Empirical study of the Bee Colony Optimization (BCO) algorithm

The Bee Colony Optimization (BCO) meta-heuristic deals with combinatorial optimization problems. It is biologically inspired method that explores collective intelligence applied by the honey bees during nectar collecting process. In this paper we perform empirical study of the BCO algorithm. We apply BCO to optimize numerous numerical test functions. The obtained results are compared with the results in the literature. The numerical experiments performed on well-known benchmark functions show that the BCO is competitive with other methods and it can generate high-quality solutions within negligible CPU times.     

A simultaneous transit network design and frequency setting: Computing with bees

The transit network design problem belongs to the class of hard combinatorial optimization problem, whose optimal solution is not easy to find out. We consider in this paper the transit network design problem in a way that we simultaneously determine the links to be included in the transit network, assemble chosen links into bus routes, and determine bus frequency on each of the designed routes. Our approach to the transit network design problem is based on the Bee Colony Optimization (BCO) metaheuristic. The BCO algorithm is a stochastic, random-search technique that belongs to the class of population-based algorithms. This technique uses a similarity among the way in which bees in nature look for food, and the way in which optimization algorithms search for an optimum of a combinatorial optimization problem. The numerical experiments are performed on known benchmark problems. We clearly show that our approach, based on the BCO algorithm is competitive with the other approaches in the literature and that can generate high-quality solutions.     

Transit network design by Bee Colony Optimization

The transit network design problem is one of the most significant problems faced by transit operators and city authorities in the world. This transportation planning problem belongs to the class of difficult combinatorial optimization problem, whose optimal solution is difficult to discover. The paper develops a Swarm Intelligence (SI) based model for the transit network design problem. When designing the transit network, we try to maximize the number of satisfied passengers, to minimize the total number of transfers, and to minimize the total travel time of all served passengers. Our approach to the transit network design problem is based on the Bee Colony Optimization (BCO) metaheuristics. The BCO algorithm is a stochastic, random-search technique that belongs to the class of population-based algorithms. This technique uses a similarity among the way in which bees in nature look for food, and the way in which optimization algorithms search for an optimum of a combinatorial optimization problem. The numerical experiments are performed on known benchmark problems. We clearly show that our approach, based on the BCO algorithm, is competitive with other approaches in the literature, and it can generate high-quality solutions.     

Multiobjective optimization using population-based extremal optimization

In recent years, a general-purpose local-search heuristic method called Extremal Optimization (EO) has been successfully applied in some NP-hard combinatorial optimization problems. In this paper, we present a novel Pareto-based algorithm, which can be regarded as an extension of EO, to solve multiobjective optimization problems. The proposed method, called Multiobjective Population-based Extremal Optimization (MOPEO), is validated by using five benchmark functions and metrics taken from the standard literature on multiobjective evolutionary optimization. The experimental results demonstrate that MOPEO is competitive with the state-of-the-art multiobjective evolutionary algorithms. Thus MOPEO can be considered as a viable alternative to solve multiobjective optimization problems.     

The travelling salesman problem with time windows: Adapting algorithms from travel-time to makespan optimization

In combinatorial optimization it is not rare to find problems whose mathematical structure is nearly the same, differing only in some aspect related to the motivating application. For example, many problems in machine scheduling and vehicle routing have equivalent formulations and only differ with respect to the optimization objective, or particular constraints. Moreover, while some problems receive a lot of attention from the research community, their close relatives receive hardly any attention at all. Given two closely related problems, it is intuitive that it may be effective to adapt state-of-the-art algorithms—initially introduced for the well-studied problem variant—to the less-studied problem variant. In this paper we provide an example based on the travelling salesman problem with time windows that supports this intuition. In this context, the well-studied problem variant minimizes the travel time, while the less-studied problem variant minimizes the makespan. Indeed, the results show that the algorithms that we adapt from travel-time minimization to makespan minimization significantly outperform the existing state-of-the-art approaches for makespan minimization.     

Hybrid bee colony optimization for examination timetabling problems

Swarm intelligence is a branch of artificial intelligence that focuses on the actions of agents in self-organized systems. Researchers have proposed a bee colony optimization (BCO) algorithm as part of swarm intelligence. BCO is a meta-heuristic algorithm based on the foraging behavior of bees. This study presents a hybrid BCO algorithm for examination timetabling problems. Bees in the BCO algorithm perform two main actions: forward pass and backward pass. Each bee explores the search space in forward pass and then shares information with other bees in the hive in backward pass. This study found that a bee decides to be either a recruiter that searches for a food source or a follower that selects a recruiter bee to follow on the basis of roulette wheel selection. In forward pass, BCO is supported along with other local searches, including the Late Acceptance Hill Climbing and Simulated Annealing algorithms. We introduce three selection strategies (tournament, rank and disruptive selection strategies) for the follower bees to select a recruiter to maintain population diversity in backward pass. The disruptive selection strategy outperforms tournament and rank selections. We also introduce a self-adaptive mechanism to select a neighborhood structure to enhance the neighborhood search. The proposed algorithm is evaluated against the latest methodologies in the literature with respect to two standard examination timetabling problems, namely, uncapacitated and competition datasets. We demonstrate that the proposed algorithm produces one new best result on uncapacitated datasets and comparable results on competition datasets.     

A time-varying transfer function for balancing the exploration and exploitation ability of a binary PSO

Many real-world problems belong to the family of discrete optimization problems. Most of these problems are NP-hard and difficult to solve efficiently using classical linear and convex optimization methods. In addition, the computational difficulties of these optimization tasks increase rapidly with the increasing number of decision variables. A further difficulty can be also caused by the search space being intrinsically multimodal and non-convex. In such a case, it is more desirable to have an effective optimization method that can cope better with these problem characteristics. Binary particle swarm optimization (BPSO) is a simple and effective discrete optimization method. The original BPSO and its variants have been used to solve a number of classic discrete optimization problems. However, it is reported that the original BPSO and its variants are unable to provide satisfactory results due to the use of inappropriate transfer functions. More specifically, these transfer functions are unable to provide BPSO a good balance between exploration and exploitation in the search space, limiting their performances. To overcome this problem, this paper proposes to employ a time-varying transfer function in the BPSO, namely TV_T-BPSO. To understand the search behaviour of the TV_T-BPSO, we provide a systematic analysis of its exploration and exploitation capability. Our experimental results demonstrate that TV_T-BPSO outperforms existing BPSO variants on both low-dimensional and high-dimensional classical 0–1 knapsack problems, as well as a 200-member truss problem, suggesting that TV_T-BPSO is able to better scale to high dimensional combinatorial problems than the existing BPSO variants and other metaheuristic algorithms.     

Multiobjective optimization of trusses using genetic algorithms

In this paper we propose the use of the genetic algorithm (GA) as a tool to solve multiobjective optimization problems in structures. Using the concept of min–max optimum, a new GA-based multiobjective optimization technique is proposed and two truss design problems are solved using it. The results produced by this new approach are compared to those produced by other mathematical programming techniques and GA-based approaches, proving that this technique generates better trade-offs and that the genetic algorithm can be used as a reliable numerical optimization tool.     

Algorithmic Aspects of Using Small Instance Relaxations in Parallel Branch-and-Cut

Essential for the success of branch-and-cut algorithms for solving combinatorial optimization problems are the availability of reasonable tight relaxations and effective routines for solving the associated separation problems. In this paper we introduce the concept of small instance relaxations which can be particularly useful for problems with symmetric structure. Small instance relaxations are based on the facets of polytopes associated with small instances of the combinatorial optimization problem to be solved and can be generated automatically by facet enumeration. For a certain class of symmetric problems, we describe a general approach to the separation problem. Algorithmic aspects of using small instance relaxations effectively (parallel separation, facet selection, cutting plane selection) are discussed in detail. Extensive computational results are presented for the linear ordering problem and a certain betweenness problem. Received March 31, 1998; revised November 9, 1998.     

量子群智能优化算法综述

随着科学技术的不断发展,最优化理论及其衍生出的算法已经广泛应用于人们的日常工作与生活当中,现实世界中的很多问题都可以被描述为组合优化问题。群智能优化算法这些年来被证明在解决组合优化问题方面效果显著,将当下处于研究热点的量子计算概念引入群智能优化算法形成的量子群智能优化算法,为更好地解决组合优化问题提出了一个新的研究方向。在过去的二十多年里,许多量子群智能优化算法被不断开发出来,同时在此基础上进行了大量改进与应用。综述了量子蚁群算法、量子粒子群算法、量子人工鱼群算法、量子人工蜂群算法、量子布谷鸟搜索算法、量子混合蛙跳算法、量子萤火虫算法、量子蝙蝠算法等量子群智能优化算法,并对量子群智能优化算法面临的问题以及未来研究方向进行了深入探讨。     

Follow the perturbed approximate leader for solving semi-bandit combinatorial optimization

Combinatorial optimization in the face of uncertainty is a challenge in both operational research and machine learning. In this paper, we consider a special and important class called the adversarial online combinatorial optimization with semi-bandit feedback, in which a player makes combinatorial decisions and gets the corresponding feedback repeatedly. While existing algorithms focus on the regret guarantee or assume there exists an efficient offline oracle, it is still a challenge to solve this problem efficiently if the offline counterpart is NP-hard. In this paper, we propose a variant of the Followthe-Perturbed-Leader (FPL) algorithm to solve this problem. Unlike the existing FPL approach, our method employs an approximation algorithm as an offline oracle and perturbs the collected data by adding nonnegative random variables. Our approach is simple and computationally efficient. Moreover, it can guarantee a sublinear (1+ ε)-scaled regret of order O(T^{\frac{2}{3}}) for any small ε>0 for an important class of combinatorial optimization problems that admit an FPTAS (fully polynomial time approximation scheme), in which Tis the number of rounds of the learning process. In addition to the theoretical analysis, we also conduct a series of experiments to demonstrate the performance of our algorithm.     

GISMOO: A new hybrid genetic/immune strategy for multiple-objective optimization

In this paper, we propose a new Pareto generic algorithm, called GISMOO, which hybridizes genetic algorithm and artificial immune systems. GISMOO algorithm is generic in the sense that it can be used to solve both combinatorial and continuous optimization problems. The proposed approach offers an original iterative process in two phases: a Genetic Phase and an Immune Phase. The Immune Phase is used to identify and to emphasize the solutions located in less crowded regions found during the iterative process of the algorithm. Simulation results on difficult test problems, both in combinatorial and continuous optimization, show that the proposed approach, in most problems, is able to obtain better results than state of the art algorithms.     

On the computational complexity of combinatorial flexibility problems

The concept of flexibility – originated in the context of heat exchanger networks design – is associated with a substructure which allows the same optimal value on the substructure (for example an optimal flow) as in the whole structure, for all the costs in a given range of costs. In this work, we extend the concept of flexibility to general combinatorial optimization problems, and prove several computational complexity results in this new framework. Under some monotonicity conditions, we prove that a combinatorial optimization problem can be polynomially reduced to its associated flexibility problem. However, the minimum cut, maximum weighted matching and shortest path problems have NP-complete associated flexibility problems. In order to obtain polynomial flexibility problems, we have to restrict ourselves to combinatorial optimization problems on matroids.     

Evaluating solution sets of <Emphasis Type="Italic">a posteriori</Emphasis> solution techniques for bi-criteria combinatorial optimization problems

The quality of an approximate solution for combinatorial optimization problems with a single objective can be evaluated relatively easily. However, this becomes more difficult when there are multiple objectives. One potential approach to solving multiple criteria combinatorial optimization problems when at least one of the single objective problems is NP-complete, is to use an a posteriori method that approximates the efficient frontier. A common difficulty in this type of approach, however, is evaluating the quality of approximate solutions, since sets of multiple solutions should be evaluated and compared. This necessitates the use of a comparison measure that is robust and accurate. Furthermore, a robust measure plays an important role in metaheuristic optimization for tuning various parameters for evolutionary algorithms, simulated annealing, etc., which are frequently employed for multiple criteria combinatorial optimization problems. In this paper, the performance of a new measure, which we call Integrated Convex Preference (ICP) is compared to that of other measures appearing in the literature through numerical experiments—specifically, we use two a posteriori solution techniques based on genetic algorithms for a bi-criteria parallel machine scheduling problem and evaluate their performance (in terms of solution quality) using different measures. Experimental results show that the ICP measure evaluates the solution quality of approximations robustly (i.e., similar to visual comparison results) while other alternative measures can misjudge the solution quality. We note that the ICP measure can be applied to other non-scheduling multiple objective combinatorial optimization problems, as well.     

Instance variant nearest neighbor using particle swarm optimization for function approximation

In this paper, a new approach called ‘instance variant nearest neighbor’ approximates a regression surface of a function using the concept of k nearest neighbor. Instead of fixed k neighbors for the entire dataset, our assumption is that there are optimal k neighbors for each data instance that best approximates the original function by fitting the local regions. This approach can be beneficial to noisy datasets where local regions form data characteristics that are different from the major data clusters. We formulate the problem of finding such k neighbors for each data instance as a combinatorial optimization problem, which is solved by a particle swarm optimization. The particle swarm optimization is extended with a rounding scheme that rounds up or down continuous-valued candidate solutions to integers, a number of k neighbors. We apply our new approach to five real-world regression datasets and compare its prediction performance with other function approximation algorithms, including the standard k nearest neighbor, multi-layer perceptron, and support vector regression. We observed that the instance variant nearest neighbor outperforms these algorithms in several datasets. In addition, our new approach provides consistent outputs with five datasets where other algorithms perform poorly.     

Bound sets for biobjective combinatorial optimization problems

In this paper we introduce the concept of bound sets for multiobjective discrete optimization. We prove general results on lower and upper bound sets for combinatorial optimization problems with multiple objectives. We present general algorithms for constructing lower and upper bound sets for biobjective problems and provide numerical results on five different problem types.     

A parallel algorithm for generating bicompatible elimination orderings of proper interval graphs

In this paper, we first show how a certain ordering of vertices, called bicompatible elimination ordering (BCO), of a proper interval graph can be used to solve efficiently several problems in proper interval graphs. We, then, propose an NC parallel algorithm (i.e., polylogarithmic-time employing a polynomial number of processors) in SIMD CRCW PRAM (Single Instruction Stream Multiple Data Stream Concurrent Read Concurrent Write Parallel Random Access Machine) model of parallel computation to compute a BCO of a proper interval graph. To the best of our knowledge, this is the first NC parallel algorithm to compute a BCO of a proper interval graph.     

Association rule mining using binary particle swarm optimization

In this paper, we developed a binary particle swarm optimization (BPSO) based association rule miner. Our BPSO based association rule miner generates the association rules from the transactional database by formulating a combinatorial global optimization problem, without specifying the minimum support and minimum confidence unlike the a priori algorithm. Our algorithm generates the best M rules from the given database, where M is a given number. The quality of the rule is measured by a fitness function defined as the product of support and confidence. The effectiveness of our algorithm is tested on a real life bank dataset from commercial bank in India and three transactional datasets viz. books database, food items dataset and dataset of the general store taken from literature. Based on the results, we infer that our algorithm can be used as an alternative to the a priori algorithm and the FP-growth algorithm.     

Combinatorial optimization in Biology using Probability Collectives Multi-agent Systems

We present a study of Probability Collectives Multi-agent Systems (PCMAS) for combinational optimization problems in Biology. This framework for distributed optimization is deeply connected with both game theory and statistical physics. In contrast to traditional biologically-inspired algorithms, Probability-Collectives (PC) based methods do not update populations of solutions; instead, they update an explicitly parameterized probability distribution p over the space of solutions by a collective of agents. That updating of p arises as the optimization of a functional of p. The functional is chosen so that any p that optimizes it should be p peaked about good solutions. In this paper we demonstrate PCMAS as a promising combinational optimization method for biological network construction. This computational approach to response networks enables robust prediction of activated crucial sub-networks in biological systems under the presence of specific drugs, thereby facilitating the identification of important nodes for potential drug targets and furthering hypotheses about biological and medical problems on a systems level. The application of PCMAS in this context therefore sheds light on how this multi-agent learning methodology advances the current state of research in agent-based models for combinational optimization problems in Biology.