Local Search Based Metaheuristics for Two-Echelon Distribution Network with Perishable Products

This article presents a planning problem in a distribution network incorporating two levels of inventory management. Perishable products are routed with lot-sizing, multi-sourcing and limited transport capacity using a homogeneous fleet of vehicles. A mixed integer linear programming (MILP) and a greedy heuristic have been developed to solve this real planning problem. There are some instances for which the solver cannot give a good lower bound within the limited time and for other instances it takes a lot of time to solve MILP. The greedy heuristic is an alternative to the mixed integer linear program, used to quickly solve some large instances taking into account original and difficult constraints. For some instances the gap between the solution provided by the solver (MILP) and the heuristic becomes quite significant. An iterated local search (ILS) using the variable neighborhood descent (VND) method has been implemented to improve the quality of heuristic solutions. We have included the ILS method in an APS (Advanced Planning System) and have compared it with an exact resolution of the MILP. Two types of instances are tested: models derived from actual data and models built using a random generator of instances that have wider diversity for computational evaluation. The ILS procedure significantly improves the quality of solutions and average computational time is much shorter than MILP resolution.

We study the reduction of bounded reachability analysis of timed automata (TA) to a Mixed Integer Linear Programming (MILP) problem. While bounded model checking of timed automata has been explored in the literature based on the satisfiability of Boolean constraint formulas over linear arithmetic constraints verified using SAT Modulo Theory (SMT) solvers, the approach presented in this paper opens up the alternative of using MILP solvers. We present some preliminary results comparing the two approaches and provide ideas on how linear optimization can be useful for analyzing the behavior of TA. The results are supported by a prototype implementation which relies either on a MILP solver (Gurobi) or an SMT solver (MathSAT). Certain techniques for reducing the search space and improving the performance are also discussed.

This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To tackle the nonlinearity in the constraint, we alternatively fix a subset of decision variables and optimize the remaining ones via Mixed Integer Linear Programming (MILP). We solve the MILP problem at each iteration via an off-the-shelf MILP solver. Our experimental results show that our method significantly outperforms existing heuristic methods, employing either independent optimization or joint optimization strategies. We have also verified the generalization ability of our method over grid environments with various sizes and its high robustness to the algorithm setting.

Linear programming (LP) and mixed integer linear programming (MILP) problems belong among very important class of problems that find their applications in various managerial consequences. The aim of the paper is to discuss computational performance of current optimization packages for solving large scale LP and MILP optimization problems. Current market with LP and MILP solvers is quite extensive. Probably among the most powerful solvers GUROBI 6.0, IBM ILOG CPLEX 12.6.1, and XPRESS Optimizer 27.01 belong. Their attractiveness for academic research is given, except their computational performance, by their free availability for academic purposes. The solvers are tested on the set of selected problems from MIPLIB 2010 library that contains 361 test instances of different hardness (easy, hard, and not solved).

Efficient optimization of a large-scale biorefinery system using a novel decomposition based approach

We present an efficient polynomial-time approximation scheme (EPTAS) for the problem of scheduling jobs on parallel uniform machines that improves all previously known EPTAS for the problem. Our algorithm uses a Mixed Integer Linear Program (MILP) formulation for a relaxed version of the problem. We simplify the MILP by repeatedly removing carefully selected sets of jobs and machines until all integer variables have been removed. Then, we build up the solution through the use of a dynamic programming approach, enumeration, and linear program solving. Notable about our approach is that our algorithm only uses an LP solver, different from previous EPTAS approaches where MILP solvers are necessary.

This research introduces the Pavement Maintenance and Rehabilitation (M&R) Scheduling with Treatment-Dependent Deterioration (PMRS-TDD) model that optimizes pavement network quality, measured by the pavement condition index (PCI), over a multi-period planning horizon under budget constraints. The model incorporates various M&R treatments, enforces minimum condition requirements, and accommodates problem-specific constraints. PCI deterioration is modeled as a function of prior PCI and the most recent treatment, capturing treatment-dependent degradation. The objective is to maximize total PCI and to minimize social disruption from maintenance activities. This study formulates a mixed-integer linear programming (MILP) model for small instances and develops a hybrid adaptive large neighborhood search (HALNS) algorithm for large instances. This algorithm incorporates a simulated annealing (SA) acceptance criterion and a sequential variable neighborhood descent (VND) for local search in the ALNS framework, while also presenting tailored operators for removal, insertion, and local search. Experiments are conducted on a real-world network in New Taipei City, Taiwan to evaluate the performance of HALNS and to offer practical managerial insights.

An agent-based modeling framework for the multi-UAV rendezvous recharging problem

We present a novel hybrid algorithm for training Deep Neural Networks that combines the state-of-the-art Gradient Descent (GD) method with a Mixed Integer Linear Programming (MILP) solver, outperforming GD and variants in terms of accuracy, as well as resource and data efficiency for both regression and classification tasks. Our GD+Solver hybrid algorithm, called GDSolver, works as follows: given a DNN D as input, GDSolver invokes GD to partially train D until it gets stuck in a local minima, at which point GDSolver invokes an MILP solver to exhaustively search a region of the loss landscape around the weight assignments of D’s final layer parameters with the goal of tunnelling through and escaping the local minima. The process is repeated until desired accuracy is achieved. In our experiments, we find that GDSolver not only scales well to additional data and very large model sizes, but also outperforms all other competing methods in terms of rates of convergence and data efficiency. For regression tasks, GDSolver produced models that, on average, had 31.5% lower MSE in 48% less time, and for classification tasks on MNIST and CIFAR10, GDSolver was able to achieve the highest accuracy over all competing methods, using only 50% of the training data that GD baselines required.

Modern industrial robots are increasingly deployed in dynamic environments, where unpredictable events are expected to impact the robot’s operation. Under these conditions, runtime task replanning is required to avoid failures and unnecessary stops, while keeping up productivity. Task replanning is a long-sighted complement to path replanning, which is mostly concerned with avoiding unexpected obstacles that can lead to potentially unsafe situations. This paper focuses on task replanning as a way to dynamically adjust the robot behaviour to the continuously evolving environment in which it is deployed. Analogously to probabilistic roadmaps used in path planning, we propose the concept of Task roadmaps as a method to replan tasks by leveraging an offline generated search space. A graph-based model of the robot application is converted to a task scheduling problem to be solved by a proposed Branch and Bound (B&B) approach and two benchmark approaches: Mixed Integer Linear Programming (MILP) and Planning Domain Definition Language (PDDL). The B&B approach is proposed to compute the task roadmap, which is then reused to replan for unforeseeable events. The optimality and efficiency of this replanning approach are demonstrated in a simulation-based experiment with a mobile manipulator in a kitting application. In this study, the proposed B&B Task Roadmap replanning approach is significantly faster than a MILP solver and a PDDL based planner.

A Hybrid Heuristic based on Iterated Local Search for Multivehicle Inventory Routing Problem

This paper deals with the Vehicle Routing Problem with Simultaneous Pick-up and Delivery and Time Limit (VRPSPDTL). Due to the combinatorial nature of the problem, heuristics methods are commonly used to generate good quality solutions within an acceptable computational time. Accordingly, an Iterated Local Search (ILS) procedure that uses a Variable Neighborhood Descent (VND) method to perform the local search is proposed. The algorithm was applied to test problems and, in most cases, was found to produce better results than those reported in the literature.KeywordsLocal SearchTravel Salesman ProblemVehicle Route ProblemReverse LogisticsCandidate ListThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper, we are addressing the NP-hard nurse rostering problem utilizing a 2-stage approach. In stage one, Monte Carlo Tree Search (MCTS) and Hill Climbing (HC) are hybridized in finding a feasible solution (satisfying all the hard constraints). We propose a new constant <i>C</i> value (which balances search diversification and intensification of MCTS) and tree policy/node selection function in the selection procedure of MCTS. In stage two, the feasible solution is further improved using Iterated Local Search (ILS) with Variable Neighbourhood Descent as the local search component. We introduce several unique neighbourhood structures for the ILS. In addition, we propose a novel perturbation strategy to allow the search to escape from local optimum. The proposed methodology is tested on the Shift Scheduling dataset (24 benchmark instances). New best results are reported for seven and two instances for the 10 and 60 minutes run respectively. An in-depth discussion on the attributes of the proposed methodology that lead to its good performance is provided.

We consider the problem of clustering N users into K groups such that users in the same group are assigned a common service profile over M commodities. The profile of each group k sets for each commodity m the maximum of the service quality that users in the k-th group are willing to pay. The objective is to find the clustering that maximizes the total service user quality, which corresponds to the revenue of the service provider. This Service Profile Optimization Problem (SPOP) emerges in various applications, as for example the bit-loading in Hybrid Fiber Coax data distribution systems. We propose a Mixed Integer Linear Programming (MILP) model for the problem, that allows to use state-of-the-art MILP solvers as the core tool in an original powerful heuristic. We show complexity and performance gains with respect to previously proposed methods and a direct application of a state of the art MILP solver.

Partially observable MDPs provide an elegant framework forsequential decision making. Finite-state controllers (FSCs) are often used to represent policies for infinite-horizon problems as they offer a compact representation, simple-to-execute plans, and adjustable tradeoff between computational complexityand policy size. We develop novel connections between optimizing FSCs for POMDPs and the dual linear programfor MDPs. Building on that, we present a dual mixed integer linear program (MIP) for optimizing FSCs. To assign well-defined meaning to FSC nodes as well as aid in policy search, we show how to associate history-based features with each FSC node. Using this representation, we address another challenging problem, that of iteratively deciding which nodes to add to FSC to get a better policy. Using an efficient off-the-shelf MIP solver, we show that this new approach can find compact near-optimal FSCs for severallarge benchmark domains, and is competitive with previous best approaches.