Difficult Combinatorial Optimization Problems Research Articles

Dynamic characteristic of a multiple chaotic neural network and its application

Based on chaotic neural network, a multiple chaotic neural network algorithm combining two different chaotic dynamics sources in each neuron is proposed. With the effect of self-feedback connection and non-linear delay connection weight, the new algorithm can contain more powerful chaotic dynamics to search the solution domain globally in the beginning searching period. By analyzing the dynamic characteristic and the influence of cooling schedule in simulated annealing, a flexible parameter tuning strategy being able to promote chaotic dynamics convergence quickly is introduced into our algorithm. We show the effectiveness of the new algorithm in two difficult combinatorial optimization problems, i.e., a traveling salesman problem and a maximum clique problem.

The exact solution of several classes of inventory-routing problems

In order to be competitive companies need to take advantage of synergistic interactions between different decision areas. Two of these are related to the distribution and inventory management processes. Inventory-Routing Problems (IRPs) arise when inventory and routing decisions must be made simultaneously, which yields a difficult combinatorial optimization problem. In this paper, we propose a branch-and-cut algorithm for the exact solution of several classes of IRPs. Specifically, we solve the multi-vehicle IRP with a homogeneous and a heterogeneous fleet, the IRP with transshipment options, and the IRP with added consistency features. We perform an extensive computational analysis on benchmark instances.

Hybrid Artificial Intelligence–Based PBA for Benchmark Functions and Facility Layout Design Optimization

AbstractFacility layout design (FLD) presents a particularly interesting area of study because of its relatively high level of attention to aesthetics and usability qualities, in addition to common engineering objectives such as cost and performance. However, FLD present a difficult combinatorial optimization problem for engineers. Swarm intelligence (SI), an approach to decision making that integrates collective social behavior models such as the bee algorithm (BA) and particle swarm optimization, is being increasingly used to resolve various complex optimization problems. This study proposes a new optimization hybrid swarm algorithm, the particle bee algorithm (PBA), which imitates the intelligent swarming behavior of honeybees and birds. This study also proposes a neighborhood-windows (NW) technique for improving searching efficiency and a self-parameter-updating (SPU) technique for preventing trapping into a local optimum in high-dimensional problems. This study compares the performance of PBA with th...

Multi-machine power system stabilizer design using improved particle swarm optimization (PSO) with time-varying acceleration coefficients

An efficient and most famous tool to enhance damping of the power system low frequency oscillations is the conventional widely used lead-lag Power System Stabilizer (PSS). To achieve the desired level of robust performance under transient situation, selecting a suitable design method for optimal tuning of PSS parameters is very important in multi-machine power system. Because, it is a multimodal and difficult combinatorial optimization problem, this paper presents a novel parameter automation strategy for Particle Swarm Optimization (PSO) called PSO with Time-Varying Acceleration Coefficients (PSO-TVAC). This optimization method has a strong ability to successfully control both global and local search in each iteration process for considerably increasing the probability of finding the global optimum solution. The PSO-TVAC algorithm is applied to optimal tuning PSS parameters problem in order to reduce the PSS design effort and find the best possible solution within a reasonable computation time. For this reason, the robustly selection of PSSs parameters is converted as an optimization problem based on the time domain-based objective function under different operating conditions. The robustness of the proposed method is demonstrated on a multi-machine power system in comparison with the classical PSO and conventional method based designed PSSs. It is shown through the nonlinear time domain simulation and some performance indices for a wide range of loading condition. The analysis of the results shows that the improved PSO-TVAC is not only very effective but also provides an excellent ability for damping low frequency oscillations and greatly enhance the dynamic stability of the power system. Moreover, the proposed PSO-TVAC algorithm is superior than that of the classical PSO one in terms of accuracy, convergence and computational effort. Key words: Power system stabilizer (PSS) design, particle swarm optimization, power system dynamics, time-varying acceleration coefficients.

Nested column generation applied to the crude oil tanker routing and scheduling problem with split pickup and split delivery

AbstractThe split pickup split delivery crude oil tanker routing and scheduling problem is a difficult combinatorial optimization problem, both theoretically and practically. However, because of the large expenses in crude oil shipping it is attractive to make use of optimization that exploits as many degrees of freedom as possible to save transportation cost. We propose a nested column generation algorithm for this particular split pickup split delivery problem which bears several complexities such as a heterogeneous fleet, multiple commodities, many‐to‐many relations for pickup and delivery of each commodity, sequence dependent vehicle capacities, and cargo quantity dependent pickup and delivery times. Our approach builds on a branch‐and‐price algorithm in which the column generation subproblems are solved by branch‐and‐price themselves. We describe our implementation in the branch‐cut‐and‐price framework SCIP and give computational results for realistic test instances. The high quality schedules we obtain for these instances improve on those in previous studies. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

파티클군집최적화 방법을 적용한 위치관리시스템 최적 설계

Location area planning (LAP) problem is to partition the cellular/mobile network into location areas with the objective of minimizing the total cost in location management. The minimum cost has two components namely location update cost and searching cost. Location update cost is incurred when the user changes itself from one location area to another in the network. The searching cost incurred when a call arrives, the search is done only in the location area to find the user. Hence, it is important to find a compromise between the location update and paging operations such that the cost of mobile terminal location tracking cost is a minimum. The complete mobile network is divided into location areas. Each location area consists of a group of cells. This partitioning problem is a difficult combinatorial optimization problem. In this paper, we use particle swarm optimization (PSO) to obtain the best/optimal group of cells for 16, 36, 49, and 64 cells network. Experimental studies illustrate that PSO is more efficient and surpasses those of precious studies for these benchmarking problems.

University Timetabling based on Hard Constraints using Genetic Algorithm

proposed system presents a novel approach of solving University timetabling which is NP-hard problem using Genetic Algorithm. Genetic Algorithm is frequently deployed Meta heuristics algorithm which can be effectively used to difficult combinatorial optimization problems. Although, there has been an extensive research towards this field but majority of the research results are much in its nascent stage. The previous researchers have used various methods like Tabu search, Simulated Annealing, network flow, graph coloring, etc. Genetic Algorithms are effective in solving many such optimization problems. The current work presented uses Genetic Algorithm to design an effective model for scheduling with challenging constraints considerations. The objective of the research is to create a model using Genetic Algorithm to the extent it can be used to generate the acceptable schedule using probabilistic operators like mutation and crossover. The design of the fitness function has considered the hard constraints. The simulation shows the better result in minimum time.

A hybrid swarm intelligence based particle-bee algorithm for construction site layout optimization

The construction site layout (CSL) design presents a particularly interesting area of study because of its relatively high level of attention to usability qualities, in addition to common engineering objectives such as cost and performance. However, it is difficult combinatorial optimization problem for engineers. Swarm intelligence (SI) was very popular and widely used in many complex optimization problems which was collective behavior of social systems such as honey bees (bee algorithm, BA) and birds (particle swarm optimization, PSO). This study proposed an optimization hybrid swarm algorithm namely particle-bee algorithm (PBA) based on a particular intelligent behavior of honey bee and bird swarms by integrates theirs advantages. This study compares the performance of PBA with that of BA and PSO for hypothetical construction engineering of CSL problems. The results show that the performance of PBA is comparable to those of the mentioned algorithms and can be efficiently employed to solve those hypothetical CSL problems with high dimensionality.

A GES/TS algorithm for the job shop scheduling

The job shop scheduling problem is a difficult combinatorial optimization problem. This paper presents a hybrid algorithm which combines global equilibrium search, path relinking and tabu search to solve the job shop scheduling problem. The proposed algorithm used biased random sampling to have a better covering of the solution space. In addition, a new version of N6 neighborhood is applied in a tabu search framework. In order to evaluate the algorithm, comprehensive tests are applied to it using various standard benchmark sets. Computational results confirm the effectiveness of the algorithm and its high speed. Besides, 19 new upper bounds among the unsolved problems are found.

Scatter search for the stochastic travel-time vehicle routing problem with simultaneous pick-ups and deliveries

In parallel with the growth of both domestic and international economies, there have been substantial efforts in making manufacturing and service industries more environmental friendly (i.e., promotion of environmental protection). Today manufacturers have become much more concerned with coordinating the operations of manufacturing (for new products) and recycling (for reuse of resources) together with scheduling the forward/reverse flows of goods over a supply chain network. The stochastic travel-time vehicle routing problem with simultaneous pick-ups and deliveries (STT-VRPSPD) is one of the major operations problems in bi-directional supply chain research. The STT-VRPSPD is a very challenging and difficult combinatorial optimization problem due to many reasons such as a non-monotonic increase or decrease of vehicle capacity and the stochasticity of travel times. In this paper, we develop a new scatter search (SS) approach for the STT-VRPSPD by incorporating a new chance-constrained programming method. A generic genetic algorithm (GA) approach for STT-VRPSPD is also developed and used as a reference for performance comparison. The Dethloff data will be used to evaluate the performance characteristics of both SS and GA approaches. The computational results suggest that the SS solutions are superior to the GA solutions.

Optimal solutions for the double row layout problem

The double row layout problem is how to allocate a given set of n machines on both sides of a straight line corridor so that the total cost of transporting materials between machines is minimized. This is a very difficult combinatorial optimization problem with important applications in industry. We formulate the problem as a mixed-integer program. Computational tests show that the proposed formulation presents a far superior performance than that of a previously published model.

Genetic Algorithm with Local Search for Job Shop Scheduling Problem

The job shop scheduling problem (JSSP) is a well-known difficult combinatorial optimization problem. This paper presents a hybrid genetic algorithm for the JSSP with the objective of minimizing makespan. A new generation alternation model of genetic algorithm for JSSP is designed. Every pair of randomly selected parents must pass either crossover or mutation, which are deployed in parallel. In the inner structure of crossover, mutation is partially embedded. Schedules are constructed using a procedure that generates full active schedules. In each generation, a local search heuristic based on the neighborhood structure proposed by Nowicki and Smutnicki is applied to improve the solutions. The approach is tested on a set of standard instances taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm.

A hybrid AI-based particle bee algorithm for facility layout optimization

Facility layout (FL) design presents a particularly interesting area of study because of its relatively high level of attention to aesthetics and usability qualities, in addition to common engineering objectives such as cost and performance. However, this generally presents a difficult combinatorial optimization problem for engineers. Swarm intelligence, an approach to decision making that integrates collective social behavior models such as the bee algorithm (BA) and particle swarm optimization (PSO), is being increasingly used to resolve various complex optimization problems. In order to integrate BA global search ability with the local search advantages of PSO, this study proposes a new optimization hybrid swarm algorithm—the particle bee algorithm (PBA) which imitates the intelligent swarming behavior of honeybees and birds. This study also proposes a neighborhood-windows technique for improving searching efficiency as well as a self-parameter-updating technique for preventing trapping into a local optimum in high-dimensional problems. This study compares PBA performance against BA and PSO performance in practical FL problem. Results show PBA performance is comparable to those of BA and PSO and can be efficiently employed to solve practical FL problem with high dimensionality.

A Parallel Algorithm for the Vehicle Routing Problem

The vehicle routing problem (VRP) is a difficult and well-studied combinatorial optimization problem. We develop a parallel algorithm for the VRP that combines a heuristic local search improvement ...

Enhanced stochastic optimization algorithm for finding effective multi-target therapeutics

BackgroundFor treating a complex disease such as cancer, we need effective means to control the biological network that underlies the disease. However, biological networks are typically robust to external perturbations, making it difficult to beneficially alter the network dynamics by controlling a single target. In fact, multi-target therapeutics is often more effective compared to monotherapies, and combinatory drugs are commonly used these days for treating various diseases. A practical challenge in combination therapy is that the number of possible drug combinations increases exponentially, which makes the prediction of the optimal drug combination a difficult combinatorial optimization problem. Recently, a stochastic optimization algorithm called the Gur Game algorithm was proposed for drug optimization, which was shown to be very efficient in finding potent drug combinations.ResultsIn this paper, we propose a novel stochastic optimization algorithm that can be used for effective optimization of combinatory drugs. The proposed algorithm analyzes how the concentration change of a specific drug affects the overall drug response, thereby making an informed guess on how the concentration should be updated to improve the drug response. We evaluated the performance of the proposed algorithm based on various drug response functions, and compared it with the Gur Game algorithm.ConclusionsNumerical experiments clearly show that the proposed algorithm significantly outperforms the original Gur Game algorithm, in terms of reliability and efficiency. This enhanced optimization algorithm can provide an effective framework for identifying potent drug combinations that lead to optimal drug response.

A Hybrid Differential Evolution and Tree Search Algorithm for the Job Shop Scheduling Problem

The job shop scheduling problem (JSSP) is a notoriously difficult problem in combinatorial optimization. In terms of the objective function, most existing research has been focused on the makespan criterion. However, in contemporary manufacturing systems, due‐date‐related performances are more important because they are essential for maintaining a high service reputation. Therefore, in this study we aim at minimizing the total weighted tardiness in JSSP. Considering the high complexity, a hybrid differential evolution (DE) algorithm is proposed for the problem. To enhance the overall search efficiency, a neighborhood property of the problem is discovered, and then a tree search procedure is designed and embedded into the DE framework. According to the extensive computational experiments, the proposed approach is efficient in solving the job shop scheduling problem with total weighted tardiness objective.

A filter-and-fan algorithm for the capacitated minimum spanning tree problem

The capacitated minimum spanning tree (CMST) is a notoriously difficult problem in combinatorial optimization. Extensive investigation has been devoted to developing efficient algorithms to find optimal or near-optimal solutions. This paper proposes a new CMST heuristic algorithm that effectively combines the classical node-based and tree-based neighborhoods embodied in a filter-and-fan (F&F) approach, a local search procedure that generates compound moves in a tree search fashion. The overall algorithm is guided by a multi-level oscillation strategy used to trigger each type of neighborhood while allowing the search to cross feasibility boundaries. Computational results carried out on a standard set of 135 benchmark problems show that a simple F&F design competes effectively with prior CMST metaheuristics, rivaling the best methods, which are significantly more complex.

Integer programming for optimizing habitat network permeability

PurposeNegative effects of habitat isolation that arise from landscape fragmentation can be mitigated, by connecting natural areas through a network of habitat corridors. To increase the permeability of a given network, i.e. to decrease the resistance to animal movements through this network, often many developments can be made. The available financial resources being limited, the most effective developments must be chosen. This optimization problem, suggested in Finke and Sonnenschein, can be treated by heuristics and simulation approaches, but the method is heavy and the obtained solutions are sub‐optimal. The aim of the paper is to show that the problem can be efficiently solved to optimality by mathematical programming.Design/methodology/approachThe moves of the individual in the network are modeled by an absorbing Markov chain and the development problem is formulated as a mixed‐integer quadratic program, then this program is linearized, and the best developments to make are determined by mixed‐integer linear programming.FindingsFirst, the approach allows the development problem to be solved to optimality contrary to other methods. Second, the definition of the mathematical program is relatively simple, and its implementation is immediate by using standard, commercially available, software. Third, as it is well known with mixed‐integer linear programming formulation it is possible to add new constraints easily if they are linear (or can be linearized).Research limitations/implicationsWith a view to propose a simple and efficient tool to solve a difficult combinatorial optimization problem arising in the improvement of permeability across habitat networks, the approach has been tested on simulated habitat networks. The research does not include the study of some precise species movements in a real network.Practical implicationsThe results provide a simple and efficient decision‐aid tool to try to improve the permeability of habitat networks.Originality/valueThe joint use of mathematical programming techniques and Markov chain theory is used to try to lessen the negative effects of landscape fragmentation.

A state-space solution search method for apparel industry spreading and cutting

The spreading of fabric onto cutting tables in several layers, and the cutting of this fabric in the most cost-efficient manner to produce a pre-determined number of garments is the apparel manufacturing phase that precedes assembly (sewing) and finishing. The problem consists of determining the lowest cost spreading and cutting schedule for garments of different styles, colors, and sizes, subject to physical constraints of cutting table length and cutting knife height as well as business constraints of required demand for each stock-keeping unit (SKU). The determination of this optimal spreading and cutting schedule for various garment styles is a difficult combinatorial NP-complete optimization problem. This paper proposes the use of an innovative state-space approach using heuristic rules to solve the problem: it is modeled as a least-cost search in a graph where each node represents a different spreading and cutting schedule. Several solution algorithms and heuristics are proposed and tested and an illustrative application to a Brazilian apparel company is presented.

Comments on: Routing problems with loading constraints

There exist several contexts in which routing and loading decisions are intertwined. Yet, because each gives rise to a difficult combinatorial optimization problem, it is customary to treat them separately. In recent years, a number of researchers have investigated problems in which routing and loading are optimized simultaneously. The literature on these combined problems is still relatively new, yet sufficient to warrant a survey, which Manuel Iori and Silvano Martello have done masterfully.