Constrained Multiobjective Biogeography Optimization Algorithm

Multiobjective optimization involves minimizing or maximizing multiple objective functions subject to a set of constraints. In this study, a novel constrained multiobjective biogeography optimization algorithm (CMBOA) is proposed. It is the first biogeography optimization algorithm for constrained multiobjective optimization. In CMBOA, a disturbance migration operator is designed to generate diverse feasible individuals in order to promote the diversity of individuals on Pareto front. Infeasible individuals nearby feasible region are evolved to feasibility by recombining with their nearest nondominated feasible individuals. The convergence of CMBOA is proved by using probability theory. The performance of CMBOA is evaluated on a set of 6 benchmark problems and experimental results show that the CMBOA performs better than or similar to the classical NSGA-II and IS-MOEA

Evolutionary Alternating Direction Method of Multipliers for Constrained Multi-Objective Optimization with Unknown Constraints

Constrained multi-objective optimization problems (CMOPs) pervade real-world applications in science, engineering, and design. Constraint violation has been a building block in designing evolutionary multi-objective optimization algorithms for solving constrained multi-objective optimization problems. However, in certain scenarios, constraint functions might be unknown or inadequately defined, making constraint violation unattainable and potentially misleading for conventional constrained evolutionary multi-objective optimization algorithms. To address this issue, we present the first of its kind evolutionary optimization framework, inspired by the principles of the alternating direction method of multipliers that decouples objective and constraint functions. This framework tackles CMOPs with unknown constraints by reformulating the original problem into an additive form of two subproblems, each of which is allotted a dedicated evolutionary population. Notably, these two populations operate towards complementary evolutionary directions during their optimization processes. In order to minimize discrepancy, their evolutionary directions alternate, aiding the discovery of feasible solutions. Comparative experiments conducted against five state-of-the-art constrained evolutionary multi-objective optimization algorithms, on 120 benchmark test problem instances with varying properties, as well as two real-world engineering optimization problems, demonstrate the effectiveness and superiority of our proposed framework. Its salient features include faster convergence and enhanced resilience to various Pareto front shapes.Comment: 29 pages, 17 figure

Multiobjective particle swarm optimization: Integration of dynamic population and multiple-swarm concepts and constraint handling

Scope and Method of Study: Over the years, most multiobjective particle swarm optimization (MOPSO) algorithms are developed to effectively and efficiently solve unconstrained multiobjective optimization problems (MOPs). However, in the real world application, many optimization problems involve a set of constraints (functions). In this study, the first research goal is to develop state-of-the-art MOPSOs that incorporated the dynamic population size and multipleswarm concepts to exploit possible improvement in efficiency and performance of existing MOPSOs in solving the unconstrained MOPs. The proposed MOPSOs are designed in two different perspectives: 1) dynamic population size of multiple-swarm MOPSO (DMOPSO) integrates the dynamic swarm population size with a fixed number of swarms and other strategies to support the concepts; and 2) dynamic multiple swarms in multiobjective particle swarm optimization (DSMOPSO), dynamic swarm strategy is incorporated wherein the number of swarms with a fixed swarm size is dynamically adjusted during the search process. The second research goal is to develop a MOPSO with design elements that utilize the PSO's key mechanisms to effectively solve for constrained multiobjective optimization problems (CMOPs).Findings and Conclusions: DMOPSO shows competitive to selected MOPSOs in producing well approximated Pareto front with improved diversity and convergence, as well as able to contribute reduced computational cost while DSMOPSO shows competitive results in producing well extended, uniformly distributed, and near optimum Pareto fronts, with reduced computational cost for some selected benchmark functions. Sensitivity analysis is conducted to study the impact of the tuning parameters on the performance of DSMOPSO and to provide recommendation on parameter settings. For the proposed constrained MOPSO, simulation results indicate that it is highly competitive in solving the constrained benchmark problems

A multi-stage algorithm for solving multi-objective optimization problems with multi-constraints

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.There are usually multiple constraints in constrained multi-objective optimization. Those constraints reduce the feasible area of the constrained multi-objective optimization problems (CMOPs) and make it difficult for current multi-objective optimization algorithms (CMOEAs) to obtain satisfactory feasible solutions. In order to solve this problem, this paper studies the relationship between constraints, then obtains the priority between constraints according to the relationship between the Pareto Front (PF) of the single constraint and their common PF. Meanwhile, this paper proposes a multi-stage CMOEA and applies this priority, which can save computing resources while helping the algorithm converge. The proposed algorithm completely abandons the feasibility in the early stage to better explore the objective space, and obtains the priority of constraints according to the relationship; Then the algorithm evaluates a single constraint in the medium stage to further explore the objective space according to this priority, and abandons the evaluation of some less-important constraints according to the relationship to save the evaluation times; At the end stage of the algorithm, the feasibility will be fully considered to improve the quality of the solutions obtained in the first two stages, and finally get the solutions with good convergence, feasibility, and diversity. The results on five CMOP suites and three real-world CMOPs show that the algorithm proposed in this paper can have strong competitiveness in existing constrained multi-objective optimization

Multiobjective differential evolution based on fuzzy performance feedback: Soft constraint handling and its application in antenna designs

The recently emerging Differential Evolution is considered one of the most powerful tools for solving optimization problems. It is a stochastic population-based search approach for optimization over the continuous space. The main advantages of differential evolution are simplicity, robustness and high speed of convergence. Differential evolution is attractive to researchers all over the world as evidenced by recent publications. There are many variants of differential evolution proposed by researchers and differential evolution algorithms are continuously improved in its performance. Performance of differential evolution algorithms depend on the control parameters setting which are problem dependent and time-consuming task. This study proposed a Fuzzy-based Multiobjective Differential Evolution (FMDE) that exploits three performance metrics, specifically hypervolume, spacing, and maximum spread, to measure the state of the evolution process. We apply the fuzzy inference rules to these metrics in order to adaptively adjust the associated control parameters of the chosen mutation strategy used in this algorithm. The proposed FMDE is evaluated on the well known ZDT, DTLZ, and WFG benchmark test suites. The experimental results show that FMDE is competitive with respect to the chosen state-of-the-art multiobjective evolutionary algorithms. The advanced version of FMDE with adaptive crossover rate (AFMDE) is proposed. The proof of concept AFMDE is then applied specifically to the designs of microstrip antenna array. Furthermore, the soft constraint handling technique incorporates with AFMDE is proposed. Soft constraint AFMDE is evaluated on the benchmark constrained problems. AFMDE with soft constraint handling technique is applied to the constrained non-uniform circular antenna array design problem as a case study

Approaching Sustainability in Engineering Design with Multiple Criteria Decision Analysis

This research aimed to the establishment of a general methodological framework, via which the "fuzzy" and "debatable" goal of sustainability can be practically achieved in engineering design. In-depth literature review on the sustainability concept was first conducted in an attempt to grasp its philosophical essence from various interpretations and distinct implementations. The application of the proposed framework was addressed by developing or identifying specific building block techniques, each of which accomplish a different task, such as criteria-attribute mapping, preference modeling, and search. The proposed building block techniques were selected based on systematic comparisons among a wide range of alternative methods and tested by case studies or test problems. Sustainability is a multiplex property of an integrated system. The key to make a reality of sustainability in engineering design is to properly handle its complex nature and deeply rooted conflicts. In this work, Multiple Criteria Decision Analysis (MCDA) was proven ideal for filling the vacuum of a general operational framework. To implement this framework, a four-step procedure needs to be first performed to formulate a sustainability-oriented design into a "standard" Multiple Criteria Decision Making (MCDM) problem. The proposed attribute hierarchy "Stressor-Status-Effect-Integrality-Well-being" and the 4-class metric classification scheme could help engineers to accomplish such a task in the environmental dimension. The achievement of the final "sustainable" design relies on making appropriate decisions. A MAVT-based technique developed in this study provides a rational and informed way of solving the decision problems with a discrete set of explicitly known alternatives. For Multi-Objective Programming (MOP) problems featuring an infinite and implicitly characterized alternative space, the proposed Ordinal Ranking-based Genetic Algorithm (ORGA) offers a desired searching tool by generating uniformly sampled solutions that are feasible and globally Pareto optimal.School of Chemical Engineerin

Decomposition strategies for large scale multi depot vehicle routing problems

Das Umfeld in der heutigen Wirtschaft verlangt nach immer bessern Ansätzen, um Transportprobleme möglichst effizient zu lösen. Die Klasse der ”Vehicle Routing Problems” (VRP) beschäftigt sich speziell mit der Optimierung von Tourenplanungsproblemen in dem ein Service-Leister seine Kunden möglichst effizient beliefern muss. Eine der VRP-Varianten ist das ”Multi Depot Vehicle Routing Problem with Time Windows” (MDVRPTW), in dem Kunden von verschiedenen Depots in einem fix vorgegebenen Zeitintervall beliefert beliefert werden müssen. Das MDVRPTW ist im realen Leben dank seiner realitätsnahen Restriktionen sehr oft vertreten. Typische Transportprobleme, wie sie in der Wirklichkeit auftreten, sind jedoch oftmals so groß, dass sie von optimalen Lösungsansätzen nicht zufriedenstellend gelöst werden können. In der vorliegenden Dissertation werden zwei Lösungsansätze präsentiert, wie diese riesigen, realitätsnahen Probleme zufriedenstellend bewältigt werden können. Beide Ansätze benutzen die POPMUSIC Grundstruktur, um das Problem möglichst intelligent zu dekomponieren. Die Dekomponierten und damit kleineren Subprobleme können dann von speziell entwickelten Algorithmen effizienter bearbeitet und letztendlich gelöst werden. Mit dem ersten Ansatz präsentieren wir eine Möglichkeit Transportprobleme zu dekomponieren, wenn populationsbasierte Algorithmen als Problemlöser eingesetzt werden. Dazu wurde ein maßgeschneiderter Memetischer Algorithmus (MA) entwickelt und in das Dekompositionsgerüst eingebaut um ein reales Problem eines österreichischen Transportunternehmens zu lösen. Wir zeigen, dass die Dekomponierung und Optimierung der resultierenden Subprobleme, im Vergleich zu den Ergebnissen des MA ohne Dekomposition, eine Verbesserung der Zielfunktion von rund 20% ermöglicht. Der zweite Ansatz beschäftigt sich mit der Entwicklung einer Dekomponierungsmethode für Lösungsalgorithmen, die nur an einer einzigen Lösung arbeiten. Es wurde ein ”Variable Neigborhood Search” (VNS) als Optimierer in das POPMUSIC Grundgerüst implementiert, um an das vorhandene Echtwelt-Problem heranzugehen. Wir zeigen, dass dieser Ansatz rund 7% bessere Ergebnisse liefert als der pure VNS Lösungsansatz. Außerdem präsentieren wir Ergebnisse des VNS Dekompositionsansatzes die um rund 6% besser sind als die des MA Dekompositionsansatzes. Ein weiterer Beitrag dieser Arbeit ist das Vorstellen von zwei komplett verschiedenen Ansätzen um das Problem in kleinere Sub-Probleme zu zerteilen. Dazu wurden acht verschiedene Nähe-Maße definiert und betrachtet. Es wurde der 2,3 und 4 Depot Fall getestet und im Detail analysiert. Die Ergebnisse werden präsentiert und wir stellen einen eindeutigen Gewinner vor, der alle Testinstanzen am Besten lösen konnte. Wir weisen auch darauf hin, wie einfach die POPMUSIC Dekomponierung an reale Bedürfnisse, wie zum Beispiel eine möglichst schnelle Ergebnisgenerierung, angepasst werden kann. Wir zeigen damit, dass die vorgestellten Dekomponierungsstrategien sehr effizient und flexibel sind, wenn Transportprobleme, wie sie in der realen Welt vorkommen gelöst werden müssen.The optimization of transportation activities is of high importance for companies in today’s economy. The Vehicle Routing Problem (VRP) class is dealing with the routing of vehicles so that the customer base of a company can be served in the most efficient way. One of the many variants in the VRP class is the Multi Depot Vehicle Routing Problem with Time Windows (MDVRPTW) which extends the VRP by additional depots from which customers can be served, as well as an individual time window for each customer in which he is allowed to be served. Modern carrier fleet operators often encounter these MDVRPTW in the real world, and usually they are of very large size so that exact approaches cannot solve them efficiently. This thesis presents two different approaches how this real world large scale MDVRPTWs can be solved. Both approaches are based on the POPMUSIC framework, which intelligently tries to decompose the large scale problem into much smaller sub-problems. The resulting sub-problems can then be solved more efficiently by specialized optimizers. The first approach in this thesis was developed for population based optimizers. A Memetic Algorithm (MA) was developed and used as an optimizer in the framework to solve a real world MDVPRTW from an Austrian carrier fleet operator. We show that decomposing the complete problem and solving the resulting sub-problems improves the solution quality by around 20% compared to using the MA without any decomposition. The second approach specially focuses on decomposition strategies for single solution methods. More precisely, a Variable Neighborhood Search (VNS) was implemented in the POPMUSIC framework to solve the real world instances. We show that decomposing the problem can yield improvements of around 7% compared to using the pure VNS method. Compared to the POPMUSIC MA approach the second approach can further improve the solution quality by around 6%. Another contribution in this thesis is the development of two generally different ways to measure proximity when creating sub-problems. In detail we tested eight different proximity measures and analyzed how good they decompose the problem in different environments. We tested the two, three and four depot case and present a clear winner that can outperform all other measures. Further we demonstrate that the POPMUSIC approach can flexibly be adjusted to real world demands, like a faster solution finding process, while at the same time maintaining high quality solutions. We show that a decomposition strategies combined with state of the art metaheuristic solvers are a very efficient and flexible tool to tackle real world problems with regards to solution quality as well as runtime

Type-2 Fuzzy Single and Multi-Objective Optimisation Systems for Telecommunication Capacity Planning

Capacity planning in the telecommunications industry aims to maximise the effectiveness of implemented bandwidth equipment whilst allowing for equipment to be upgraded without a loss of service. The better implemented hardware can be configured, the better the service provided to the consumers can be. Additionally, the easier it is to rearrange that existing hardware with minimum loss of service to the consumer, the easier it is to remove older equipment and replace it with newer more effect equipment. The newer equipment can provide more bandwidth whilst consuming less power and producing less heat, lowering the overall operating costs and carbon footprint of a large scale network. Resilient routing is the idea of providing multiple independent non-intersecting routes between two locations within a graph. For telecommunications organisations this can be used to reduce the downtime faced by consumers if there is a fault within a network. It can also be used to provide assurances to customers that rely on a network connection such as: financial institutions or government agencies. This thesis looks at capacity planning within telecommunications with the aspiration of creating a set of optimisation systems that can rearrange data exchange hardware to maximise their performance with minimal cost and minimising downtime while allowing adaptations to an exchange’s configuration in order to perform upgrades. The proposed systems were developed with data from British Telecom (BT) and are either deployed or are planned to be in the near future. In many cases the data used is confidential, but when this is the case an equivalent open source data set has been used for transparency. As a result of this thesis the Heated Stack (HS) algorithm was created which has been shown to outperform the popular and successful NSGA-II algorithm by up to 92 % and NSGA-III by up to 69% at general optimisation tasks. HS also outperforms NSGA-II in 100% of the physical capacity planning experiments run and NSGA-II in 68% of the physical capacity planning experiments run. Additionally, as a result of this thesis the N-Non-Intersecting-Routing algorithm was shown to outperform Dijkstra’s algorithm by up to 38% at resilient routing. Finally, a new method of performing configuration planning through backwards induction with Monte Carlo Tree Search was proposed

A new three phase method (SDP method) for the multi-objective vehicle routing problem with simultaneous delivery and pickup (VRPSDP)

Transportation service operators are witnessing a growing demand for bi-directional movement of goods. Given this, the following thesis considers an extension to the vehicle routing problem (VRP) known as the delivery and pickup transportation problem (DPP), where delivery and pickup demands may occupy the same route. The problem is formulated here as the vehicle routing problem with simultaneous delivery and pickup (VRPSDP), which requires the concurrent service of the demands at the customer location. This formulation provides the greatest opportunity for cost savings for both the service provider and recipient. The aims of this research are to propose a new theoretical design to solve the multi-objective VRPSDP, provide software support for the suggested design and validate the method through a set of experiments. A new real-life based multi-objective VRPSDP is studied here, which requires the minimisation of the often conflicting objectives: operated vehicle fleet size, total routing distance and the maximum variation between route distances (workload variation). The former two objectives are commonly encountered in the domain and the latter is introduced here because it is essential for real-life routing problems. The VRPSDP is defined as a hard combinatorial optimisation problem, therefore an approximation method, Simultaneous Delivery and Pickup method (SDPmethod) is proposed to solve it. The SDPmethod consists of three phases. The first phase constructs a set of diverse partial solutions, where one is expected to form part of the near-optimal solution. The second phase determines assignment possibilities for each sub-problem. The third phase solves the sub-problems using a parallel genetic algorithm. The suggested genetic algorithm is improved by the introduction of a set of tools: genetic operator switching mechanism via diversity thresholds, accuracy analysis tool and a new fitness evaluation mechanism. This three phase method is proposed to address the shortcoming that exists in the domain, where an initial solution is built only then to be completely dismantled and redesigned in the optimisation phase. In addition, a new routing heuristic, RouteAlg, is proposed to solve the VRPSDP sub-problem, the travelling salesman problem with simultaneous delivery and pickup (TSPSDP). The experimental studies are conducted using the well known benchmark Salhi and Nagy (1999) test problems, where the SDPmethod and RouteAlg solutions are compared with the prominent works in the VRPSDP domain. The SDPmethod has demonstrated to be an effective method for solving the multi-objective VRPSDP and the RouteAlg for the TSPSDP