Benchmark Multi-objective Optimization Research Articles

A multiagent, dynamic rank-driven multi-deme architecture for real-valued multiobjective optimization

Multiobjective real parameter optimization is a challenging problem in majority of engineering applications. This paper presents a creative multiagent and dynamic multi-deme architecture based on a novel collaboration mechanism for the solution of multiobjective real-parameter optimization problems. The proposed architecture comprises a number of multiobjective metaheuristic agents that act on subsets of a population based on a cyclic assignment order. The proposed multiagent architecture works iteratively in sessions including two consecutive phases: in the first phase, a population of solutions is divided into subpopulations based on dominance ranks of its elements. In the second phase, each multiobjective metaheuristic is assigned to work on a subpopulation based on a cyclic or round-robin order. Hence, each metaheuristic operates on a different-rank subpopulation in subsequent sessions, where a session starts with a new assignment of metaheuristics and ends when termination criteria for the session are satisfied. Individual agents have their local archives of non-dominated solutions extracted in a session, while there is a global archive keeping all non-dominated solutions found so far. At the end of each session, all subpopulations are combined into one global population to be used for the initialization of the next session. Similarly, all local archives are merged with the global archive to get the set of all non-dominated solutions found by all metaheuristics through working on subsets of different rank-levels. This way, the metaheuristics cooperate with each other by sharing their search experiences through collecting them in a common population and a common global archive. The proposed multiagent system is experimentally evaluated using the well-known CEC2009 multiobjective optimization benchmark problems set. Analysis of the experimental results demonstrated that the proposed architecture achieves better performance compared to majority of its state-of-the-art competitors in almost all problem instances.

A preference-based multi-objective evolutionary algorithm R-NSGA-II with stochastic local search

Incorporation of a decision maker’s preferences into multi-objective evolutionary algorithms has become a relevant trend during the last decade, and several preference-based evolutionary algorithms have been proposed in the literature. Our research is focused on improvement of a well-known preference-based evolutionary algorithm R-NSGA-II by incorporating a local search strategy based on a single agent stochastic approach. The proposed memetic algorithm has been experimentally evaluated by solving a set of well-known multi-objective optimization benchmark problems. It has been experimentally shown that incorporation of the local search strategy has a positive impact to the quality of the algorithm in the sense of the precision and distribution evenness of approximation.

Universal partially evolved parallelization of MOEA/D for multi-objective optimization on message-passing clusters

This paper presents a universal partially evolved parallelization of the multi-objective evolutionary algorithm based on decomposition (MOEA/D) for multi-objective optimization on message-passing clusters to reduce its computation time. The partially evolved MOEA/D (peMOEA/D) is suitable not only for the bi-objective space, but also for higher dimensional objective spaces by using a partially evolved island model. This model improves the algorithm universality and population diversity by keeping a subpopulation equal in size to the entire population, but only evolving a partial (equal to a partition size) subpopulation on each separate processor in a cluster. Furthermore, a nearest-neighbor partitioning approach, hybrid migration policy and adaptive neighbor-based topology are adopted in the peMOEA/D. The fat partitions generated by the nearest-neighbor partitioning can reduce migration traffic of elitist individuals across subpopulations. Then, hybrid migration of both elitist individuals and utopian points helps separate subpopulations to cooperate in guiding the search quickly towards a complete front. Next, the adaptive neighbor-based topology connects neighbor partitions only and achieves an excellent balance between convergence speed and migration traffic. Experimental results on benchmark multi-objective optimization problems with two or more objectives demonstrate the satisfactory overall performance of the peMOEA/D in terms of both convergence performance and speedup on message-passing clusters.

An anchorage planning strategy with safety and utilization considerations

Heavy maritime traffic and the subsequent increase in vessel density in anchorages have recently become a focal issue in maritime traffic safety. In this study, we consider the problem of determining the optimal berth locations of incoming vessels in an anchorage area with the goals of maximizing utilization and minimizing the risk of accidents. We introduce novel performance metrics aimed at measuring achievement of these two goals. In this context, we propose a multi-objective optimization strategy and benchmark it against current state-of-the-art anchorage planning algorithms using real-world data as well as Monte Carlo simulations. Our results indicate that the proposed strategy yields much safer berth locations while maintaining similar utilization levels.

Choice function based hyper-heuristics for multi-objective optimization

A selection hyper-heuristic is a high level search methodology which operates over a fixed set of low level heuristics. During the iterative search process, a heuristic is selected and applied to a candidate solution in hand, producing a new solution which is then accepted or rejected at each step. Selection hyper-heuristics have been increasingly, and successfully, applied to single-objective optimization problems, while work on multi-objective selection hyper-heuristics is limited. This work presents one of the initial studies on selection hyper-heuristics combining a choice function heuristic selection methodology with great deluge and late acceptance as non-deterministic move acceptance methods for multi-objective optimization. A well-known hypervolume metric is integrated into the move acceptance methods to enable the approaches to deal with multi-objective problems. The performance of the proposed hyper-heuristics is investigated on the Walking Fish Group test suite which is a common benchmark for multi-objective optimization. Additionally, they are applied to the vehicle crashworthiness design problem as a real-world multi-objective problem. The experimental results demonstrate the effectiveness of the non-deterministic move acceptance, particularly great deluge when used as a component of a choice function based selection hyper-heuristic.

A Simple and Fast Hypervolume Indicator-Based Multiobjective Evolutionary Algorithm.

To find diversified solutions converging to true Pareto fronts (PFs), hypervolume (HV) indicator-based algorithms have been established as effective approaches in multiobjective evolutionary algorithms (MOEAs). However, the bottleneck of HV indicator-based MOEAs is the high time complexity for measuring the exact HV contributions of different solutions. To cope with this problem, in this paper, a simple and fast hypervolume indicator-based MOEA (FV-MOEA) is proposed to quickly update the exact HV contributions of different solutions. The core idea of FV-MOEA is that the HV contribution of a solution is only associated with partial solutions rather than the whole solution set. Thus, the time cost of FV-MOEA can be greatly reduced by deleting irrelevant solutions. Experimental studies on 44 benchmark multiobjective optimization problems with 2-5 objectives in platform jMetal demonstrate that FV-MOEA not only reports higher hypervolumes than the five classical MOEAs (nondominated sorting genetic algorithm II (NSGAII), strength Pareto evolutionary algorithm 2 (SPEA2), multiobjective evolutionary algorithm based on decomposition (MOEA/D), indicator-based evolutionary algorithm, and S-metric selection based evolutionary multiobjective optimization algorithm (SMS-EMOA)), but also obtains significant speedup compared to other HV indicator-based MOEAs.

Multiobjective nondominated neighbor coevolutionary algorithm with elite population

A nondominated neighbor coevolutionary algorithm (NNCA) with a novel coevolutionary mechanism is proposed for multiobjective optimization, where elite individuals are used to guide the search. All the nondominated individuals are divided into two subpopulations, namely, the elite population and the common population according to their crowding-distance values. The elite individual located in less-crowded region will have more chances to select more team members for its own team and thus this region can be explored more sufficiently. Therefore, the elite population will guide the search to the more promising and less-crowded region. Secondly, to avoid the `search stagnation' situation which means that algorithms fail to find enough nondominated solutions, a size guarantee mechanism (SGM) is proposed for elite population by emigrating some dominated individuals to the elite population when necessary. The SGM can prevent the algorithm from searching around limited nondominated individuals and being trapped into the `search stagnation' situation. In addition, several different kinds of crossover and mutation operator are used to generate offspring, which are benefits for the diversity property. Tests on 20 multiobjective optimization benchmark problems including five ZDT problems, five DTLZ problems and ten unconstrained CEC09 test problems show that NNCA is very competitive compared with seven the state-of-the-art multiobjective optimization algorithms.

A multi-objective hyper-heuristic based on choice function

Hyper-heuristics are emerging methodologies that perform a search over the space of heuristics in an attempt to solve difficult computational optimization problems. We present a learning selection choice function based hyper-heuristic to solve multi-objective optimization problems. This high level approach controls and combines the strengths of three well-known multi-objective evolutionary algorithms (i.e. NSGAII, SPEA2 and MOGA), utilizing them as the low level heuristics. The performance of the proposed learning hyper-heuristic is investigated on the Walking Fish Group test suite which is a common benchmark for multi-objective optimization. Additionally, the proposed hyper-heuristic is applied to the vehicle crashworthiness design problem as a real-world multi-objective problem. The experimental results demonstrate the effectiveness of the hyper-heuristic approach when compared to the performance of each low level heuristic run on its own, as well as being compared to other approaches including an adaptive multi-method search, namely AMALGAM.

A preference multi-objective optimization based on adaptive rank clone and differential evolution

Evolutionary multi-objective optimization (EMO) algorithms have been used in various real-world applications. However, most of the Pareto domination based multi-objective optimization evolutionary algorithms are not suitable for many-objective optimization. Recently, EMO algorithm incorporated decision maker's preferences became a new trend for solving many-objective problems and showed a good performance. In this paper, we first use a new selection scheme and an adaptive rank based clone scheme to exploit the dynamic information of the online antibody population. Moreover, a special differential evolution (DE) scheme is combined with directional information by selecting parents for the DE calculation according to the ranks of individuals within a population. So the dominated solutions can learn the information of the non-dominated ones by using directional information. The proposed method has been extensively compared with two-archive algorithm, light beam search non-dominated sorting genetic algorithm II and preference rank immune memory clone selection algorithm over several benchmark multi-objective optimization problems with from two to ten objectives. The experimental results indicate that the proposed algorithm achieves competitive results.

A particle swarm optimizer for constrained multi-objective engineering design problems

This article presents a particle swarm optimizer (PSO) capable of handling constrained multi-objective optimization problems. The latter occur frequently in engineering design, especially when cost and performance are simultaneously optimized. The proposed algorithm combines the swarm intelligence fundamentals with elements from bio-inspired algorithms. A distinctive feature of the algorithm is the utilization of an arithmetic recombination operator, which allows interaction between non-dominated particles. Furthermore, there is no utilization of an external archive to store optimal solutions. The PSO algorithm is applied to multi-objective optimization benchmark problems and also to constrained multi-objective engineering design problems. The algorithmic effectiveness is demonstrated through comparisons of the PSO results with those obtained from other evolutionary optimization algorithms. The proposed particle swarm optimizer was able to perform in a very satisfactory manner in problems with multiple constraints and/or high dimensionality. Promising results were also obtained for a multi-objective engineering design problem with mixed variables.

Multi-objective optimization of water-using systems

Industrial water systems often allow efficient water uses via water reuse and/or recirculation. The design of the network layout connecting water-using processes is a complex problem which involves several criteria to optimize. Most of the time, this design is achieved using Water Pinch technology, optimizing the freshwater flow rate entering the system. This paper describes an approach that considers two criteria: (i) the minimization of freshwater consumption and (ii) the minimization of the infrastructure cost required to build the network. The optimization model considers water reuse between operations and wastewater treatment as the main mechanisms to reduce freshwater consumption. The model is solved using multi-objective distributed Q-learning (MDQL), a heuristic approach based on the exploitation of knowledge acquired during the search process. MDQL has been previously tested on several multi-objective optimization benchmark problems with promising results [C. Mariano, Reinforcement learning in multi-objective optimization, Ph.D. thesis in Computer Science, Instituto Tecnológico y de Estudios Superiores de Monterrey, Campus Cuernavaca, March, 2002, Cuernavaca, Mor., México, 2001]. In order to compare the quality of the results obtained with MDQL, the reduced gradient method was applied to solve a weighted combination of the two objective functions used in the model. The proposed approach was tested on three cases: (i) a single contaminant four unitary operations problem where freshwater consumption is reduced via water reuse, (ii) a four contaminants real-world case with ten unitary operations, also with water reuse, and (iii) the water distribution network operation of Cuernavaca, Mexico, considering reduction of water leaks, operation of existing treatment plants at their design capacity, and design and construction of new treatment infrastructure to treat 100% of the wastewater produced. It is shown that the proposed approach can solved highly constrained real-world multi-objective optimization problems.

A Preference-Based Multi-Objective Concordance Genetic Algorithm

Recently various evolutionary approaches have been developed for multi-objective optimization. Most of them take Pareto dominance as their selection strategy and do not require any preference information. However these algorithms cannot perform well on problems involving many objectives. By introducing preferences among different criteria, a multi-objective concordance genetic algorithm (MOCGA) is proposed to deal with the problems in the paper. As the number of objectives to be simultaneously optimized increases, the weak dominance is used to compare among the individuals with decision-maker’s information. It is proven that the algorithm can guarantee the convergence towards the global optimum. Experimental results of the multi-objective optimization benchmark problems demonstrate the validity of the new algorithm.