Constraint Optimization Research Articles

Scheduling operations in a large hospital by multiple agents

The scheduling of operations in a large hospital is performed jointly by several groups of people, each with its own objective and constraints. It is a two-phase process, starting with the allocation of operating rooms to wards, and followed by the scheduling of operations in each operating room of the hospital on each day. The final schedule must satisfy all inter-ward hard constraints, such as the allocation of anesthetists, nurses, and equipment to operations that are taking place in parallel, and ideally, it should also address soft constraints such as taking the urgency and complexity of operations into consideration.This study contributes to the ongoing effort of adapting multi-agent optimization models and algorithms to real-world applications by modeling the problems in both phases as distributed constraint optimization problems (DCOPs), with different properties. The first phase includes partially cooperative ward-representing agents, allocating operating rooms for daily usage among themselves. In the second phase, ward-representing agents interact with agents representing constraining elements, in order to generate daily operation schedules for each operating room, thus forming a unique bipartite constraint graph. On one side are the ward representatives, while on the other are the agents representing the constraining resources. Each agent has a non-trivial local problem to solve, and its solution serves as the proposed assignment in the distributed algorithm.The study begins by discussing the properties required of the algorithms needed to solve the two phases. It then proposes adjustments to existing distributed partially cooperative algorithms and local search algorithms to solve these problems, and compares the results of different variants of these algorithms. The results obtained for both phases emphasize that successful collaboration is predicated on two requirements: that agents hold consistent information regarding their peers’ states and that the degree of exploration undertaken by the algorithm is restricted in order to produce high-quality solutions.

Modal-Aware Resource Allocation for Cross-Modal Collaborative Communication in IIoT

With the development of human-machine interactions, users are increasingly evolving towards an immersion experience with multi-dimensional stimuli. Facing this trend, cross-modal collaborative communication is considered an effective technology in the Industrial Internet of Things (IIoT). In this paper, we focus on open issues about resource reuse, pair interactivity, and user assurance in cross-modal collaborative communication to improve quality of service (QoS) and users’ satisfaction. Therefore, we propose a novel architecture of modal-aware resource allocation to solve these contradictions. First, taking all the characteristics of multi-modal into account, we introduce network slices to visualize resource allocation, which is modeled as a Markov Decision Process (MDP). Second, we decompose the problem by the transformation of probabilistic constraint and Lyapunov Optimization. Third, we propose a deep reinforcement learning (DRL) decentralized method in the dynamic environment. Meanwhile, a federated DRL framework is provided to overcome the training limitations of local DRL models. Finally, numerical results demonstrate that our proposed method performs better than other decentralized methods and achieves superiority in cross-modal collaborative communications.

Learning to select SAT encodings for pseudo-Boolean and linear integer constraints

Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the literature with widely varying performance, and the problem of selecting suitable encodings for a given problem instance is not trivial. We explore the problem of selecting encodings for pseudo-Boolean and linear constraints using a supervised machine learning approach. We show that it is possible to select encodings effectively using a standard set of features for constraint problems; however we obtain better performance with a new set of features specifically designed for the pseudo-Boolean and linear constraints. In fact, we achieve good results when selecting encodings for unseen problem classes. Our results compare favourably to AutoFolio when using the same feature set. We discuss the relative importance of instance features to the task of selecting the best encodings, and compare several variations of the machine learning method.

Proposed residual stress model for hot‐rolled wide flange steel cross sections

AbstractResidual stresses in hot‐rolled wide flange steel cross sections may lead to premature yielding, accelerated corrosion and brittle fracture of steel members. The above phenomena lead to a loss of a steel member's stiffness and resistance under mechanical loading. Available residual stress models are mostly based on residual stress measurements that date back to 1950s. Some of the drawbacks of these models relate to the lack of consistency in the considered parameters that affect the residual stress development within a steel cross section. Motivated by this, this paper proposes a new residual stress model for hot‐rolled wide flange steel cross sections. The proposed residual stress model relies on a dataset of 80 experiments that are complemented by additional measurements done as part of the present study. A parabolic residual stress distribution, which is deduced from a constraint optimization problem, is fitted to the assembled data. The proposed residual stress distributions are generalized with the aid of rigorous statistical analyses. The results suggest that the residual stress model is highly dependent on the cross‐sectional area and the depth‐to‐width ratio of a hot‐rolled wide flange steel cross section. The proposed residual stress model reduces the error, on average, by 60‐70% compared to available residual stress models (e.g., European Convention for Constructional Steelwork model), regardless of the cross‐sectional geometry of the hot‐rolled cross section.

Study on reservoir optimal operation based on coupled adaptive ε constraint and multi strategy improved Pelican algorithm

The optimal operation of reservoir groups is a strongly constrained, multi-stage, and high-dimensional optimization problem. In response to this issue, this article couples the standard Pelican optimization algorithm with adaptive ε constraint methods, and further improves the optimization performance of the algorithm by initializing the population with a good point set, reverse differential evolution, and optimal individual t-distribution perturbation strategy. Based on this, an improved Pelican algorithm coupled with adaptive ε constraint method is proposed (ε-IPOA). The performance of the algorithm was tested through 24 constraint testing functions to find the optimal ability and solve constraint optimization problems. The results showed that the algorithm has strong optimization ability and stable performance. In this paper, we select Sanmenxia and Xiaolangdi reservoirs as the research objects, establish the maximum peak-cutting model of terrace reservoirs, apply the ε-IPOA algorithm to solve the model, and compare it with the ε-POA (Pelican algorithm coupled with adaptive ε constraint method) and ε-DE (Differential Evolution Algorithm) algorithms, the results indicate that ε. The peak flow rate of the Huayuankou control point solved by the IPOA algorithm is 12,319 m3/s, which is much lower than the safe overflow flow rate of 22,000 m3/s at the Huayuankou control point, with a peak shaving rate of 44%, and other algorithms do not find effective solutions meeting the constraint conditions. This paper provides a new idea for solving the problem of flood control optimal operation of cascade reservoirs.

A computationally efficient sequential convex programming using Chebyshev collocation method

This paper aims to develop a computationally efficient sequential convex programming algorithm for a class of nonlinear systems. A Chebyshev collocation discretization (CCD) technique is proposed that transforms the continuous convex optimization problem into a finite-dimensional discrete optimization problem. The CCD technique uses Chebyshev polynomials to construct a closed-form approximate solution to the convex dynamic equation. Moreover, it establishes a linear mapping between the control inputs and the system states. This enables the constraints of the dynamics equations to be externalized from the optimization problem and computed using efficient linear equation solving algorithms. On the one hand, this strategy significantly reduces the number of constraint equations and optimization variables, improving the speed of the optimizer. On the other hand, it preserves the path constraints on the system states in the optimization problem. A numerical simulation example of the perching maneuver for a fixed-wing unmanned aerial vehicle is presented to validate the efficiency of the algorithm. The result shows significant improvements in both speed and accuracy compared to the Euler discretization, and greatly improves the solution speed while maintaining almost the same solution accuracy compared to the Gauss pseudospectral optimization method.

A fusion algorithm based on whale and grey wolf optimization algorithm for solving real-world optimization problems

In order to better understand and analyze population-based meta-heuristic optimization algorithms, this paper proposed a new hybrid algorithm combined Lévy flight with modified Whale Optimization Algorithm (WOA) and Grey Wolf Optimizer (GWO) , which is called LMWOAGWO to discard the dross and select the essence. Firstly, the population is initialized by using the uniform distribution space combined with the pseudo-reverse learning strategy, which lays the foundation for global search. Then, modifications were made to both WOA and GWO. For WOA algorithm, random adjustment control parameters strategy and different chaotic maps are used to adjust the main parameters of WOA to avoid the algorithm falling into local optimum in the later stage. For GWO algorithm, a new optimal solution is added to the grey wolf population to increase the optimal update position of the algorithm. On this basis, the dynamic weighting strategy is introduced to improve the convergence accuracy and convergence speed of the algorithm. Subsequently, new conditions were added during the WOA exploitation phase to formulate LMWOAGWO and the greedy strategy is used to retain better iteration update locations. Finally, Lévy flight is used to improve the global search ability of the algorithm. Extensive numerical experiments were conducted using 23 standard test benchmark functions, 25 CEC2005 functions, 15 popular benchmark functions and 10 CEC2019 functions to test the performance of LMWOAGWO compared with other well-known swarm optimization algorithms. Experimental and statistical results show that the performance of LMWOAGWO algorithm is better than many state-of-the-art algorithms. Then, 22 real-world optimization problems were used to further study the effectiveness of LMWOAGWO. Winners of CEC2020 Real World Single Objective Constraint Optimization Competition, such as iLSHADEϵ algorithm, sCMAgES algorithm, COLSHADE algorithm and EnMODE algorithm are selected as four comparison algorithms in real world optimization problems. Experimental results show that the proposed LMWOAGWO has the capability to solve real-world optimization problems. Finally, the application efficiency of LMWOAGWO in solving two basic optimization problems in wireless networks is briefly introduced, and compared with the original WOA and GWO. Simulation results show that the performance of the LMWOAGWO is better than WOA and GWO.

Airfoil shape optimization using genetic algorithm coupled deep neural networks

To alleviate the computational burden associated with the computational fluid dynamics (CFD) simulation stage and improve aerodynamic optimization efficiency, this work develops an innovative procedure for airfoil shape optimization, which is implemented through coupling the genetic algorithm (GA) optimizer with the aerodynamic coefficients prediction network (ACPN) model. The ACPN is established using a fully connected neural network with the airfoil geometry as the input and aerodynamic coefficients as the output. The results show that the ACPN's mean prediction accuracy for the lift and drag coefficient is high up to about 99.02%. Moreover, the prediction time of each aerodynamic coefficient is within 5 ms, four orders of magnitude faster compared to the CFD solver (3 min). Taking advantage of the fast and accurate prediction, the proposed ACPN model replaces the expensive CFD simulations and couples with GA to force the airfoil shape change to maximize the lift–drag ratio under multiple constraints. In terms of time efficiency, optimized airfoils can be fast obtained within 25 s. Even considering an extra 50 h spent on data preparing and 20 s for model training, the overall calculation cost is reduced by a remarkable 62.1% compared to the GA-CFD optimization method (5.5 days). Furthermore, the GA-ACPN model improves the lift–drag ratio with and without constraint by 51.4% and 55.4% for NACA0012 airfoil, respectively, while 50.3% and 60.0% improvement achieved by the GA-CFD optimization method. These results indicate that the GA-ACPN optimization approach significantly enhances the optimization efficiency and has great potential to address varying constraint optimization problems.

A Methodology for Fault-tolerant Pareto-optimal Approximate Designs of FPGA-based Accelerators

Approximate Computing Techniques (ACTs) take advantage of resilience computing applications to trade off among output precision, area, power, and performance. ACTs can lead to significant gains at affordable costs when efficiently implemented on Field Programmable Gate Array– (FPGA) based accelerators. Although several novel ACTs works have been proposed for FPGA accelerators, their applicability to high-assurance systems has not been explored as much. ACTs are becoming necessary in many critical Edge computing systems, such as self-driving cars and Earth observation satellites, to increase computational efficiency. However, an important question comes to mind when targeting critical systems: Does ACT optimization negatively affect the reliability of the system and how can one find optimal design architectures that blend classic mitigation techniques like Triple Modular Redundancy with approximation- and precise-based arithmetic hardware units to achieve the best possible computational efficiency without compromising dependability? This work aims to solve this research problem by introducing a Design Space Exploration (DSE) methodology that employs ACTs in arithmetic units of the design and identifies Pareto-optimal microarchitectures that balance all relevant gains of ACTs, such as area, speed, power, failure rate, and precision, by inserting the correct amount of approximation in the design. In a nutshell, our DSE methodology has formulated the DSE with a Multi-Objective Optimization Problem (MOP). Each Pareto-optimal solution of our tool finds which arithmetic units of the design to implement with precise and approximate circuits and which units to selectively triplicate to remove single points of failure that compromise system reliability below acceptable thresholds. We also suggest another formulation of the DSE into a Single-Objective constraint Optimization Problem (ScOP) producing a single optimal point, and that the user may demand, as a less time-consuming alternative to the MOP if a complete Pareto-front is not needed. Our methodology generates fault-tolerant versions of the Pareto-optimal approximate designs (or simple optimized approximate designs if the ScOP choice is picked) by selectively applying mitigation techniques in a way that the overheads of redundant resources for fault-tolerance do not negate the gains of approximation in comparison to the fault-tolerant versions of the precise design. We evaluate our method on two FPGA-based accelerators: a JPEG encoder and an H.264/Advanced Video Coding decoder. Our experimental results show significant gains in area, frequency, and power consumption without compromising output quality and system reliability compared to classic solutions that replicate all or a part of the resources of the precise design to increase dependability metrics.

Coordinated control of AFS and DYC for electric vehicles with mechanical elastic electric wheels considering the roll effects and uncertain parameters

In order to improve the lateral stability of in-wheel motors electric vehicles (IMEV) equipped with mechanical elastic electric wheels (MEEW) under extreme conditions, this paper proposes an integral sliding mode control (ISMC) algorithm based on the coordination of active front steering (AFS) and direct yaw moment control (DYC) considering the roll effects and the uncertainty of tire cornering stiffness. Firstly, the AFS control algorithm based on adaptive integral terminal sliding mode is proposed, which uses radial-basis-function neural network (RBFNN) to adaptively approximate the integrated nonlinear unknown disturbance. Secondly, considering the roll effects and uncertain cornering stiffness, a mismatched uncertain system for integrated control of AFS and DYC is established. An integral sliding mode control algorithm based on linear matrix inequality (LMI) is designed, and the asymptotic stability of sliding mode dynamics is proved. Further, a constraint optimization algorithm is used to distribute the additional yaw moment. Then, a coordinated control strategy based on the elliptical stable region of the phase plane and the rollover index is designed to activate the integrated controller of AFS and DYC at the right time. Finally, the effectiveness of the control algorithm is verified by high-fidelity CarSim-Matlab simulations. The results show that the proposed controller can effectively and robustly ensure the vehicle lateral stability under extreme conditions.

Dynamic Matching and Spatial Optimization of Land Use and Resource-Environment Constraints in Typical Regions of the Yellow River Basin in China

Accurately identifying the matching relationships between territorial space evolution and the resources and environment carrying capacity will directly guide the sustainable use of territorial space. Based on the evaluation of the territorial space dynamics of the lower Yellow River, this paper evaluates the suitability of territorial space development by focusing on ecological protection, agricultural development, and urban construction. Specifically, the resources and environment carrying capacity is estimated by identifying and mediating potential conflicts in the development of territorial space. The matching relationship between the evolution of territorial space and the resources and environment carrying capacity is identified using the matching degree model. The results demonstrated that: (1) Between 2000 and 2020, the agricultural space of the lower Yellow River was relatively stable, while the ecological space was generally shrinking, and the urban space continued to increase; (2) The characteristics of suitability for the agricultural development and urban construction of the lower Yellow River are characterized by landform and land-sea differentiation. The carrying scale of resources and the environment is based on agricultural space and is increasing yearly, followed by ecological space, which is gradually decreasing, and urban space, which first increased and then decreased; (3) Between 2000 and 2020, the matching index of the ecological and agricultural space evolution and the resource and environmental carrying capacity in the lower Yellow River exhibited a downward trend, while the regional difference increased. Furthermore, the matching index of urban space and the resources and environment carrying capacity indicated an upward trend, while the regional difference decreased.

Automatic generation of dominance breaking nogoods for a class of constraint optimization problems

Constraint Optimization Problems (COPs) ask for an assignment of values to variables in order to optimize an objective subject to constraints that restrict the value combinations in the assignment. They are usually solved by the classical Branch and Bound (B&B) search algorithm. Dominance breaking is an important technique in B&B to prune assignments that are subordinate to others concerning the objective value and/or the satisfiability of constraints. In practice, the addition of constraints for dominance breaking can drastically speed up the B&B search for solving many COPs. However, identification of suboptimal assignments in COPs and derivation of useful constraints for dominance breaking are usually problem-specific and require sophisticated human insights on the problem structure.This paper proposes the first theoretical and practical framework for automatic generation of dominance breaking constraints for a class of COPs consisting of efficiently checkable objectives and constraints. In particular, the framework focuses on generating nogood constraints representing incompatible value assignments and formulates nogood generation as solving auxiliary constraint satisfaction problems. The proposed method can generate nogoods of varying strengths for dominance breaking by controlling the number of involved variables. Experimentation on various benchmarks demonstrates the effectiveness of the proposal in both efficiency and ease of use. The superior performance is also supported by a theoretical analysis to compare the relative strength of automatically generated nogoods with manually derived dominance breaking constraints in the literature.

Federated learning application in distributed energy trading in integrated energy system

Privacy protection in electricity market transactions is a long-term topic, and it must be considered in the application of any new power system project today. This paper explores a new welfare optimization method considering privacy protection in the field of energy trading based on federated learning (FL). First, this paper models an integrated energy system (IES) with one distributed network manager (DNM) and multiple load aggregators (LAs). This model adopts the idea of Stackelberg game, makes DNM dominate the trading game, and makes LAs as followers. Then, it uses the FL-Stackelberg method proposed for the first time to solve the established individual welfare optimization model participating in the game and compares the results with those of the traditional hierarchical optimization method and the Mathematical Program with Equilibrium Constraint optimization method. Numerical results at the end of the paper prove the good accuracy and calculation speed of the proposed FL-Stackelberg​ optimization algorithm, and demonstrate the reliability of FL in engineering practice of IES.

Core Expansion in Optimization Crosswords

In constraint optimization many problem instances remain challenging to current technology. We focus on the Romanian Crosswords Competition Problem. It is a challenging, NP-hard constraint optimization problem where state-of-the-art AI has been lagging significantly behind top human performance. We present an approach that first builds a core, a portion of the problem that will have a high contribution to the objective function. A core is grown into a seed, a partial solution with a subset of variables defined and instantiated. Seeds are further extended into full solutions. Our approach takes as input the size of a rectangular core to consider, and the locations of zero or more black cells inside the core. The results advance state-of-the-art substantially. We report a boost in the scores obtained, bringing our top solutions in the vicinity of top human entries.

An Adaptive Ant Colony Algorithm Based on Local Information Entropy to Solve Distributed Constraint Optimization Problems

As a meta-heuristic algorithm, the ant colony algorithm has been successfully used to solve various combinatorial optimization problems. However, the existing algorithm that takes the power of ants to solve distributed constraint optimization problems (ACO_DCOP) is easy to fall into local optima. To deal with this issue, this paper presents an adaptive ant colony algorithm based on local information entropy to solve distributed constraint optimization problems, named LIEAD. In LIEAD, the local information entropy is introduced to help agents adaptively select the pheromone update strategy and value selection strategy, which improves the convergence speed and the quality of the solution. Moreover, a restart mechanism is designed to break the accumulation state of pheromone, which increases the population diversity and helps the algorithm jump out of the local optima. The extensive experimental results indicate that LIEAD can significantly outperform ACO_DCOP and is competitive with the state-of-the-art DCOPs algorithms.

Constraint Optimization over Semirings

Interpretations of logical formulas over semirings (other than the Boolean semiring) have applications in various areas of computer science including logic, AI, databases, and security. Such interpretations provide richer information beyond the truth or falsity of a statement. Examples of such semirings include Viterbi semiring, min-max or access control semiring, tropical semiring, and fuzzy semiring. The present work investigates the complexity of constraint optimization problems over semirings. The generic optimization problem we study is the following: Given a propositional formula phi over n variable and a semiring (K,+, . ,0,1), find the maximum value over all possible interpretations of phi over K. This can be seen as a generalization of the well-known satisfiability problem (a propositional formula is satisfiable if and only if the maximum value over all interpretations/assignments over the Boolean semiring is 1). A related problem is to find an interpretation that achieves the maximum value. In this work, we first focus on these optimization problems over the Viterbi semiring, which we call optConfVal and optConf. We first show that for general propositional formulas in negation normal form, optConfVal and optConf are in FP^NP. We then investigate optConf when the input formula phi is represented in the conjunctive normal form. For CNF formulae, we first derive an upper bound on the value of optConf as a function of the number of maximum satisfiable clauses. In particular, we show that if r is the maximum number of satisfiable clauses in a CNF formula with m clauses, then its optConf value is at most 1/4^(m-r). Building on this we establish that optConf for CNF formulae is hard for the complexity class FP^NP[log]. We also design polynomial-time approximation algorithms and establish an inapproximability for optConfVal. We establish similar complexity results for these optimization problems over other semirings including tropical, fuzzy, and access control semirings.

Periodic Multi-Agent Path Planning

Multi-agent path planning (MAPP) is the problem of planning collision-free trajectories from start to goal locations for a team of agents. This work explores a relatively unexplored setting of MAPP where streams of agents have to go through the starts and goals with high throughput. We tackle this problem by formulating a new variant of MAPP called periodic MAPP in which the timing of agent appearances is periodic. The objective with periodic MAPP is to find a periodic plan, a set of collision-free trajectories that the agent streams can use repeatedly over periods, with periods that are as small as possible. To meet this objective, we propose a solution method that is based on constraint relaxation and optimization. We show that the periodic plans once found can be used for a more practical case in which agents in a stream can appear at random times. We confirm the effectiveness of our method compared with baseline methods in terms of throughput in several scenarios that abstract autonomous intersection management tasks.

NuWLS: Improving Local Search for (Weighted) Partial MaxSAT by New Weighting Techniques

Maximum Satisfiability (MaxSAT) is a prototypical constraint optimization problem, and its generalized version is the (Weighted) Partial MaxSAT problem, denoted as (W)PMS, which deals with hard and soft clauses. Considerable progress has been made on stochastic local search (SLS) algorithms for solving (W)PMS, which mainly focus on clause weighting techniques. In this work, we identify two issues of existing clause weighting techniques for (W)PMS, and propose two ideas correspondingly. First, we observe that the initial values of soft clause weights have a big effect on the performance of the SLS solver for solving (W)PMS, and propose a weight initialization method. Second, we propose a new clause weighting scheme that for the first time employs different conditions for updating hard and soft clause weights. Based on these two ideas, we develop a new SLS solver for (W)PMS named NuWLS. Through extensive experiments, NuWLS performs much better than existing SLS solvers on all 6 benchmarks from the incomplete tracks of MaxSAT Evaluations (MSEs) 2019, 2020, and 2021. In terms of the number of winning instances, NuWLS outperforms state-of-the-art SAT-based incomplete solvers on all the 6 benchmarks. More encouragingly, a hybrid solver that combines NuWLS and an SAT-based solver won all four categories in the incomplete track of the MaxSAT Evaluation 2022.

Separate but Equal: Equality in Belief Propagation for Single Cycle Graphs

Belief propagation is a widely used incomplete optimization algorithm, whose main theoretical properties hold only under the assumptions that beliefs are not equal. Nevertheless, there is much evidence that equality between beliefs does occur. A method to overcome belief equality by using unary function-nodes is assumed to resolve the problem. We focus on Min-sum, the belief propagation version for solving constraint optimization problems. We prove that on a single cycle graph, belief equality can be avoided only when the algorithm converges to the optimal solution. In any other case, the unary function methods will not prevent equality, rendering some existing results in need of reassessment. We differentiate between belief equality, which includes equal beliefs in a single message, and assignment equality, that prevents a coherent selection of assignments to variables. We show the necessary and satisfying conditions for both.

Finding Good Partial Assignments during Restart-Based Branch and Bound Search

Restart-based Branch-and-Bound Search (BBS) is a standard algorithm for solving Constraint Optimization Problems (COPs). In this paper, we propose an approach to find good partial assignments to jumpstart search at each restart for general COPs, which are identified by comparing different best solutions found in different restart runs. We consider information extracted from historical solutions to evaluate the quality of the partial assignments. Thus the good partial assignments are dynamically updated as the current best solution evolves. Our approach makes restart-based BBS explore different promising sub-search-spaces to find high-quality solutions. Experiments on the MiniZinc benchmark suite show how our approach brings significant improvements to a black-box COP solver equipped with the state of the art search techniques. Our method finds better solutions and proves optimality for more instances.