a maximization problem with a finite number of constraints. Then, an efficient two-block alternating difference-of-concave (DC) programming approach is proposed to iteratively solve the SDR problem, with one of the blocks computed in closed form. In addition, a specific robust rank-one solution construction procedure is presented to extract a feasible solution for the original robust SSRM problem from the SDR solution. The efficacy of the proposed method is demonstrated by numerical simulations.

Priority Rule-Based Construction Procedure Combined with Genetic Algorithm for Flexible Job-Shop Scheduling Problem

The heuristic method we propose solves the flexible job-shop scheduling problem (FJSP) using a solution construction procedure with priority rules. FJSP is more complex than classical scheduling problems in that operations are processed on one of multiple candidate machines, one of which must be selected to get a feasible solution. The solution construction procedure with priority rules is implemented on top of the efficient existing method for solving the FJSP which consists of a genetic algorithm and a local search method. The performance of the proposed method is analyzed using various benchmark problems and it is confirmed that our proposed method outperforms the existing method on problems with particular conditions. The conditions are further investigated by applying the proposed method on newly created benchmark.

Solving the task assignment problem with ant colony optimisation incorporating ideas from the clonal selection algorithm

The task assignment problem commonly appears in distributed computing environments. It asks an assignment of tasks to processors is found such that it satisfies the imposed constraints and that the total execution and communication cost of the tasks is minimal. This paper presents an algorithm based on ant colony optimisation that incorporates ideas from the clonal selection algorithm. Namely, the ant colony optimisation algorithm includes the cloning of the iteration-best ant and mutation of its clones' solutions; the goal being a better exploitation of promising parts of the search space. Besides that, the solution construction procedure is modified to take the memory constraints into account and the pheromone update mechanism is modified to enable the best clone to deposit pheromone. The experimental analysis, conducted on a large number of problem instances, showed that the proposed algorithm performs better compared to the MAX-MIN ant system, a differential evolution and a particle swarm optimisation algorithm.

Optimal Selection of Parameters for Nonuniform Embedding of Chaotic Time Series Using Ant Colony Optimization

The optimal selection of parameters for time-delay embedding is crucial to the analysis and the forecasting of chaotic time series. Although various parameter selection techniques have been developed for conventional uniform embedding methods, the study of parameter selection for nonuniform embedding is progressed at a slow pace. In nonuniform embedding, which enables different dimensions to have different time delays, the selection of time delays for different dimensions presents a difficult optimization problem with combinatorial explosion. To solve this problem efficiently, this paper proposes an ant colony optimization (ACO) approach. Taking advantage of the characteristic of incremental solution construction of the ACO, the proposed ACO for nonuniform embedding (ACO-NE) divides the solution construction procedure into two phases, i.e., selection of embedding dimension and selection of time delays. In this way, both the embedding dimension and the time delays can be optimized, along with the search process of the algorithm. To accelerate search speed, we extract useful information from the original time series to define heuristics to guide the search direction of ants. Three geometry- or model-based criteria are used to test the performance of the algorithm. The optimal embeddings found by the algorithm are also applied in time-series forecasting. Experimental results show that the ACO-NE is able to yield good embedding solutions from both the viewpoints of optimization performance and prediction accuracy.

Manufactured solutions and the verification of three-dimensional Stokes ice-sheet models

Abstract. The manufactured solution technique is used for the verification of computational models in many fields. In this paper, we construct manufactured solutions for the three-dimensional, isothermal, nonlinear Stokes model for flows in glaciers and ice sheets. The solution construction procedure starts with kinematic boundary conditions and is mainly based on the solution of a first-order partial differential equation for the ice velocity that satisfies the incompressibility condition. The manufactured solutions depend on the geometry of the ice sheet, basal sliding parameters, and ice softness. Initial conditions are taken from the periodic geometry of a standard problem of the ISMIP-HOM benchmark tests. The upper surface is altered through the manufactured solution procedure to generate an analytic solution for the time-dependent flow problem. We then use this manufactured solution to verify a parallel, high-order accurate, finite element Stokes ice-sheet model. Simulation results from the computational model show good convergence to the manufactured analytic solution.

New metaheuristics approaches for biclustering of gene expression Data

Motivations. Biclustering or simultaneous clustering of both genes and conditions have generated considerable interest over the past few decades, particularly related to the analysis of high-dimensional gene expression data in information retrieval, knowledge discovery, and data mining [1]. Given a gene expression data matrix, a bicluster is a submatrix of genes and conditions that exhibits a high correlation of expression activity across both rows and columns. The problem of locating the most significant bicluster has been shown to be NP-complete. Therefore, given the inner intractability of the problem from a computational point of view, to efficiently find good solutions in a reasonable running times we have designed and implemented several different metaheuristics based on a GRASP framework. Methods. All the procedures are based on a GRASP (Greedy Randomized Adaptive Search Procedure) framework [2]. A GRASP is a randomized multistart iterative metaheuristic consisting of two phases: a construction phase and a local search phase. The construction phase builds iteratively a feasible solution in a greedy randomized fashion. Once a feasible solution is obtained, a local search procedure attempts to improve it by producing a locally optimal solution with respect to suitable defined neighborhood structure. The construction and the local search phases are repeatedly applied. The best local optimum solution found is returned as an approximation of the optimal one. We designed and implemented several different GRASP-based metaheuristics that differ in both construction and local search phase. In the construction phase, one implements a k-means and a second one a greedy randomized procedure inspired by a minimum spanning tree of a suitable weighted graph. Then, two types of local searches have been implemented: one has been already proposed [3] and a second one is an Iterated Local Search [4]. All the designed algorithms have been tested and compared using the lymphoma dataset [5]. Results. Both the solution construction procedure and the local search procedure use a gain function that combines the mean squared residue [1], the row variance, and the size of the bicluster. Experimental results on Lymphoma microarray data set [5] are promising indicating that the methods are able to find significant biclusters, also from a biological point of view. Acknowledgements A.M. and L.M. are supported by MIUR FIRB ITALBIONET (RBPR05ZK2Z and RBIN064YAT_003). The work has been made in the frame of the Flagship Project InterOmics.

The Entropy Solutions for the Lighthill-Whitham-Richards Traffic Flow Model with a Discontinuous Flow-Density Relationship

In this paper we explicitly construct the entropy solutions for the Lighthill-Whitham-Richards (LWR) traffic flow model with a flow-density relationship which is piecewise quadratic, concave, but not continuous at the junction points where two quadratic polynomials meet, and with piecewise linear initial condition and piecewise constant boundary conditions. The existence and uniqueness of entropy solutions for such conservation laws with discontinuous fluxes are not known mathematically. We have used the approach of explicitly constructing the entropy solutions to a sequence of approximate problems in which the flow-density relationship is continuous but tends to the discontinuous flux when a small parameter in this sequence tends to zero. The limit of the entropy solutions for this sequence is explicitly constructed and is considered to be the entropy solution associated with the discontinuous flux. We apply this entropy solution construction procedure to solve four representative traffic flow cases, compare them with numerical solutions obtained by a high order weighted essentially nonoscillatory (WENO) scheme, and discuss the results from traffic flow perspectives.

A new ant colony optimization algorithm for the multidimensional Knapsack problem

The paper proposes a new ant colony optimization (ACO) approach, called binary ant system (BAS), to multidimensional Knapsack problem (MKP). Different from other ACO-based algorithms applied to MKP, BAS uses a pheromone laying method specially designed for the binary solution structure, and allows the generation of infeasible solutions in the solution construction procedure. A problem specific repair operator is incorporated to repair the infeasible solutions generated in every iteration. Pheromone update rule is designed in such a way that pheromone on the paths can be directly regarded as selecting probability. To avoid premature convergence, the pheromone re-initialization and different pheromone intensification strategy depending on the convergence status of the algorithm are incorporated. Experimental results show the advantages of BAS over other ACO-based approaches for the benchmark problems selected from OR library.