Pareto Simulated Annealing Research Articles

GOKA: A Network Partition and Cluster Fusion Algorithm for Controller Placement Problem in SDN

Software Defined Networking (SDN) is a new promising network architecture, with the property of decoupling the data plane from the control plane and centralizing the network topology logically, making the network more agile than traditional networks. However, with the continuous expansion of network scales, the single-controller SDN architecture is unable to meet the performance requirements of the network. As a result, the logically centralized and physically separated SDN multi-controller architecture comes into being, and thereupon the Controller Placement Problem (CPP) is proposed. In order to minimize the propagation latency in Wide Area Network (WAN), we propose Greedy Optimized K-means Algorithm (GOKA) which combines K-means with greedy algorithm. The main thought is to divide the network into multiple clusters, merge them greedily and iteratively until the given number of controllers is satisfied, and place a controller in each cluster through the K-means algorithm. With the purpose of proving the effectiveness of GOKA, we conduct experiments to compare with Pareto Simulated Annealing (PSA), Adaptive Bacterial Foraging Optimization (ABFO), K-means and K-means[Formula: see text] on 6 real topologies from the Internet Topology Zoo and Internet2 OS3E. The results demonstrate that GOKA has a better and more stable solution than other four heuristic algorithms, and can decrease the propagation latency by up to [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] in contrast to PSA, ABFO, K-means and K-means[Formula: see text], respectively. Moreover, the error rate between GOKA and the best solution is always less than [Formula: see text], which promises the precision of our proposed algorithm.

A Pareto-based discrete particle swarm optimization for parallel casting workshop scheduling problem with fuzzy processing time

The parallel casting workshop scheduling problem is essentially a type of unrelated parallel machine scheduling (UPMS) problem with fuzzy order processing time. In this paper, a tri-objective parallel casting workshop optimization model is investigated to minimize the order advance/delay penalty, makespan, and workload imbalance, and a formula of the solution scale with the number of orders and workshops is derived. In line with the multi-objective integer programming model, a new Pareto-based discrete particle swarm optimization (PDPSO) is proposed. In this algorithm, the particles are encoded with integers. A novel two-phase heuristic is developed for integer-encoded particle updates. The first phase determines the order assignment through a weighting vote, and the second phase sorts the orders according to their dominance in each workshop. Every particle’s update is simultaneously guided by the best compromise solution selected from the personal and global Pareto solution. Meanwhile, the Pareto simulated annealing strategy is introduced in PDPSO to enhance its exploration ability. Multiple simulations under different scales are tested to validate the effectiveness of our proposed model and algorithm. The results show that the proposed PDPSO outperforms the other two multi-objective algorithms and has large advantages in finding the Pareto frontier (PF) with an acceptable solution number and solving speed, especially for small and medium-sized instances.

Using Pareto simulated annealing to address algorithmic bias in machine learning

Abstract Algorithmic bias arises in machine learning when models that may have reasonable overall accuracy are biased in favor of ‘good’ outcomes for one side of a sensitive category, for example gender or race. The bias will manifest as an underestimation of good outcomes for the under-represented minority. In a sense, we should not be surprised that a model might be biased when it has not been ‘asked’ not to be; reasonable accuracy can be achieved by ignoring the under-represented minority. A common strategy to address this issue is to include fairness as a component in the learning objective. In this paper, we consider including fairness as an additional criterion in model training and propose a multi-objective optimization strategy using Pareto Simulated Annealing that optimizes for both accuracy and underestimation bias. Our experiments show that this strategy can identify families of models with members representing different accuracy/fairness tradeoffs. We demonstrate the effectiveness of this strategy on two synthetic and two real-world datasets.

A robust multiobjective model for the integrated berth and quay crane scheduling problem at seaside container terminals

The ever increasing demand for container transportation has led to the congestion of maritime container terminals in the world. In this work, the two interrelated problems of berth and quay crane scheduling are considered in an integrated multiobjective mathematical model. A special character of this model is that the arrival times of vessels and the failure (working) times of quay cranes are not deterministic and can vary based on some scenarios. Hence, a robust model is devised for the problem having three objectives of minimising the deviations from target berthing locations and times as well as departure delays of all vessels. This robust optimisation seeks to minimise the value of the objectives regarding all the scenarios. An exact solution approach based on the \U0001d716-constraint method by the Gurobi software is applied. Moreover, regarding the complexity of the problem, two Simulated Annealing (SA) based metaheuristics, namely a Multi-Objective Simulated Annealing (MOSA) and a Pareto Simulated Annealing (PSA) approach are adapted with a novel solution encoding scheme. The three methods are compared based on some multiobjective metrics and a statistical test. The advantage of the integration of berth and quay crane scheduling is examined as well.

A bi-objective robust resource allocation model for the RCPSP considering resource transfer costs

Resource allocation is one of the core issues in project scheduling to ensure the effective use of scare renewable resources, and has been regularly encountered in production systems in the manufacturing and service industries. The transfers of renewable resources between activities generally incur certain scheduling costs and affect the robustness of a certain schedule in an uncertain environment. To address this issue, a bi-objective optimisation model is proposed to make the resource transfer decisions, which aims to minimise the transfer cost and maximise solution robustness in the presence of activity duration variability. The proposed model employs a novel resource-oriented flow formulation that is different from those of the previous literature. A NSGA-II and a Pareto simulated annealing (PSA) algorithm have been applied as the solution methodologies. Besides, the effectiveness of the metaheuristics are evaluated in comparison with a -constraint method. In detail, the algorithms are carried out on a set of benchmarks and are compared to test their efficiencies based on four performance metrics: number of non-dominated solutions, general distance, hypervolume and spacing. Finally, a case study of a real project further indicates that the suggested model and algorithms are applicable and beneficial to the problem in practice.

Joint optimization of maintenance planning and workforce routing for a geographically distributed networked infrastructure

It is paramount to perform timely and appropriate maintenance actions on networked infrastructures, such as power transmission, transportation, telecommunications, and so forth, in order to ensure their reliability in satisfying the prescribed demand required by the economic development and social well-being of a society. For this purpose, the time of travelling between the components to be maintained needs to be considered, as the components of a real-world infrastructure are usually geographically widely distributed. To address this problem, we propose a holistic bi-objective optimization approach for the joint optimization of maintenance planning and workforce routing for a networked infrastructure, in order to determine a practical maintenance plan that can simultaneously maximize its reliability and minimize the incurred cost. To deal with the complexity of the proposed problem, we develop a Two-level Pareto Simulated Annealing algorithm to approximate the Pareto-optimal solutions of the proposed problem. Finally, two numerical examples are employed to illustrate the ability of the proposed approach in dealing with the maintenance optimization problem of a geographically distributed networked infrastructure.

An improved artificial immune system for seeking the Pareto front of land-use allocation problem in large areas

The Pareto front can provide valuable information on land-use planning decision by revealing the possible trade-offs among multiple, conflicting objectives. However, seeking the Pareto front of land-use allocation is much more difficult than finding a unique optimal solution, especially when dealing with large-area regions. This article proposes an improved artificial immune system for multi-objective land-use allocation (AIS-MOLA) to tackle this challenging task. The proposed AIS is equipped with three modified operators, namely (1) a heuristic hypermutation based on compromise programming, (2) a non-dominated neighbour-based proportional cloning and (3) a novel crossover operator that preserves connected patches. To validate the proposed algorithm, it was applied in a hypothetical land-use allocation problem. Compared with the Pareto Simulated Annealing (PSA) method, AIS-MOLA can generate solutions more approximate to the Pareto front, with computation time amounting to only 5.1% of PSA. In addition, AIS-MOLA was also applied in the case study of Panyu, Guangdong, PR China, a large area with cells. Experimental results indicate that this algorithm, even dealing with large-area land-use allocation problems, is capable of generating optimal alternative solutions approximate to the true Pareto front. Moreover, the distribution of these solutions can quantitatively demonstrate the complex trade-offs between the spatial suitability and the compactness in the study area. Software and supplementary materials are available at http://www.geosimulation.cn/AIS-MOLA/.

Pareto simulated annealing for the design of experiments: illustrated by a gene expression study

Abstract Experimental design is concerned with the problem of allocating resources within an experiment to ensure that objectives of the experiment are achieved at the minimum cost. This paper focuses on the generation of optimal or near-optimal designs for large and complex experiments where it is infeasible to carry out an ex- haustive search of the design space. Optimal designs for gene expression studies, aimed at investigating the behaviour of genes, are considered, where the optimality criterion employed is Pareto optimality. We develop an adaptation of the metaheuris- tic method of Pareto simulated annealing to generate an approximation to the set of Pareto optimal designs for large and complex experiments. We develop algorithms that utilise response surface methodology to search systematically for the optimal values of parameters associated with Pareto simulated annealing and performance is evaluated using quality measures.

A Simulated Annealing-based parallel multi-objective approach to vehicle routing problems with time windows

The Capacitated Vehicle Routing Problem with Time Windows (VRPTW) consists in determining the routes of a given number of vehicles with identical capacity stationed at a central depot which are used to supply the demands of a set of customers within certain time windows. This is a complex multi-constrained problem with industrial, economic, and environmental implications that has been widely analyzed in the past. This paper deals with a multi-objective variant of the VRPTW that simultaneously minimizes the travelled distance and the imbalance of the routes. This imbalance is analyzed from two perspectives: the imbalance in the distances travelled by the vehicles, and the imbalance in the loads delivered by them. A multi-objective procedure based on Simulated Annealing, the Multiple Temperature Pareto Simulated Annealing (MT-PSA), is proposed in this paper to cope with these multi-objective formulations of the VRPTW. The procedure MT-PSA and an island-based parallel version of MT-PSA have been evaluated and compared with, respectively, sequential and island-based parallel implementations of SPEA2. Computational results obtained on Solomon’s benchmark problems show that the island-based parallelization produces Pareto-fronts of higher quality that those obtained by the sequential versions without increasing the computational cost, while also producing significant reduction in the runtimes while maintaining solution quality. More specifically, for the most part, our procedure MT-PSA outperforms SPEA2 in the benchmarks here considered, with respect to the solution quality and execution time.

Decision-Theoretic Design Space Exploration of Multiprocessor Platforms

This paper presents an efficient technique to perform design space exploration of a multiprocessor platform that minimizes the number of simulations needed to identify a Pareto curve with metrics like energy and delay. Instead of using semi-random search algorithms (like simulated annealing, tabu search, genetic algorithms, etc.), we use the domain knowledge derived from the platform architecture to set-up the exploration as a discrete-space <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Markov decision process</i> . The system walks the design space changing its parameters, performing simulations only when probabilistic information becomes insufficient for a decision. A learning algorithm updates the probabilities of decision outcomes as simulations are performed. The proposed technique has been tested with two multimedia industrial applications, namely the ffmpeg transcoder and the parallel pigz compression algorithm. Results show that the exploration can be performed with 5% of the simulations necessary for the most used algorithms (Pareto simulated annealing, nondominated sorting genetic algorithm, etc.), increasing the exploration speed by more than one order of magnitude.

Pareto simulated annealing and colonial competitive algorithm to solve an offline scheduling problem with rejection

The present paper considers the problem of scheduling a set of jobs where some jobs may be rejected. The objective function consists of minimizing two criteria simultaneously: the sum of the weighted completion times of the accepted jobs and the sum of the rejection costs. Although the characteristics of this problem have been discussed in the literature, no solution algorithm has yet been proposed. Herein, solution algorithms are developed using two meta-heuristic methods: Pareto simulated annealing (PSA), a multiple-objective optimization approach; and colonial competitive algorithm (CCA), a novel method which is adopted for the first time in a discrete multiple-objective optimization problem. Computational testing illustrates the practicality of both algorithms to find a good estimation of the Pareto optimal set. The quality of the proposed algorithms are evaluated and compared by some available performance measures and a new measure introduced in the paper. The comparative results show that CCA offers better estimation of the Pareto optimal set than PSA.

Theoretical aspects of multicriteria flight gate scheduling: deterministic and fuzzy models

This paper addresses the airport flight gate scheduling problem with multiple objectives. The objectives are to maximize the total flight gate preferences, to minimize the number of towing activities, and to minimize the absolute deviation of the new gate assignment from a so-called reference schedule. The problem examined is a multicriteria multi-mode resource-constrained project scheduling problem with generalized precedence constraints or time windows. While in previous approaches the problem has been simplified to a single objective counterpart, we tackle it directly by a multicriteria metaheuristic, namely Pareto Simulated Annealing, in order to get a representative approximation of the Pareto front. Possible uncertainty of input data is treated by means of fuzzy numbers.

Optimal Design of Gravity-Fed Looped Water Distribution Networks Considering the Resilience Index

The optimization of looped water distribution networks (WDN) implies achieving the best tradeoff between reliability and cost. Many works have dealt with minimizing the cost, but few have considered both cost and reliability. This paper aims to evaluate the performance of several multiobjective metaheuristics (MOMHs) to optimize the design of looped water distribution networks, taking into consideration two objective functions: Minimizing costs and maximizing the resilience index. The MOMHs used are: Strength Pareto Evolutionary Algorithm 2 (SPEA2), Pareto Archived Evolution Strategy, Pareto Envelope-based Selection Algorithm, Pareto Simulated Annealing, and Multiobjective Simulated Annealing and Tabu Search. These algorithms are tested and compared by applying them to two case studies: The first is a small well-known benchmark network (Hanoi), whereas the second one is a larger looped irrigation network (Balerma). Results of this work show that SPEA2 outperforms the remaining methods in terms of Pareto d...

Multicriteria airport gate assignment and Pareto simulated annealing

This paper addresses an airport gate assignment problem with multiple objectives. The objectives are to minimize the number of ungated flights and the total passenger walking distances or connection times as well as to maximize the total gate assignment preferences. The problem examined is an integer program with multiple objectives (one of them being quadratic) and quadratic constraints. Of course, such a problem is inherently difficult to solve. We tackle the problem by Pareto simulated annealing in order to get a representative approximation for the Pareto front. Results of computational experiments are presented. To the best of our knowledge, this is the first attempt to consider the airport gate assignment problem with multiple objectives.

Metamodeling by symbolic regression and Pareto simulated annealing

The subject of this paper is a new approach to symbolic regression. Other publications on symbolic regression use genetic programming. This paper describes an alternative method based on Pareto simulated annealing. Our method is based on linear regression for the estimation of constants. Interval arithmetic is applied to ensure the consistency of a model. To prevent overfitting, we merit a model not only on predictions in the data points, but also on the complexity of a model. For the complexity, we introduce a new measure. We compare our new method with the Kriging metamodel and against a symbolic regression metamodel based on genetic programming. We conclude that Pareto-simulated-annealing-based symbolic regression is very competitive compared to the other metamodel approaches.

Efficient architecture/compiler co-exploration using analytical models

The hardware/software co-exploration is a critical phase for a broad range of embedded platforms based on the System-On-Chip approach. Traditionally, the compilation and the architectural design sub-spaces have been explored independently. Only recently, some approaches have analyzed the problem of the concurrent exploration of the compilation/architecture sub-spaces. This paper proposes a framework to support the co-exploration phase of the design space composed of architectural parameters and source program transformations. The objective space is multi-dimensional, including conflicting objectives such as energy and delay. In the proposed framework, heuristic co-exploration techniques based on Pareto Simulated Annealing (PSA) have been used to efficiently explore the architecture/compiler co-design space. A first result of this paper consists of showing how the architecture/compiler co-exploration can be more effective than a traditional two-phase exploration. Since the co-exploration space is quite large, to speed up the co-exploration phase by several orders of magnitude over simulation-based approaches, a methodology based on analytical models has been introduced in the co-exploration framework. The goal of analytical models is to quickly evaluate energy/delay metrics at the systems level, while maintaining accuracy with respect to simulation-based co-exploration. The proposed co-exploration framework has been applied to a parameterized SoC superscalar architecture during the execution of a selected set of multimedia applications.

Knowledge-informed Pareto simulated annealing for multi-objective spatial allocation

Spatial allocation is the process of assigning different attributes (e.g., land-use or land-cover) to spatial entities (e.g., map polygons or grid cells). It is an exercise that often requires the analysis of multiple, sometimes conflicting, objectives. Multi-objective spatial allocation problems often exhibit substantial computational complexity, especially when spatial pattern characteristics are specified as the allocation objectives. Optimization techniques that incorporate heuristics or knowledge-informed rules have been found to be more effective in solving spatial allocation problem. In this article, we (1) develop and demonstrate a knowledge-informed Pareto simulated annealing approach to tackle specifically multi-objective allocation problems that consider spatial patterns as objectives and (2) determine whether the knowledge-informed approach is more effective than standard Pareto simulation annealing in solving multi-objective spatial allocation problems. Four multi-objective spatial allocation problems were formulated in a gridded two-dimensional discrete space to benchmark the performance of our knowledge-informed algorithms and a standard Pareto simulated annealing algorithm. These four problems, each with two objectives, represent all combinations of cases in which there are (1) conflicting or concordant objectives and (2) two pattern objectives or one pattern objective and one non-pattern objective, representing objectives with similar or different degrees of difficulty. We generated 1200 sets of solutions, represented as allocation maps. Performance indices that measure the computational effectiveness and efficiency were developed for evaluation. The results suggest that the solutions generated by the knowledge-informed approach are more effective in approximating the set of Pareto optimal solutions than those generated by the standard Pareto simulated annealing.

PETRI NET BASED MODEL FOR JOB SHOP SCHEDULING PROBLEM IN GREEN MANUFACTURING AND ITS HYBRID METAHEURISTIC SEARCH

Job shop scheduling problem in green manufacturing not only aims to minimize the makespan and process cost, but also to decrease consumption of resource and negative effects on the environment. A Perti net model whose transitions are endowed with process time, process cost, resource consumption and negative effects on the environment is developed. The conflicts, which are caused by jobs sharing the same machine places in the model, are eliminated by arranging machining order for different jobs, and then a marked graph that stands for a feasible scheduling is derived. Three methods are proposed to produce a marked graph of feasible scheduling from another. A hybrid multi-objective heuristic which ingrates Mu-rata's Multi-objective genetic algorithm and Czyzak's Pareto simulated annealing algorithm is used to optimize the feasible scheduling. Numerical simulation demonstrates that the proposed heuristic is feasible and effective.

Parallelization of population-based multi-objective meta-heuristics: An empirical study

In single-objective optimization it is possible to find a global optimum, while in the multi-objective case no optimal solution is clearly defined, but several that simultaneously optimize all the objectives. However, the majority of this kind of problems cannot be solved exactly as they have very large and highly complex search spaces. Recently, meta-heuristic approaches have become important tools for solving multi-objective problems encountered in industry as well as in the theoretical field. Most of these meta-heuristics use a population of solutions, and hence the runtime increases when the population size grows. An interesting way to overcome this problem is to apply parallel processing. This paper analyzes the performance of several parallel paradigms in the context of population-based multi-objective meta-heuristics. In particular, we evaluate four alternative parallelizations of the Pareto simulated annealing algorithm, in terms of quality of the solutions, and speedup.

PARETO SIMULATED ANNEALING (SA)-BASED MULTI-OBJECTIVE OPTIMIZATION FOR MEMS DESIGN AND APPLICATION

In this paper we present a global optimization method for multiple objective functions using the Pareto Simulated Annealing (SA). This novel optimization method is very useful and promising for design and application in the field of Micro-Electro-Mechanical Systems (MEMS). Previously published global optimization method has been reported by us for only single objective function. The proposed method automatically assigns different objective weights to each objective functions so that it can generate multiple solutions simultaneously. It also offers the trade-off between the objective functions so that we will be able to select the most suitable solution for MEMS design and applications. Based on the global Pareto ranking of the solutions, the optimization method can provide the best solution (the first Pareto ranking) as well.