Complex Combinatorial Optimization Problem Research Articles

A modified biogeography-based optimization algorithm with guided bed selection mechanism for patient admission scheduling problems

One of the complex combinatorial optimization problems is the Patient admission scheduling problem (PASP), which is concerned with assigning the patients arriving into a hospital to available beds to get medical services. The objective of PASP is to maximize the patients comfort, medical treatment effectiveness, and hospital utilization. This research proposes a new approach based on Biogeography-Based Optimization (BBO) algorithm for tacking the PASP. BBO was inspired from the idea of species migration between different habitats. Due to the complexity of the search space in PASP, the original BBO has been equipped with a guided bed selection (GBS) mechanism in order to improve its results and performance, as well as the operator capabilities of BBO which are modified to improve its diversity. These three variants of BBO are compared with each other using six de facto data sets that are widely used in the literature with varying sizes and complexity. The modified BBO is able to yield better results than the other variants. In a nutshell, this paper provides a new PASP method that can be considered an efficient alternative for the scheduling domain to be used by other researchers.

Optimal Integration and Management of Solar Generation and Battery Storage System in Distribution Systems under Uncertain Environment

The simultaneous placement of solar photovoltaics (SPVs) and battery energy storage systems (BESSs) in distribution systems is a highly complex combinatorial optimization problem. It not only involves siting and sizing but is also embedded with charging and discharging dispatches of BESSs under dynamically varying system states with intermittency of SPVs and operational constraints. This makes the simultaneous allocation a nested problem, where the operational part acts as a constraint for the planning part and adds complexity to the problem. This paper presents a bi-layer optimization strategy to optimally place SPVs and BESSs in distribution system. A simple and effective operating BESS strategy model is developed in order to mitigate reverse power flow, enhance load deviation index and absorb variability of load and power generation which are essential features for the faithful exploitation of available renewable energy sources (RESs). In proposed optimization strategy, the inner layer optimizes energy management of BESSs for the sizing and siting as suggested by the outer layer. Since the inner layer optimizes each system state separately, the problem search space of GA is significantly reduced. The application results on a benchmark 33-bus test distribution system highlight the importance of the proposed method.

Spatio-temporal planning for tower cranes in construction projects with simulated annealing

Tower crane planning plays an important role in the progress and cost of construction projects. Finding the optimal tower crane planning scheme from a large number of potential candidates is typically regarded as a complex combinatorial optimization problem. To tackle this issue, researchers have attempted to develop mathematical models combined with various optimization algorithms. However, a major limitation is that most previous studies only focused on a specific stage of a construction project rather than all stages or used two-dimensional project data (i.e., quantity and place) without time dimension, neglecting the dynamic nature and changes that occur during the different construction stages. Another problem is that the service period of tower cranes as well as the height ranking among them, which are highly important when multiple tower cranes are used, were rarely taken into account. To address those challenges, this study proposes a spatio-temporal planning model for tower cranes in construction projects with simulated annealing. The interacting planning objects, consisting of number, type, location, service period, and height ranking, are incorporated into a mathematical model, and it pays particular attention to estimating delays caused by waiting for new lifting tasks and avoiding collisions among tower cranes. The capabilities of the proposed planning model are demonstrated through an example of a high-rise building project by testing all feasible initial solutions. The results show that the calculated optimal solutions can provide the savings ranging from 23.27% to 41.73% depending on the different cases, with an average saving of 31.10% of the total cost when compared to the initial solutions.

Analog Coupled Oscillator Based Weighted Ising Machine

We report on an analog computing system with coupled non-linear oscillators which is capable of solving complex combinatorial optimization problems using the weighted Ising model. The circuit is composed of a fully-connected 4-node LC oscillator network with low-cost electronic components and compatible with traditional integrated circuit technologies. We present the theoretical modeling, experimental characterization, and statistical analysis our system, demonstrating single-run ground state accuracies of 98% on randomized MAX-CUT problem sets with binary weights and 84% with 5-bit weight resolutions. Solutions are obtained within 5 oscillator cycles, and the time-to-solution has been demonstrated to scale directly with oscillator frequency. We present scaling analysis which suggests that large coupled oscillator networks may be used to solve computationally intensive problems faster and more efficiently than conventional algorithms. The proof-of-concept system presented here provides the foundation for realizing such larger scale systems using existing hardware technologies and could pave the way towards an entirely novel computing paradigm.

A Novel Genetic Algorithm for the Synthetical Sensor-Weapon-Target Assignment Problem

The sensor-weapon–target assignment (S-WTA) problem is a crucial decision issue in C4ISR. The cooperative engagement capability (CEC) of sensors and weapons depends on the S-WTA schemes, which can greatly affect the operational effectiveness. In this paper, a mathematical model based on the synthetical framework of the S-WTA problem is established, combining the dependent and independent cooperative engagement modes of sensors and weapons. As this problem is a complex combinatorial optimization problem, a novel genetic algorithm is proposed to improve the solution of this formulated S-WTA model. Based on the prior knowledge of this problem, a problem-specific population initialization method and two novel repair operators are introduced. The performances of the proposed algorithm have been validated on the known benchmarks. Extensive experimental studies compared with three state-of-the-art approaches demonstrate that the proposed algorithm can generate better assignment schemes for the most of the benchmarks.

Selective maintenance process optimization based on an improved gravitational search algorithm, from the perspective of energy consumption

Maintenance is indispensable for ensuring that multi-component systems successfully complete the next mission. Maintenance activities require an enormous amount of energy consumption in engineering problems. For selective maintenance, many studies focus on the trade-off between system reliability and other resources, such as time and cost. The enormous energy consumption of maintenance processes has been ignored in previous research. In this work, a novel energy consumption model considering the actual maintenance process is proposed. Moreover, system reliability is added to the optimization model as a crucial constraint, which makes the optimization process of energy consumption meaningful. The selective maintenance process is a complex combinatorial optimization problem. Hence, a hybrid differential evolution and gravitational search algorithm (DGSA) is proposed to solve the selective maintenance problem considering energy consumption. In addition, several experiments with DGSA, particle swarm optimization and differential evolution are designed to demonstrate the effectiveness of the proposed algorithm.

Network reconfiguration for the DG‐integrated unbalanced distribution system

Distribution system reconfiguration is a complex combinatorial optimisation problem. Finding a globally optimal solution to this problem in a short span of time is a challenging task. Two different network reconfiguration methodologies, namely a look-up table-based algorithm and a Pareto-optimisation-based algorithm have been discussed. Power loss minimisation and reliability maximisation are taken as objectives for both the methodologies when the system is in the normal operating state. The same algorithms also work for maximum service restoration under the post-fault condition. For reliability assessment in the presence of distributed generators (DGs), an algorithm is also proposed using the probabilistic model of components. In the other algorithm, reconfiguration is performed in the presence of DGs using a look-up table. The look-up table is prepared with the help of the proposed Pareto-optimisation-based reconfiguration algorithm to train the system for various loading conditions. The feasibility and effectiveness of the proposed methods are demonstrated using the IEEE 34- and IEEE 123-bus unbalanced radial distribution systems under normal and faulty conditions. The algorithms are also tested on a 13-bus practical distribution system in the field.

Optimizing virtual machine placement in IaaS data centers: taxonomy, review and open issues

The unprecedented growth of energy consumption in data centers created critical concern in recent years for both the research community and industry. Besides its direct associated cost; high energy consumption also results in a large amount of CO2 emission and incurs extra cooling expenditure. The foremost reason for overly energy consumption is the underutilization of data center resources. In modern data centers, virtualization provides a promising approach to improve the hardware utilization level. Virtual machine placement is a process of mapping a group of virtual machines (VMs) onto a set of physical machines (PMs) in a data center with the aim of maximizing resource utilization and minimizing the total power consumption by PMs. An optimal virtual machine placement algorithm substantially contributes to cutting down the power consumption through assigning the input VMs to a minimum number of PMs and allowing the dispensable PMs to be turned off. However, VM Placement Problem is a complex combinatorial optimization problem and known to be NP-Hard problem. This paper presents an extensive review of virtual machine placement problem along with an overview of different approaches for solving virtual machine placement problem. The aim of this paper is to illuminate challenges and issues for current virtual machine placement techniques. Furthermore, we present a taxonomy of virtual machine placement based on various aspects such as methodology, number of objectives, operation mode, problem objectives, resource demand type and number of clouds. The state-of-the-art VM Placement techniques are classified in single objectives and multi-objective groups and a number of prominent works are reviewed in each group. Eventually, some open issues and future trends are discussed which serve as a platform for future research work in this domain.

Synthesis of simultaneously heat integrated and thermally coupled nonsharp distillation sequences based on stochastic optimization

Synthesizing simultaneously heat integrated and thermally coupled distillation sequences (HITCDSs) is a complex combinatorial optimization problem and it is difficult to solve this problem, especially when considering nonsharp splits. Based on stochastic optimization, we propose an efficient approach to synthesize nonsharp HITCDSs. First, an implicit mathematical formulation for the HITCDS optimization is presented. Next, encoding strategies are used tactfully to represent HITCDS structures and evolving rules are developed to generate neighboring HITCDS structures. Finally, simultaneously optimizing the distillation sequences, thermal coupling structures, heat integrated networks, and operating parameters of the columns is easily attained through an improved simulated annealing algorithm. Three cases are studied to validate the high solution efficiency of the approach. The optimization results show that nonsharp HITCDSs are more energy efficient than the sharp ones. Besides, HITCDSs have lower total annual cost than conventional distillation configurations, configurations only employing heat integration, and configurations only employing thermal coupling.

AN IMPROVED SIMULATED ANNEALING FOR THE CAPACITATED VEHICLE ROUTING PROBLEM (CVRP)

In the industrial sector, in order to increase the company's competitive profit and ratio, must be able to suppress as much expenditure as possible. Product distribution is one of the logistics processes in the industry which consumes the most costs. Products must be distributed to customers in different locations and also with varying requests. The problem belongs to Capacitated Vehicle Routing Problem (CVRP) that is considered as one of the complex combinatorial optimization problems included in the NP-Hard Problem category, which is a problem that requires difficult computation and a lot of time along with the increasing size of the problem data. So, in this study improvisation will be carried out in the form of modifying the simulated annealing method to solve the combinatorial problem so that the optimal distance in the case of distribution will be obtained. In addition, in this study a comparison will be made between basic simulated annealing and also improved simulated annealing. Based on the results of the research it is proven that Improved Simulated Annealing can provide a better solution.

Optimisation of tower site locations for camera-based wildfire detection systems

Early forest fire detection can effectively be achieved by systems of specialised tower-mounted cameras. With the aim of maximising system visibility of smoke above a prescribed region, the process of selecting multiple tower sites from a large number of potential site locations is a complex combinatorial optimisation problem. Historically, these systems have been planned by foresters and locals with intimate knowledge of the terrain rather than by computational optimisation tools. When entering vast new territories, however, such knowledge and expertise may not be available to system planners. A tower site-selection optimisation framework that may be used in such circumstances is described in this paper. Metaheuristics are used to determine candidate site layouts for an area in the Nelspruit region in South Africa currently monitored by the ForestWatch detection system. Visibility cover superior to that of the existing system in the region is achieved and obtained in several days, whereas traditional approaches normally require months of speculation and planning. Following the results presented here, the optimisation framework is earmarked for use in future ForestWatch system planning.

A modified harmony search algorithm applied to capacitor placement of radial distribution networks considering voltage stability index

In power system, capacitor placement of distribution networks is a complex combinatorial optimisation problem. In this paper, in order to effectively solve optimal capacitor placement (OCP), an aggregate harmony search (AHS) optimiser, a stochastic population-based metaheuristic algorithm, is proposed which introduces a new pitch adjustment mechanism for harmony search (HS). The objective function contains three goals: 1) minimisation of the power losses; 2) minimisation of the capacitor installation cost; 3) improvement of the voltage stability index at the weakest bus. On two case studies, 23 kV nine-section feeder and 33-bus radial system, simulation results show that the proposed AHS not only finds more accurate results than the other investigated HS variants and particle swarm optimisation (PSO) techniques but also has the best robustness. Promising performance of AHS makes this technique as an efficient alternative to solve capacitor placement problem.

Energy-Conscious Scheduling Problem in a Flexible Job Shop Using a Discrete Water Wave Optimization Algorithm

As more and more attention is paid to green manufacturing, production scheduling has been proved to be an efficient method for the reduction of environmental pollution. It is well-known that the flexible job shop scheduling problem (FJSP) is a very complex combinatorial optimization problem with strong theoretical and background for application. However, the problem has been extensively investigated and historically concerned with some indicators related to time, e.g., flow time, makespan, and workload. In this study, an energy-conscious FJSP is investigated with the consideration of the energy consumption. First, a mathematical model of the energy-conscious FJSP is built with the objective of optimizing the sum of the energy consumption cost and the completion-time cost. Due to the fact that the basic water wave optimization (WWO) was developed for various continuous problems, a discrete water wave optimization (DWWO) algorithm is proposed to solve the model. In our DWWO algorithm, a three-string encoding approach is first adopted to represent each individual wave. To make the algorithm adapt for the considered scheduling problem, three discrete evolutionary operations are redesigned according to the characteristics of the problem, i.e., propagation, refraction, and breaking. Finally, extensive experimental simulations are conducted to test the proposed DWWO algorithm. The comparison results demonstrate that the proposed DWWO algorithm is efficient for the energy-conscious FJSP.

A modified harmony search algorithm applied to capacitor placement of radial distribution networks considering voltage stability index

In power system, capacitor placement of distribution networks is a complex combinatorial optimisation problem. In this paper, in order to effectively solve optimal capacitor placement (OCP), an aggregate harmony search (AHS) optimiser, a stochastic population-based metaheuristic algorithm, is proposed which introduces a new pitch adjustment mechanism for harmony search (HS). The objective function contains three goals: 1) minimisation of the power losses; 2) minimisation of the capacitor installation cost; 3) improvement of the voltage stability index at the weakest bus. On two case studies, 23 kV nine-section feeder and 33-bus radial system, simulation results show that the proposed AHS not only finds more accurate results than the other investigated HS variants and particle swarm optimisation (PSO) techniques but also has the best robustness. Promising performance of AHS makes this technique as an efficient alternative to solve capacitor placement problem.

RETRACTED ARTICLE: A-COA: an adaptive cuckoo optimization algorithm for continuous and combinatorial optimization

Cuckoo optimization algorithm (COA) is inspired from the special and exotic lifestyle of a bird family called the cuckoo and her amazing and unique behavior in egg laying and breeding. Just like any other population-based swarm intelligence metaheuristic algorithms, the basic COA starts with a set of randomly generated solutions called “habitats.” Actually, the habitats can be the current locations of either the mature cuckoos or their eggs. In an iterative manner, cuckoos lay their eggs around their habitats inside the other birds’ nests by mimicking their eggs’ color, pattern, and size, and this is a kind of parasitic brooding behavior. Some hosts may discriminate the strange eggs and throw them out while the others not. The survival competition between cuckoos and their hosts, and migration of cuckoos in swarm are two main underlying motivations to introduce the COA. In this paper, an adaptive cuckoo optimization algorithm named A-COA is proposed in which three novelties in egg-laying and migration phases are applied. These modifications have made the basic algorithm more efficient with faster convergence to solve continuous and discrete optimization problems. A comprehensive comparison study of A-COA versus not only the basic COA but also some other conventional metaheuristics like GA, PSO, ABC, and TLBO has been made on a variety of unimodal and multimodal numerical benchmark functions with different characteristics, and the results show an overall 25.85% of improvement in terms of performance with a faster convergence speed compared to the basic COA, where the statistical Wilcoxon rank-sum test certifies our conclusions. In addition, a discretized version of A-COA and its application to the multiprocessor task scheduling problem as a complex combinatorial optimization problem are investigated where the proposed A-COA is very competitive with not only the strongest conventional heuristics, for example, MCP, ETF, and DLS, but also the basic COA and the newly proposed ACO-based approach.

Multiprocessor task scheduling problem using hybrid discrete particle swarm optimization

Task Scheduling is a complex combinatorial optimization problem and known to be an NP hard. It is an important challenging issue in multiprocessor computing systems. Discrete Particle Swarm Optimization (DPSO) is a newly developed swarm intelligence technique for solving discrete optimization problems efficiently. In DPSO, each particle should limit its communication with the previous best solution and the best solutions of its neighbors. This learning restriction may reduce the diversity of the algorithm and also the possibility of occurring premature convergence problem. In order to address these issues, the proposed work presents a hybrid version of DPSO which is a combination of DPSO and Cyber Swarm Algorithm (CSA). The efficiency of the proposed algorithm is evaluated based on a set of benchmark instances and the performance criteria such as makespan, mean flow time and reliability cost.

Value recovery options portfolio optimization for remanufacturing end of life product

Recovering valuable components from End-of-Life (EOL) product is regarded as a means to extend remaining useful life and reduce production cost of used components in the context of remanufacturing. There are three value recovery options for each component including new, reuse, and reconditioning, making the value recovery of EOL product a complex combinatorial optimization problem. To obtain the optimal value recovery options portfolio of used components and improve the economic benefits from remanufacturing, a multi-objective optimization method of value recovery is applied to the remanufacturing of EOL product. Firstly, an evaluation criterion in terms of quantified damage level and remaining life of used components is established, which aims to identify value recovery options for each used component. Then, the concept of Life Span Equilibrium (LSE) is proposed and a multi-objective optimization model is established, in which LSE, value recovery efficiency, and cost are taken as the objectives. An adaptive Epsilon-dominance based Strength Pareto Evolution Algorithm (AE-SPEA2) is employed to obtain an optimal value recovery portfolio, and its results are compared with an Elitist-based Non-dominated Sorting Genetic Algorithm (NSGA-II) and a Pareto Envelope based Selection Algorithm (PESA-II). Finally, a used lathe (model C6132) is taken as an example to verify the practicality and effectiveness of the proposed method, the results of which indicate that the proposed method is effective in optimizing the value recovery of EOL product.

Enhancing and extending the classical GRASP framework with biased randomisation and simulation

Greedy Randomised Adaptive Search Procedure (GRASP) is one of the best-known metaheuristics to solve complex combinatorial optimisation problems (COPs). This paper proposes two extensions of the typical GRASP framework. On the one hand, applying biased randomisation techniques during the solution construction phase enhances the efficiency of the GRASP solving approach compared to the traditional use of a restricted candidate list. On the other hand, the inclusion of simulation at certain points of the GRASP framework constitutes an efficient simulation–optimisation approach that allows to solve stochastic versions of COPs. To show the effectiveness of these GRASP improvements and extensions, tests are run with both deterministic and stochastic problem settings related to flow shop scheduling, vehicle routing, and facility location.

Combining variable neighborhood search with simulation for the inventory routing problem with stochastic demands and stock-outs

Abstract Vendor managed inventory aims at reducing supply chain costs by centralizing inventory management and vehicle routing decisions. This integrated supply chain approach results in a complex combinatorial optimization problem known as the inventory routing problem (IRP). This paper presents a variable neighborhood search metaheuristic hybridized with simulation to solve the IRP under demand uncertainty. Our simheuristic approach is able to solve large sized instances for the single period IRP with stochastic demands and stock-outs in very short computing times. A range of experiments underline the algorithm’s competitiveness compared to previously used heuristic approaches. The results are analyzed in order to provide closer managerial insights.

Cost-based filtering algorithms for a Capacitated Lot Sizing Problem and the Constrained Arborescence Problem

Constraint Programming (CP) is a paradigm derived from artificial intelligence, operational research, and algorithmics that can be used to solve combinatorial problems. CP solves problems by interleaving search (assign a value to an unassigned variable) and propagation. Constraint propagation aims at removing/filtering inconsistent values from the domains of the variables in order to reduce the search space of the problem. In this thesis, we develop filtering algorithms for two complex combinatorial optimization problems: a Capacitated Lot Sizing Problem (CLSP) and the Constrained Arborescence Problem (CAP). Each of these problems has many variants and practical applications. The CLSP is the problem of finding an optimal production plan for single or multiple items while satisfying demands of clients and respecting resource restrictions. The CLSP finds important applications in production planning. In this thesis, we introduce a CLSP in CP. In many lot sizing and scheduling problems, in particular when the planning horizon is discrete and finite, there are stocking costs to be minimized. These costs depend on the time spent between the production of an order and its delivery. We focus on developing specialized filtering algorithms to handle the stocking cost part of a class of the CLSP. We propose the global optimization constraint StockingCost when the perperiod stocking cost is the same for all orders; and its generalized version, the IDStockingCost constraint (ID stands for Item Dependent). In this thesis, we also deal with a well-known problem in graph theory: the Minimum Weight Arborescence (MWA) problem. Consider a weighted directed graph in which we distinguish one vertex r as the root. An MWA rooted at r is a directed spanning tree rooted at r with minimum total weight. We focus on the CAP that requires one to find an arborescence that satisfies some side constraints (for example resource, degree, or diameter constraints) and that has minimum weight. The CAP has many real life applications in telecommunication networks, computer networks, transportation problems, scheduling problems, etc. After sensitivity analysis of the MWA, we introduce the CAP in CP. We propose a dedicated global optimization constraint to handle any known variant of the CAP in CP: the MinArborescence constraint. All the proposed filtering algorithms are analyzed theoretically and evaluated experimentally. The different experimental evaluations of these propagators against the state-of-the-art propagators show their respective efficiencies.