A Parallel Algorithm for Matheuristics: A Comparison of Optimization Solvers

The generalized lock scheduling problem (GLSP) is a mixed integer optimization problem which consists of a ship placement (SP) and a lockage operation scheduling (LOS) sub-problem. In previous research, the GLSP is solved by different exact and heuristic methods, which are confirmed inferior with respect to computation time and solution quality. Consequently, none of those methods is efficient for handling practical large-scale GLSP. For the first time, we show that high-quality solutions of GLSP can be efficiently obtained by using an innovative approach proposed in this paper. Specifically, an ingenious solution structure of GLSP is designed, by which the GLSP is converted to a combinatorial optimization problem. Furthermore, an adaptive large neighborhood search (ALNS) heuristic based on the principle of destruction and reconstruction of solutions is proposed for solving the GLSP. Test results using a large number of instances reported in the literature are compared with those obtained by two exact methods, the mixed integer linear programming (MILP) and combinatorial Benders' decomposition (CBD) method. The results show that our ALNS achieves optimal solutions within less time in terms of most of the small-scale instances. Much better solutions are obtained by the ALNS within a few minutes for those large-scale instances that cannot be solved to optimality by exact methods within 2 h. Especially, the advantage of the proposed method is more remarkable when there is no specific chronological rules forced, which indicates that the proposed method is capable of handling the GLSP in a broader scope of situations.

Predictive route choice control of destination coded vehicles with mixed integer linear programming optimization

Purpose The purpose of this paper is to maximize the total demand covered by the established additive manufacturing and distribution centers and maximize the total literal weight assigned to the drones. Design/methodology/approach Disaster management or humanitarian supply chains (HSCs) differ from commercial supply chains in the fact that the aim of HSCs is to minimize the response time to a disaster as compared to the profit maximization goal of commercial supply chains. In this paper, the authors develop a relief chain structure that accommodates emerging technologies in humanitarian logistics into the two phases of disaster management – the preparedness stage and the response stage. Findings Solving the model by the genetic and the cuckoo optimization algorithm (COA) and comparing the results with the ones obtained by The General Algebraic Modeling System (GAMS) clear that genetic algorithm overcomes other options as it has led to objective functions that are 1.6% and 24.1% better comparing to GAMS and COA, respectively. Originality/value Finally, the presented model has been solved with three methods including one exact method and two metaheuristic methods. Results of implementation show that Non-dominated sorting genetic algorithm II (NSGA-II) has better performance in finding the optimal solutions.

Minimizing energy consumption by joint radio and computing resource allocation in Cloud-RAN

This paper deals with a multiobjective parallel machines scheduling problem. It consists in scheduling n independent jobs on m identical parallel machines. The job data such as processing times, release dates, due dates and sequence dependent setup times are considered. The goal is to optimize two different objectives: the makespan and the total tardiness. A mixed integer linear program is proposed to model the studied problem. As this problem is NP-hard in the strong sense, a metaheuristic method which is the second version of the non dominated sorting genetic algorithm (NSGA-II) is proposed to solve this problem. Since the parameters setting of a genetic algorithm is difficult, a fuzzy logic controller coupled with the NSGA-II (FLC-NSGA-II) is therefore proposed. The role of the fuzzy logic is to better set the crossover and the mutation probabilities in order to update the search ability. After that, an exact method based on the two phase method is also developed. We have used four measuring criteria to compare these methods. The experimental results show the advantages and the efficiency of FLC-NSGA-II.

This paper considers disassembly sequencing problems subjected to sequence dependent disassembly costs. In practice, the methods for dealing with such problems rely mainly on metaheuristic and heuristic methods, which intrinsically generate suboptimum solutions. Exact methods are NP-hard and therefore unsuitable to most of the practical problems. Nevertheless, it is useful to have exact methods available that can be applied in order to check, at least medium sized problems, to what extent the heuristically obtained solutions deviate from the optimum solution. The existing exact approaches, which are based on integer linear programming (ILP), become unmanageable, even for the cases of modest product complexity. To alleviate this problem to some extent, the iterative method that has been proposed by Lambert (2006) is applied here. This method is based on repeatedly solving a binary integer linear programming (BILP) problem instead of an ILP problem. The method appears to converge sufficiently quickly to be valuable for dealing with medium sized problems. We then use the iterative method for the validation of a new heuristic method that is also proposed in this paper. Finally, both the heuristic and the iterative BILP methods are implemented on a cellphone from practice consisting of 25 components that are represented, according to a set of precedence relationships, via a disassembly precedence graph.

The Unmanned Aerial Vehicles (UAVs), commonly known as drones, are significant in the agriculture sphere to automate the work such as: data acquisition, crop spraying among others. This paper proposes a path planning solution for a team of UAVs that is required to whiten a greenhouse’s roof, this problem having both social-economic impact, as well as scientific-technical impact. First, the space around the roof is partitioned into cells based on a 3D cell decomposition technique, labeling the cells including the surface of the roof as regions of interest (ROIs). Based on this representation, a Petri net (PN) model captures the motion of drones, while their trajectories are returned by a Mixed Integer Linear Programming (MILP) problem which optimizes the energy consumption. An adaptable strategy is used such that the MILP problem considers only the available UAVs with enough energy to reach the ROIs. The algorithm is implemented in MATLAB and the simulation results are captured in a video link, evaluating the impact of the size of the team and the precision used for mapping the environment over the running time.

The surveillance problem is to find optimal trajectories of agents that patrol a given area as evenly as possible. In this paper, we consider multiple agents with fuel constraints. The surveillance area is given by a weighted directed graph, where the weight assigned to each arc corresponds to the fuel consumption/supply. For each node, the penalty to evaluate the unattended time is introduced. Penalties, agents, and fuels are modeled by a mixed logical dynamical system model. Then, the surveillance problem is reduced to a mixed integer linear programming (MILP) problem. Based on the policy of model predictive control, the MILP problem is solved at each discrete time. In this paper, the feasibility condition for the MILP problem is derived. Finally, the proposed method is demonstrated by a numerical example.

Redundancy allocation problems (RAPs) have attracted much attention for the past thirty years due to its wide applications in improving the reliability of various engineering systems. Because RAP is an NP-hard problem, and exact methods are only applicable to small instances, various heuristic and meta-heuristic methods have been proposed to solve it. In the literature, most studies on RAPs have been conducted for single-level systems. However, real-world engineering systems usually contain multiple levels. In this paper, the RAP on multi-level systems is investigated. A novel memetic algorithm (MA) is proposed to solve this problem. Two genetic operators, namely breadth-first crossover and breadth-first mutation, and a local search method are designed for the MA. Comprehensive experimental studies have shown that the proposed MA outperformed the state-of-the-art approach significantly on two representative examples.

Biogeography-based Optimization (BBO) Algorithm for Single Machine Total Weighted Tardiness Problem (SMTWTP)

Process systems engineering is one of the many areas in which mixed integer optimisation formulations have been successfully applied. The nature of the problems requires specialised solution strategies and computer packages or callable libraries able to be extended and modified in order to accommodate new solution techniques. Object-oriented programming languages have been identified to offer these features. Process system applications are usually of large scale, and require modelling and solution techniques with high level of customisation. ooMILP is a library of C++ callable procedures for the definition, manipulation and solution of large, sparse mixed integer linear programming (MILP) problems without the disadvantages of many existing modelling languages. We first present a general approach to the packaging of numerical solvers as software components, derived from material developed for the CAPE-OPEN project. The presentation is in the context of construction and solution of Mixed Integer Linear Programming (MILP) problems. We then demonstrate how this package, based on the use of CORBA interfaces for synchronous execution within a single process, can be adapted with a minimum of problem-specific changes to provide a distributed solution.

Knowledge representation of mathematical optimization problems and constructs for modeling

We present a general approach to the FPGA technology mapping problem that applies to any logic block composed of lookup tables (LUTs) and can yield optimal solutions. The connections between LUTs of a logic block are modeled by virtual switches, which define a set of multiple-LUT blocks (MLBs) called an MLB-basis. We identify the MLB-bases for various commercial logic blocks. Given a n MLB-basis, we formulate FPGA mapping as a mixed integer linear programming (MILP) problem to achieve both the generality and the optimality objectives. We solve the MILP models using a general-purpose MILP solver, and present the results of mapping some ISCAS.85 benchmark circuits with a variety of commercial FPGAs. Circuits of a few hundred gates can be mapped in reasonable time using the MILP approach directly. Larger circuits can be handled by partitioning them prior to technology mapping. We show that optimal or provably near-optimal solutions can be obtained for the large ISCAS.85 benchmark circuits using partitions defined by their high-level functions.

This paper presents a metaheuristic approach to solve the transmission network expansion planning (TNEP) problem considering non-conventional solution candidates. The TNEP consists on finding the set of new elements required in a power system to meet a given future demand at a minimum cost. The TNEP traditionally considers as candidate solutions the addition of new lines and transformers. The main contribution of this work is the inclusion of non-conventional solution candidates. Such non-conventional solution candidates are namely: repowering of existing circuits and reactive shunt compensation. Also, an AC modeling of the network that allows obtaining more realistic results than the traditional DC model has been considered. The TNEP is represented by means of a non linear mixed integer programming problem which is solved through a hybrid genetic algorithm (HGA). Several tests were performed on two benchmark power systems to show the applicability and effectiveness of the proposed approach.

In this paper we study the coordination of different activities in a supply chain issued from a real case. Multiple suppliers send raw materials (RMs) to a distribution center (DC) that delivers them to a unique plant where the storage of the RMs and the finished goods is not possible. Then, the finished goods are directly shipped to multiple customers having just‐in‐time (JIT) demands. Under these hypotheses, we show that the problem can be reduced to multiple suppliers and one DC. Afterwards, we analyze two cases; in the first, we consider an uncapacitated storage at DC, and in the second, we analyze the capacitated storage case. For the first case, we show that the problem is NP‐hard in the ordinary sense using the Knapsack decision problem. We then propose two exact methods: a mixed integer linear program (MILP) and a pseudopolynomial dynamic program. A classical dynamic program and an improved one using the idea of Shaw and Wagelmans are given. With numerical tests we show that the dynamic program gives the optimal solution in reasonable time for quite large instances compared with the MILP. For the second case, the capacity limitation in DC is assumed, which makes the problem solving more challenging. We propose an MILP and a dynamic programming‐based heuristic that provides solutions close to the optimal solution in very short times.