Problem Decomposition Techniques Research Articles

A relax-and-fix Pareto-based algorithm for a bi-objective vaccine distribution network considering a mix-and-match strategy in pandemics

Mass vaccination in pandemics is one of the most effective strategies to halt disease transmission. A well-organized vaccination plan is essential for guaranteeing its success in cases with limited vaccines. On the other hand, most vaccines need more than one dose for appropriate immunity, intensifying the vaccine shortage probability and complicating decision-making. This study presents a bi-objective mixed-integer linear model for a vaccine distribution chain problem, simultaneously considering economic and social objectives, with multi-dose vaccination adaptable even for booster doses. Moreover, the compatible vaccines in each vaccination process are considered a mix-and-match strategy to diversify vaccination alternatives and alleviate the vaccine shortage risk. It is shown that the problem is NP-hard, and we develop two heuristic and meta-heuristic algorithms to solve real-size instances in a reasonable time. Both algorithms use problem size reduction and problem decomposition techniques to produce an approximate Pareto front for the problem. The heuristic algorithm employs relax-and-fix and fix-and-optimize techniques, and an epsilon-constraint method to solve the multi-objective problem. The proposed meta-heuristic algorithm is based on the hybrid of two well-known evolutionary algorithms, particle swarm optimization, and genetic algorithm. It also uses a multi-objective framework called PESA-II to generate the Pareto front. Both proposed heuristic and meta-heuristic algorithms can employ parallel computing, which significantly reduces computational time. Finally, we investigate the proposed algorithms’ performance using 30 random problem instances and a case study from Iran. The results demonstrate that heuristic and meta-heuristic algorithms have obtained a reasonable solution with a maximum of 6.9% and 16.3% cost objective function gap respectively. The heuristic algorithm is superior to the meta-heuristic in terms of Pareto front quality metrics.

Optimal Deployment of Flood Emergency Response Materials under Stochastic Demands

This study aims to develop a planning model for the deployment of flood emergency response materials under stochastic demands. For ease of modeling, a deterministic demand model is first proposed, from which the stochastic model is further extended. These models are used to determine the allocation of materials the transport truck routes and distribution of the stockpiled materials to emergency sites. The models are formulated as multiple integer network flow problems with special side constraints which are characterized as NP-hard in terms of optimization. To solve the complicated stochastic model efficiently, we also develop a solution algorithm based on a problem decomposition technique coupled with a variable fixing technique. Finally, to preliminarily evaluate the proposed models and solution algorithm, we perform numerical tests using data related to a Taiwan flood emergency response system. The test results are good, indicating the potential usefulness of the models and solution algorithm in practice.

Optimizing electronic structure simulations on a trapped-ion quantum computer using problem decomposition

Quantum computers have the potential to advance material design and drug discovery by performing costly electronic structure calculations. A critical aspect of this application requires optimizing the limited resources of the quantum hardware. Here, we experimentally demonstrate an end-to-end pipeline that focuses on minimizing quantum resources while maintaining accuracy. Using density matrix embedding theory as a problem decomposition technique, and an ion-trap quantum computer, we simulate a ring of 10 hydrogen atoms without freezing any electrons. The originally 20-qubit system is decomposed into 10 two-qubit problems, making it amenable to currently available hardware. Combining this decomposition with a qubit coupled cluster circuit ansatz, circuit optimization, and density matrix purification, we accurately reproduce the potential energy curve in agreement with the full configuration interaction energy in the minimal basis set. Our experimental results are an early demonstration of the potential for problem decomposition to accurately simulate large molecules on quantum hardware.

A Survey of Algorithms for Black-Box Safety Validation of Cyber-Physical Systems

Autonomous cyber-physical systems (CPS) can improve safety and efficiency for safety-critical applications, but require rigorous testing before deployment. The complexity of these systems often precludes the use of formal verification and real-world testing can be too dangerous during development. Therefore, simulation-based techniques have been developed that treat the system under test as a black box operating in a simulated environment. Safety validation tasks include finding disturbances in the environment that cause the system to fail (falsification), finding the most-likely failure, and estimating the probability that the system fails. Motivated by the prevalence of safety-critical artificial intelligence, this work provides a survey of state-of-the-art safety validation techniques for CPS with a focus on applied algorithms and their modifications for the safety validation problem. We present and discuss algorithms in the domains of optimization, path planning, reinforcement learning, and importance sampling. Problem decomposition techniques are presented to help scale algorithms to large state spaces, which are common for CPS. A brief overview of safety-critical applications is given, including autonomous vehicles and aircraft collision avoidance systems. Finally, we present a survey of existing academic and commercially available safety validation tools.

Empirical problem decomposition — the key to the evolutionary effectiveness in solving a large-scale non-binary discrete real-world problem

In this paper, we consider an NP-hard, real-world optimization problem from the field of computer networks. The problem refers to the network survivability and may be considered hard due to its scale. Such problems are usually successfully solved by various Genetic Algorithms (GAs). The recent advances in the development of Evolutionary Algorithms (EAs) dedicated to solving discrete-encoded problems show that GAs employing modern linkage learning techniques seem to have exceptional potential in proposing high-quality results. Many of such GAs are the state-of-the-art methods for various optimization problems, including various domain types and single- and multi-objective optimization problems. These GAs have also been shown effective in solving theoretical and practical problems. Thus, linkage learning development may lead to proposing GAs that are significantly more effective than their predecessors. Therefore, we develop the recently proposed linkage learning technique, namely the linkage learning based on local optimization (3LO) that is (to the best of our knowledge) based on fundamentally different ideas than all other linkage-based problem decomposition techniques. Due to these differences, 3LO has some exceptional features — it is proven that it will never commit some of the possible problem decomposition inconsistencies. However, 3LO was only proposed for binary-encoded problems. Therefore, to fill this gap and adjust 3LO to the considered problem, we propose linkage learning based on local optimization for discrete non-binary search spaces (3LO-nb). The obtained results show that 3LO-nb allows for reaching excellent results. Additionally, our proposition is generic, and its effectiveness may be verified on other non-binary discrete problems.

GPU: A New Enabling Platform for Real-Time Optimization in Wireless Networks

Optimization methods are a common tool to maximize the performance of wireless networks and systems. When addressing complex optimization problems in wireless networks, a key technical challenge is to find an optimal or near-optimal solution in real-time, especially when such a timing constraint is extremely short. Due to this challenge, there is usually a serious disparity between what a system can achieve optimally (if an optimal solution were found in real time) and what is actually achieved in the field (due to the use of fast heuristics). in this article, we present a novel approach that exploits problem decomposition techniques and the massive parallel processing capability of GPU platforms to address this challenge. Under the new approach, an original complex optimization problem is first decomposed into a large number of small and mutually independent sub-problems. Then the resulting sub-problems are fitted into massively parallel GPU cores and solved simultaneously. The optimal (or near-optimal) solution is chosen among the solutions from all the parallel sub-problems solved by GPU. We use the classic proportional-fair (PF) scheduling problem in 5G cellular networks as a case study to illustrate this approach. Finally, we briefly review recent advances in applying this approach to addressing a wide array of real-time optimization problems in wireless networks.

Game theoretic approach for predictive lane-changing and car-following control

This contribution puts forward a receding horizon control approach for automated driving systems, where tactical-level lane change decisions and control-level accelerations are jointly evaluated under a central mathematical framework. The key idea is that controlled vehicles predictively determine discrete desired lane sequences and continuous accelerations to minimise a cost function reflecting undesirable future situations. The interactions between controlled vehicles and surrounding vehicles are captured in the cost function. The approach is flexible in terms of application to controller design for both non-cooperative control systems where controlled vehicles only optimise their own cost and cooperative control systems where controlled vehicles coordinate their decisions to optimise the collective cost. To determine the controller behaviour, the problem is formulated as a differential game where controlled vehicles make decisions based on the expected behaviour of other vehicles. The control decisions are updated at regular frequency, using the newest information regarding the state of controlled vehicles and surrounding vehicles available. A problem decomposition technique is employed to reduce the dimensionality of the original problem by introducing a finite number of sub-problems and an iterative algorithm based on Pontryagin’s Principle is used to solve sub-problems efficiently. The proposed controller performance is demonstrated via numerical examples. The results show that the proposed approach can produce efficient lane-changing manoeuvres while obeying safety and comfort requirements. Particularly, the approach generates optimal lane change decisions in the predicted future, including strategic overtaking, cooperative merging and selecting a safe gap.

A constraint programming approach for integrated spatial and temporal scheduling for clustered architectures

Many embedded processors use clustering to scale up instruction-level parallelism in a cost-effective manner. In a clustered architecture, the registers and functional units are partitioned into smaller units and clusters communicate through register-to-register copy operations. Texas Instruments, for example, has a series of architectures for embedded processors which are clustered. Such an architecture places a heavier burden on the compiler, which must now assign instructions to clusters (spatial scheduling), assign instructions to cycles (temporal scheduling), and schedule copy operations to move data between clusters. We consider instruction scheduling of local blocks of code on clustered architectures to improve performance. Scheduling for space and time is known to be a hard problem. Previous work has proposed greedy approaches based on list scheduling to simultaneously perform spatial and temporal scheduling and phased approaches based on first partitioning a block of code to do spatial assignment and then performing temporal scheduling. Greedy approaches risk making mistakes that are then costly to recover from, and partitioning approaches suffer from the well-known phase ordering problem. In this article, we present a constraint programming approach for scheduling instructions on clustered architectures. We employ a problem decomposition technique that solves spatial and temporal scheduling in an integrated manner. We analyze the effect of different hardware parameters—such as the number of clusters, issue-width, and intercluster communication cost—on application performance. We found that our approach was able to achieve an improvement of up to 26%, on average, over a state-of-the-art technique on superblocks from SPEC 2000 benchmarks.

Optimal schedule adjustments for supplying ready mixed concrete following incidents

In this study, the authors develop a systematic network flow model designed to help RMC carriers effectively adjust schedules following RMC mixer breakdowns. A time–space network technique is employed to formulate the production of the RMC and truck fleet flows in the dimensions of time and space. A solution algorithm, incorporating a problem decomposition technique and the use of a mathematical programming solver, is developed to efficiently solve the problem. Finally, the model and solution method are evaluated by performing a case study. The test results show that, with the application of the model and the solution algorithm, mixer breakdowns do not lead to much deterioration in the system operating performance. In addition, the system operating cost is significantly improved (by 10.75 %) compared to that obtained using the manual approach. As a result, the model and the solution algorithm could be useful for actual operations.

Short-term manpower planning for MRT carriage maintenance under mixed deterministic and stochastic demands

The purpose of this research is to develop two manpower supply planning models and a solution algorithm for mass rapid transit carriage maintenance under mixed deterministic and stochastic demands. These models are formulated as mixed integer programs that are characterized as NP-hard. We employ problem decomposition techniques, coupled with the CPLEX mathematical programming solver, to develop an algorithm that is capable of efficiently solving the problems. The models and the method used currently in actual operations are evaluated by a simulation-based evaluation method. Finally, we perform a case study using real operating data from a Taiwan MRT maintenance facility. The preliminary results are good, showing that the models could be useful for planning carriage maintenance manpower supply.

A comparison of problem decomposition techniques for the FAP

This paper proposes a problem decomposition approach to solve hard Frequency Assignment Problem instances with standard meta-heuristics. The proposed technique aims to divide the initial problem in...

Exploring problem decomposition in conceptual design among novice designers

Conceptual product design is commonly described as problem solving. In the present study we attempt to expand this view. Focusing on the solution search phase, we analyse explicit and implicit problem decomposition techniques and integrate them into a descriptive cognitive model. To evaluate the prevalence of decomposition modes empirically, we provide results from a verbal protocol analysis study involving 16 senior students of mechanical engineering. Data indicated that the subjects apply top–down control strategies coupled to implicit decomposition. Explicit decomposition was used seldom and without obvious benefits. We relate these results to the model that considers implicit decomposition as an integral part of the problem interpretation process and discuss the role of decomposition in a structured idea generation process.

A genetic algorithm for frequency assignment with problem decomposition

The FAP is an optimisation problem which assigns frequencies to ransmitters in as efficient way as possible, either in terms of interference, FS-FAP, or range of channels used, MS-FAP. The FAP can be modelled in graph theoretic terms. This paper uses a 'permutation-based' steady-state GA adapted to solve both types of FAP. Problem decomposition techniques have been introduced to improve the GA performance. A large problem is decomposed into smaller subproblems consisting of distinct induced subgraphs. Then the GA is applied to each of them in turn producing partial solutions. Finally, these are recombined into a final solution of the original problem. We have used a basic decomposition based on the generalised-degree of the graph vertices and one obtained by solving the balanced graph partitioning problem. The GA produces better or comparable results with other widely known meta-heuristics in all the test problems considered.

Constraint Propagation and Decomposition Techniques forHighly Disjunctive and Highly Cumulative Project Scheduling Problems

In recent years, constraint satisfaction techniques have been successfully applied to ’’disjunctive‘‘ scheduling problems, i.e., scheduling problems where each resource can execute at most one activity at a time. Less significant and less generally applicable results have been obtained in the area of ’’cumulative‘‘ scheduling. Multiple constraint propagation algorithms have been developed for cumulative resources but they tend to be less uniformly effective than their disjunctive counterparts. Different problems in the cumulative scheduling class seem to have different characteristics that make them either easy or hard to solve with a given technique. The aim of this paper is to investigate one particular dimension along which problems differ. Within the cumulative scheduling class, we distinguish between ’’highly disjunctive‘‘ and ’’highly cumulative‘‘ problems: a problem is highly disjunctive when many pairs of activities cannot execute in parallel, e.g., because many activities require more than half of the capacity of a resource; on the contrary, a problem is highly cumulative if many activities can effectively execute in parallel. New constraint propagation and problem decomposition techniques are introduced with this distinction in mind. This includes an O(n^2) ’’edge-finding‘‘ algorithm for cumulative resources (where n is the number of activities requiring the same resource) and a problem decomposition scheme which applies well to highly disjunctive project scheduling problems. Experimental results confirm that the impact of these techniques varies from highly disjunctive to highly cumulative problems. In the end, we also propose a refined version of the ’’edge-finding‘‘ algorithm for cumulative resources which, despite its worst case complexity in O(n^3), performs very well on highly cumulative instances.

A Problem Decomposition Technique with Application to the Optimal Distribution of Enzymes

A model for enzyme-driven reactions in steady state is given which involves the enzyme concentrations linearly and the reactant concentrations nonlinearly. From this model an optimization problem is set up for the enzyme distributions, which involves only nonnegativity and integral constraints. Using some earlier theoretical work of Holmåker and Stewart [SIAM J. Control Optim. 25 (1987), pp. 1032–1052], a problem decomposition principle is proven. Results for a single enzyme-driven reaction is then used to produce a dynamic programming technique for trees and chains of enzyme driven reactions. This is extended to a give a technique for determining the optimal amount of each enzyme subject to an overall cost limit. Numerical results are given for a test problem of the author’s devising.

A comprehensive approach to production planning in multipurpose batch plants

A number of algorithms have been developed—including enumeration of feasible production sequences, alternative task selection and the generation of alternative production lines—to determine the optimal sequence in which products and by-products should be produced and the times at which the various production operations for each product should be carried out to meet a given product demand pattern, taking into account the available equipment, storage costs, stopover penalties and other plant limitations. Product interdependencies, utility requirements and constraints, which limit the number of operations that can be carried out in parallel, are also considered. These algorithms have been integrated into a single, efficient computer package intended for routine use in industrial operational practice. Production planning in an already existing plant has been successfully achieved for short- and medium-term production using problem decomposition techniques and integer-linear programming with restrictions. The industrial case presented here demonstrates the practical use of the package under different plant production conditions.