Similar Subproblems Research Articles

A decomposition-based multi-objective evolutionary algorithm for hybrid flowshop rescheduling problem with consistent sublots

ABSTRACT Lot streaming is the most widely used technique to facilitate the overlap of successive operations. Considering the consistent sublots and machine breakdown, this study investigates the multi-objective hybrid flowshop rescheduling problem with consistent sublots (MOHFRP_CS), which aims at optimising the total completion time, starting time deviations of operations, and average adjustment of sublot sizes simultaneously. By introducing the decomposition strategy and effective migrating birds optimisation framework, this paper develops a multi-objective migrating birds optimisation algorithm based on decomposition (MMBO/D). In MMBO/D, the problem is decomposed into a series of sub-problems, and its solutions are initialised by the Glover operator and further optimised by the variable neighbourhood descent strategy. The weights assigned to the sub-problems are adapted dynamically according to a variable weight strategy, and a global update strategy is employed to update the solutions. A novel sharing and benefiting mechanism is proposed to implement coevolution among different sub-problems. Competitive mechanisms are modified by considering similar sub-problems to improve population quality. A criterion is designed to check whether a subproblem is stuck in the local optima. The comprehensive computational results demonstrate that MMBO/D outperforms other state-of-the-art multi-objective evolutionary algorithms (MOEAs) for the addressed problem.

UAV-Aided Cooperative Data Collection Scheme for Ocean Monitoring Networks

In this article, we present an unmanned aerial vehicle (UAV)-aided ocean monitoring network for remote oceanic data collection, in which monitoring data are transmitted first from battery-powered underwater sensor nodes (USNs) to sea surface sink nodes (SNs) in a data collection cycle using underwater acoustic communication, and then a UAV hovering in air collects all the data from SNs and relays them to a ground base station via wireless communication links. Aiming at maximizing network lifetime, we model the resource allocation, USN-to-SN access, and SN-to-UAV access issues as a mixed-integer nonconvex optimization problem. To efficiently solve it, we decompose the optimization into two stages. The first stage is to minimize time consumption in an SN-to-UAV nonorthogonal multiple access process and we solve it by designing a UAV deployment scheme, a subchannel matching scheme, and a joint power and time allocation scheme, based on which, the second stage is to maximize the residual energies of USNs in USN-to-SN transmissions under a modified frequency-division multiple access strategy in each collection cycle. The second-stage optimization is further decomposed into some similar subproblems, and each of them is considered as a bipartite graph matching problem between USNs and underwater acoustic channels. For each subproblem, we propose improved weight-based matching and bisection-based searching algorithms. Finally, we design a low-complexity iteration algorithm to approximate the optimal solution of the original problem by solving these subproblems. The simulation results validate the effectiveness of our proposals.

A Fuzzy Decomposition-Based Multi/Many-Objective Evolutionary Algorithm.

Performance of multi/many-objective evolutionary algorithms (MOEAs) based on decomposition is highly impacted by the Pareto front (PF) shapes of multi/many-objective optimization problems (MOPs), as their adopted weight vectors may not properly fit the PF shapes. To avoid this mismatch, some MOEAs treat solutions as weight vectors to guide the evolutionary search, which can adapt to the target MOP's PF automatically. However, their performance is still affected by the similarity metric used to select weight vectors. To address this issue, this article proposes a fuzzy decomposition-based MOEA. First, a fuzzy prediction is designed to estimate the population's shape, which helps to exactly reflect the similarities of solutions. Then, N least similar solutions are extracted as weight vectors to obtain N constrained fuzzy subproblems ( N is the population size), and accordingly, a shared weight vector is calculated for all subproblems to provide a stable search direction. Finally, the corner solution for each of m least similar subproblems ( m is the objective number) is preserved to maintain diversity, while one solution having the best aggregated value on the shared weight vector is selected for each of the remaining subproblems to speed up convergence. When compared to several competitive MOEAs in solving a variety of test MOPs, the proposed algorithm shows some advantages at fitting their different PF shapes.

ADMM-based problem decomposition scheme for vehicle routing problem with time windows

Emerging urban logistics applications need to address various challenges, including complex traffic conditions and time-sensitive requirements. In this study, in the context of urban logistics, we consider a vehicle routing problem with time-dependent travel times and time windows (VRPTW), and the goal is to minimize the total generalized costs including the transportation, waiting time, and fixed costs associated with each vehicle. We adopt a high-dimensional space–time network flow model to formulate an underlying vehicle routing problem (VRP) with a rich set of criteria and constraints. A difficult issue, when solving VRPs, is how to iteratively improve both the primal and dual solution quality in general and how to break the symmetry generated by many identical solutions, particularly with homogeneous vehicles. Along this line, many coupling constraints, such as the consensus constraints across different agents or decision makers, need to be carefully addressed to find high-quality optimal or close-to-optimal solutions under medium- or large-scale instances. Currently, the alternating direction method of multipliers (ADMM) is widely used in the field of convex optimization, as an integration of the augmented Lagrangian relaxation and block coordinate descent methods, for machine learning and large-scale continuous systems optimization and control. In this work, we introduce the use of ADMM to solve the multi-VRP, which is a special case of integer linear programming, and demonstrate a manner to reduce the quadratic penalty terms used in ADMM into simple linear functions. In a broader context, a computationally reliable decomposition framework is developed to iteratively improve both the primal and dual solution quality. Essentially, the least-cost path subproblem or other similar subproblems involving binary decisions can be embedded into a sequential solution scheme with an output of both lower bound estimates and upper bound feasible solutions. We examine the performance of the proposed approach using classical Solomon VRP benchmark instances. We also evaluate our approach on a real-world instance based on a problem-solving competition by Jingdong Logistics, a major E-commerce company.

Using column generation to compute lower bound sets for bi-objective combinatorial optimization problems

We discuss the use of column generation in a bi-objective setting. Just as in single objective combinatorial optimization, the role of column generation in the bi-objective setting is to compute dual bounds (i.e. lower bounds for minimization problems and upper bounds for maximization problems) which can be used to guide the search for efficient solutions or to evaluate the quality of approximate solutions. The general idea used in this paper is to first transform the bi-objective problem into single objective by a scalarization method and then solve the transformed problem several times by varying the necessary parameters. We show that irrespective of the scalarization method used, similar subproblems are solved when applying column generation. For this reason, we investigate possible ways of intelligently searching for columns for these subproblems in order to accelerate the column generation method.

Employing a Parametric Model for Analytic Provenance

We introduce a propagation-based parametric symbolic model approach to supporting analytic provenance. This approach combines a script language to capture and encode the analytic process and a parametrically controlled symbolic model to represent and reuse the logic of the analysis process. Our approach first appeared in a visual analytics system called CZSaw. Using a script to capture the analyst’s interactions at a meaningful system action level allows the creation of a parametrically controlled symbolic model in the form of a Directed Acyclic Graph (DAG). Using the DAG allows propagating changes. Graph nodes correspond to variables in CZSaw scripts, which are results (data and data visualizations) generated from user interactions. The user interacts with variables representing entities or relations to create the next step’s results. Graph edges represent dependency relationships among nodes. Any change to a variable triggers the propagation mechanism to update downstream dependent variables and in turn updates data views to reflect the change. The analyst can reuse parts of the analysis process by assigning new values to a node in the graph. We evaluated this symbolic model approach by solving three IEEE VAST Challenge contest problems (from IEEE VAST 2008, 2009, and 2010). In each of these challenges, the analyst first created a symbolic model to explore, understand, analyze, and solve a particular subproblem and then reused the model via its dependency graph propagation mechanism to solve similar subproblems. With the script and model, CZSaw supports the analytic provenance by capturing, encoding, and reusing the analysis process. The analyst can recall the chronological states of the analysis process with the CZSaw script and may interpret the underlying rationale of the analysis with the symbolic model.

A Class of Collocating Problem in Production and its Optimization Models

The paper gives a general description of a typical combinatorial optimization problem-the collocation problem of production, and respectively establish the integer linear programming model based on the collocation ways and the integer linear programming model based on the optimal collocation amounts and the integer nonlinear programming model based on the local optimum. In the solving methods of the models, we have mainly analyzed the enumeration method and the method by using LINGO optimization software to solve the model. The instance shows that the models and solutions are all effective. The first model reflects the mechanism of the collocation problem better and gets the global optimal solution most likely, but more difficult to solve large-scale; the second model can quickly obtain the optimal the numbers of the finished products and all kinds of materials consumptions, but still need to enumerate the collocation ways step by step; the third model can gets the local optimal solution and the specific collocation ways through solving the model circularly. The optimization models and solution methods in this paper can be extended to the similar sub-problems of the combinatorial optimization problems, such as assembly problem, packing problem, the cutting problem, etc.

Achieving Maximum Energy-Efficiency in Multi-Relay OFDMA Cellular Networks: A Fractional Programming Approach

In this paper, the joint power and subcarrier allocation problem is solved in the context of maximizing the energy-efficiency (EE) of a multi-user, multi-relay orthogonal frequency division multiple access (OFDMA) cellular network, where the objective function is formulated as the ratio of the spectral-efficiency (SE) over the total power dissipation. It is proven that the fractional programming problem considered is quasi-concave so that Dinkelbach's method may be employed for finding the optimal solution at a low complexity. This method solves the above-mentioned master problem by solving a series of parameterized concave secondary problems. These secondary problems are solved using a dual decomposition approach, where each secondary problem is further decomposed into a number of similar subproblems. The impact of various system parameters on the attainable EE and SE of the system employing both EE maximization (EEM) and SE maximization (SEM) algorithms is characterized. In particular, it is observed that increasing the number of relays for a range of cell sizes, although marginally increases the attainable SE, reduces the EE significantly. It is noted that the highest SE and EE are achieved, when the relays are placed closer to the BS to take advantage of the resultant line-of-sight link. Furthermore, increasing both the number of available subcarriers and the number of active user equipment (UE) increases both the EE and the total SE of the system as a benefit of the increased frequency and multi-user diversity, respectively. Finally, it is demonstrated that as expected, increasing the available power tends to improve the SE, when using the SEM algorithm. By contrast, given a sufficiently high available power, the EEM algorithm attains the maximum achievable EE and a suboptimal SE.

Rapid blockwise multi-resolution clustering of facial images for intelligent watermarking

Population-based evolutionary computation (EC) is widely used to optimize embedding parameters in intelligent watermarking systems. Candidate solutions generated with these techniques allow finding optimal embedding parameters of all blocks of a cover image. However, using EC techniques for full optimization of a stream of high-resolution grayscale face images is very costly. In this paper, a blockwise multi-resolution clustering (BMRC) framework is proposed to reduce this cost. During training phase, solutions obtained from multi-objective optimization of reference face images are stored in an associative memory. During generalization operations, embedding parameters of an input image are determined by searching for previously stored solutions of similar sub-problems in memory, thereby eliminating the need for full optimization for the whole face image. Solutions for sub-problems correspond to the most common embedding parameters for a cluster of similar blocks in the texture feature space. BMRC identifies candidate block clusters used for embedding watermark bits using the robustness score metric. It measures the texture complexity of image block clusters and can thereby handle watermarks of different lengths. The proposed framework implements a multi-hypothesis approach by storing the optimization solutions according to different clustering resolutions and selecting the optimal resolution at the end of the watermarking process. Experimental results on the PUT face image database show a significant reduction in complexity up to 95.5 % reduction in fitness evaluations compared with reference methods for a stream of 198 face images.

A Constraint Satisfaction Framework for Executing Perceptions and Actions in Diagrammatic Reasoning

Diagrammatic reasoning (DR) is pervasive in human problem solving as a powerful adjunct to symbolic reasoning based on language-like representations. The research reported in this paper is a contribution to building a general purpose DR system as an extension to a SOAR-like problem solving architecture. The work is in a framework in which DR is modeled as a process where subtasks are solved, as appropriate, either by inference from symbolic representations or by interaction with a diagram, i.e., perceiving specified information from a diagram or modifying/creating objects in a diagram in specified ways according to problem solving needs. The perceptions and actions in most DR systems built so far are hand-coded for the specific application, even when the rest of the system is built using the general architecture. The absence of a general framework for executing perceptions/actions poses as a major hindrance to using them opportunistically -- the essence of open-ended search in problem solving. Our goal is to develop a framework for executing a wide variety of specified perceptions and actions across tasks/domains without human intervention. We observe that the domain/task-specific visual perceptions/actions can be transformed into domain/task-independent spatial problems. We specify a spatial problem as a quantified constraint satisfaction problem in the real domain using an open-ended vocabulary of properties, relations and actions involving three kinds of diagrammatic objects -- points, curves, regions. Solving a spatial problem from this specification requires computing the equivalent simplified quantifier-free expression, the complexity of which is inherently doubly exponential. We represent objects as configuration of simple elements to facilitate decomposition of complex problems into simpler and similar subproblems. We show that, if the symbolic solution to a subproblem can be expressed concisely, quantifiers can be eliminated from spatial problems in low-order polynomial time using similar previously solved subproblems. This requires determining the similarity of two problems, the existence of a mapping between them computable in polynomial time, and designing a memory for storing previously solved problems so as to facilitate search. The efficacy of the idea is shown by time complexity analysis. We demonstrate the proposed approach by executing perceptions and actions involved in DR tasks in two army applications.

An ontology-based similarity measurement for problem-based case reasoning

Traditional case-based reasoning uses a table/frame or scenario to represent a case. It assumed that similar input/event results in similar output/event state. However, similar cases may not have similar output/event states since problem solver may have different way to break down the problem. Thus, authors previously proposed problem-based case reasoning to overcome the limitation of the traditional approaches and used clustered ontology to represent the problem spaces of a case. However, synonym problem causes the mismatch of similar sub-problems of historical cases for new case. Thus, this paper proposed ontology-based similarity measurement to retrieve the similar sub-problems that overcomes the synonym problems on case retrieval. The recall and precise of ontology-based similarity measurement were higher than that of the traditional similarity measurement.

On decentralised eigenvalue assignment for large-scale systems with dynamic interconnections

Characterisation for the class of decentralised control that assigns a prescribed set of eigenvalues for a large-scale dynamically delayed interconnected system is given in the paper. By expanding the system state space the delay disappears and a higher dimensional state space is created. The equivalent systems controllability originates from substystems interconnections controllability. Increased dimensionality is no longer a problem, because, by partitioning the composite eigenvectors, the augmented problem is decomposed to several similar subproblems that subsystems interconnections are required to solve. Sufficient conditions for global eigenvalue assignment are established in terms of subsystems-interconnections matrices. A synthesis procedure for the characterisation is presented through exploiting the available freedom within subsystems/interconnections kernel spaces.