### Table 3. Density estimation techniques in multi-objective evolutionary algorithms and operators used in this study.

2001

"... In PAGE 11: ... Many advanced multi-objective evolutionary algorithms use some form of density dependent selection. Furthermore, nearly all techniques can be expressed in terms of density estimation, a classification is given in Table3 . We will make use of this as a further step towards a common framework of evolutionary multi-objective optimizers, and present the relevant enhancement of the unified model.... ..."

Cited by 20

### Table 3. Density estimation techniques in multi-objective evolutionary algorithms and operators used in this study.

2001

"... In PAGE 11: ... Many advanced multi-objective evolutionary algorithms use some form of density dependent selection. Furthermore, nearly all techniques can be expressed in terms of density estimation, a classification is given in Table3 . We will make use of this as a further step towards a common framework of evolutionary multi-objective optimizers, and present the relevant enhancement of the unified model.... ..."

Cited by 20

### Table 2 gives an overview of these different techniques and the implementations we use in our experiments. As a baseline, the D8D6D9D2CRCPD8CT BC operator is included, which represents the unlimited archive.

2001

"... In PAGE 9: ... Table2 . Archive truncation methods in multi-objective evolutionary algorithms and operator instances for this study.... ..."

Cited by 20

### Table 2 gives an overview of these different techniques and the implementations we use in our experiments. As a baseline, the D8D6D9D2CRCPD8CTBC operator is included, which represents the unlimited archive.

2001

"... In PAGE 9: ... Table2 . Archive truncation methods in multi-objective evolutionary algorithms and operator instances for this study.... ..."

Cited by 20

### Table 1. Existing frameworks for multi-objective optimization (hybrid. stands for hy- bridization features, // for parallel features, lang. for programming language, ref. for reference, EA for Evolutionary Algorithm, LS for Local Search, SA for Simulated An- nealing, TS for Tabu Search, ACO for Ant Colony Optimization and PSO for Particle Swarm Optimization).

### Table 3: Multi-objective optimisation algorithms based on simulated annealing. Dominance energy Volume energy

"... In PAGE 92: ...based or volume based) and whether the search is exploratory (computational temperature T gt; 0) or greedy (T = 0). Table3 summarises greedy and exploratory algorithms using dominance and volume energies, together with single solution and set states, which are described in this section; their performance on standard test problems is compared in section 4.4.... In PAGE 99: ... Results on MOSA and SAMOSA give a direct comparison of single solution states against set states, while dominance based and volume based energy measures are compared via the SAMOSA and VOLMOSA algorithms. As displayed in Table3 , the temperature zero versions of the algorithms are denoted by MOSA0 and SAMOSA0. Performance is evaluated on well-known test functions from the literature, namely the DTLZ test suite problems 1-6 [Deb et al.... ..."

### Table 2. Results of the our proposed multi-objective approach after 1-hour runtime

2007

"... In PAGE 13: ...99 and the num ber of iterations within SA to be 1,000,000. Table2 lists the re- sults of using different evaluation functions on the obtained solutions. For the weighted-sum objective function, we use the sam e set of weight values as in formula (29), and list the num - ber of archived non-dom inated solutions (see colum n 2) and the best solution under this evaluation function (see colum n 3).... In PAGE 14: ...Table 2. Results of the our proposed multi-objective approach after 1-hour runtime A ccording to the results in Table2 , we can see that our proposed approach is very prom ising in solving the m ulti-objective nurse scheduling problem . In terms of the solution quality evaluated by the sam e objective function, our approach performs similar to the IP-based VNS, and significantly improve the best results of the hybrid genetic algorithm and the hybrid VNS by 25.... ..."

### Table 3: Computation effort (CE) metric values (number of evaluations) Instance size Single-objective techniques Multi-objective techniques

"... In PAGE 6: ... 5.2 Results We analyze first the results obtained with the CE metric by all the algorithms, which are included in Table3 . At a first glance, it can be observed that the multi-objective al- gorithms are more efficient than the single-objective ones.... ..."

### Table 3: Computation e ort (CE) metric values (number of evaluations) Instance size Single-objective techniques Multi-objective techniques

"... In PAGE 6: ... 5.2 Results We analyze rst the results obtained with the CE metric by all the algorithms, which are included in Table3 . At a rst glance, it can be observed that the multi-objective al- gorithms are more e cient than the single-objective ones.... ..."

### Table 2. Results on several system level synthesis problems. Given is the number of processes and resources and the number of feasible solutions or size of the valid search space Xf, respectively. The runtime of the algorithms were calculated as an average each with 10 instances in which the variance is given in the brackets.

"... In PAGE 13: ...mple namely a H.264 Video Decoder. The specification graph contains 68 processes, 15 resources and 276 mapping edges what leads to approximately 2136 possible solu- tions. The proposed algorithms are solving this problem easily, the runtimes are stated in Table2 . Moreover, a multi-objective Evolutionary Algorithm (MOEA) that is usually used to solve these problems will not find the Pareto-optimal solutions even after one hour whereas Algorithm 2 needs just a fraction of one second.... ..."